Noncommutativity and scalar field cosmology
Guzman, W.; Sabido, M.; Socorro, J.
2007-10-15
In this work we extend and apply a previous proposal to study noncommutative cosmology to the Friedmann-Robertson-Walker cosmological background coupled to a scalar field. This is done in classical and quantum scenarios. In both cases noncommutativity is introduced in the gravitational field as well as in the scalar field through a deformation of minisuperspace, and we are able to find exact solutions. Finally, the effects of noncommutativity on the classical evolution are analyzed.
Noncommutative Quantum Scalar Field Cosmology
Diaz Barron, L. R.; Lopez-Dominguez, J. C.; Sabido, M.; Yee, C.
2010-07-12
In this work we study noncommutative Friedmann-Robertson-Walker (FRW) cosmology coupled to a scalar field endowed with an exponential potential. The quantum scenario is analyzed in the Bohmian formalism of quantum trajectories to investigate the effects of noncommutativity in the evolution of the universe.
Noncommutative scalar fields from symplectic deformation
Daoud, M.; Hamama, A.
2008-02-15
This paper is concerned with the quantum theory of noncommutative scalar fields in two dimensional space-time. It is shown that the noncommutativity originates from the the deformation of symplectic structures. The quantization is performed and the modes expansions of the fields, in the presence of an electromagnetic background, are derived. The Hamiltonian of the theory is given and the degeneracies lifting, induced by the deformation, is also discussed.
Scalar field theory on noncommutative Snyder spacetime
Battisti, Marco Valerio; Meljanac, Stjepan
2010-07-15
We construct a scalar field theory on the Snyder noncommutative space-time. The symmetry underlying the Snyder geometry is deformed at the co-algebraic level only, while its Poincare algebra is undeformed. The Lorentz sector is undeformed at both the algebraic and co-algebraic level, but the coproduct for momenta (defining the star product) is non-coassociative. The Snyder-deformed Poincare group is described by a non-coassociative Hopf algebra. The definition of the interacting theory in terms of a nonassociative star product is thus questionable. We avoid the nonassociativity by the use of a space-time picture based on the concept of the realization of a noncommutative geometry. The two main results we obtain are (i) the generic (namely, for any realization) construction of the co-algebraic sector underlying the Snyder geometry and (ii) the definition of a nonambiguous self-interacting scalar field theory on this space-time. The first-order correction terms of the corresponding Lagrangian are explicitly computed. The possibility to derive Noether charges for the Snyder space-time is also discussed.
Noncommutative scalar field minimally coupled to nonsymmetric gravity
Kouadik, S.; Sefai, D.
2012-06-27
We construct a non-commutative non symmetric gravity minimally coupled model (the star product only couples matter). We introduce the action for the system considered namely a non-commutative scalar field propagating in a nontrivial gravitational background. We expand the action in powers of the anti-symmetric field and the graviton to second order adopting the assumption that the scalar is weekly coupled to the graviton. We compute the one loop radiative corrections to the self-energy of a scalar particle.
Self-quartic interaction for a scalar field in an extended DFR noncommutative space-time
NASA Astrophysics Data System (ADS)
Abreu, Everton M. C.; Neves, M. J.
2014-07-01
The framework of Dopliche-Fredenhagen-Roberts (DFR) for a noncommutative (NC) space-time is considered as an alternative approach to study the NC space-time of the early Universe. Concerning this formalism, the NC constant parameter, θ, is promoted to coordinate of the space-time and consequently we can describe a field theory in a space-time with extra-dimensions. We will see that there is a canonical momentum associated with this new coordinate in which the effects of a new physics can emerge in the propagation of the fields along the extra-dimensions. The Fourier space of this framework is automatically extended by the addition of the new momenta components. The main concept that we would like to emphasize from the outset is that the formalism demonstrated here will not be constructed by introducing a NC parameter in the system, as usual. It will be generated naturally from an already NC space. We will review that when the components of the new momentum are zero, the (extended) DFR approach is reduced to the usual (canonical) NC case, in which θ is an antisymmetric constant matrix. In this work we will study a scalar field action with self-quartic interaction ϕ4⋆ defined in the DFR NC space-time. We will obtain the Feynman rules in the Fourier space for the scalar propagator and vertex of the model. With these rules we are able to build the radiative corrections to one loop order of the model propagator. The consequences of the NC scale, as well as the propagation of the field in extra-dimensions, will be analyzed in the ultraviolet divergences scenario. We will investigate about the actual possibility that this kμν conjugate momentum has the property of healing the combination of IR/UV divergences that emerges in this recently new NC spacetime quantum field theory.
Covariant Noncommutative Field Theory
Estrada-Jimenez, S.; Garcia-Compean, H.; Obregon, O.; Ramirez, C.
2008-07-02
The covariant approach to noncommutative field and gauge theories is revisited. In the process the formalism is applied to field theories invariant under diffeomorphisms. Local differentiable forms are defined in this context. The lagrangian and hamiltonian formalism is consistently introduced.
Noncommutativity and the Friedmann Equations
Sabido, M.; Socorro, J.; Guzman, W.
2010-07-12
In this paper we study noncommutative scalar field cosmology, we find the noncommutative Friedmann equations as well as the noncommutative Klein-Gordon equation, interestingly the noncommutative contributions are only present up to second order in the noncommutitive parameter.
Natural discretization in noncommutative field theory
NASA Astrophysics Data System (ADS)
Acatrinei, Ciprian Sorin
2015-12-01
A discretization scheme for field theory is developed, in which the space time coordinates are assumed to be operators forming a noncommutative algebra. Generic waves without rotational symmetry are studied in (2+1) - dimensional scalar field theory with Heisenberg-type noncommutativity. In the representation chosen, the radial coordinate is naturally rendered discrete. Nonlocality along this coordinate, induced by noncommutativity, accounts for the angular dependence of the fields. A complete solution and the interpretation of its nonlocal features are given. The exact form of standing and propagating waves on such a discrete space is found in terms of finite series. A precise correspondence is established between the degree of nonlocality and the angular momentum of a field configuration. At small distance no classical singularities appear, even at the location of the sources. At large radius one recovers the usual commutative/continuum behaviour.
Natural discretization in noncommutative field theory
Acatrinei, Ciprian Sorin
2015-12-07
A discretization scheme for field theory is developed, in which the space time coordinates are assumed to be operators forming a noncommutative algebra. Generic waves without rotational symmetry are studied in (2+1) - dimensional scalar field theory with Heisenberg-type noncommutativity. In the representation chosen, the radial coordinate is naturally rendered discrete. Nonlocality along this coordinate, induced by noncommutativity, accounts for the angular dependence of the fields. A complete solution and the interpretation of its nonlocal features are given. The exact form of standing and propagating waves on such a discrete space is found in terms of finite series. A precise correspondence is established between the degree of nonlocality and the angular momentum of a field configuration. At small distance no classical singularities appear, even at the location of the sources. At large radius one recovers the usual commutative/continuum behaviour.
Wedge-local quantum fields on a nonconstant noncommutative spacetime
Much, A.
2012-08-15
Within the framework of warped convolutions we deform the massless free scalar field. The deformation is performed by using the generators of the special conformal transformations. The investigation shows that the deformed field turns out to be wedge-local. Furthermore, it is shown that the spacetime induced by the deformation with the special conformal operators is nonconstant noncommutative. The noncommutativity is obtained by calculating the deformed commutator of the coordinates.
On the scalar curvature for the noncommutative four torus
NASA Astrophysics Data System (ADS)
Fathizadeh, Farzad
2015-06-01
The scalar curvature for noncommutative four tori TΘ 4 , where their flat geometries are conformally perturbed by a Weyl factor, is computed by making the use of a noncommutative residue that involves integration over the 3-sphere. This method is more convenient since it does not require the rearrangement lemma and it is advantageous as it explains the simplicity of the final functions of one and two variables, which describe the curvature with the help of a modular automorphism. In particular, it readily allows to write the function of two variables as the sum of a finite difference and a finite product of the one variable function. The curvature formula is simplified for dilatons of the form sp, where s is a real parameter and p ∈ C ∞ ( TΘ 4 ) is an arbitrary projection, and it is observed that, in contrast to the two dimensional case studied by Connes and Moscovici, J. Am. Math. Soc. 27(3), 639-684 (2014), unbounded functions of the parameter s appear in the final formula. An explicit formula for the gradient of the analog of the Einstein-Hilbert action is also calculated.
Haag's theorem in noncommutative quantum field theory
Antipin, K. V.; Mnatsakanova, M. N.; Vernov, Yu. S.
2013-08-15
Haag's theorem was extended to the general case of noncommutative quantum field theory when time does not commute with spatial variables. It was proven that if S matrix is equal to unity in one of two theories related by unitary transformation, then the corresponding one in the other theory is equal to unity as well. In fact, this result is valid in any SO(1, 1)-invariant quantum field theory, an important example of which is noncommutative quantum field theory.
Conformal scalar field wormholes
NASA Technical Reports Server (NTRS)
Halliwell, Jonathan J.; Laflamme, Raymond
1989-01-01
The Euclidian Einstein equations with a cosmological constant and a conformally coupled scalar field are solved, taking the metric to be of the Robertson-Walker type. In the case Lambda = 0, solutions are found which represent a wormhole connecting two asymptotically flat Euclidian regions. In the case Lambda greater than 0, the solutions represent tunneling from a small Tolman-like universe to a large Robertson-Walker universe.
Quantum fields with noncommutative target spaces
NASA Astrophysics Data System (ADS)
Balachandran, A. P.; Queiroz, A. R.; Marques, A. M.; Teotonio-Sobrinho, P.
2008-05-01
Quantum field theories (QFT’s) on noncommutative spacetimes are currently under intensive study. Usually such theories have world sheet noncommutativity. In the present work, instead, we study QFT’s with commutative world sheet and noncommutative target space. Such noncommutativity can be interpreted in terms of twisted statistics and is related to earlier work of Oeckl [R. Oeckl, Commun. Math. Phys. 217, 451 (2001).CMPHAY0010-361610.1007/s002200100375], and others [A. P. Balachandran, G. Mangano, A. Pinzul, and S. Vaidya, Int. J. Mod. Phys. A 21, 3111 (2006)IMPAEF0217-751X10.1142/S0217751X06031764; A. P. Balachandran, A. Pinzul, and B. A. Qureshi, Phys. Lett. B 634, 434 (2006)PYLBAJ0370-269310.1016/j.physletb.2006.02.006; A. P. Balachandran, A. Pinzul, B. A. Qureshi, and S. Vaidya, arXiv:hep-th/0608138; A. P. Balachandran, T. R. Govindarajan, G. Mangano, A. Pinzul, B. A. Qureshi, and S. Vaidya, Phys. Rev. D 75, 045009 (2007)PRVDAQ0556-282110.1103/PhysRevD.75.045009; A. Pinzul, Int. J. Mod. Phys. A 20, 6268 (2005)IMPAEF0217-751X10.1142/S0217751X05029290; G. Fiore and J. Wess, Phys. Rev. D 75, 105022 (2007)PRVDAQ0556-282110.1103/PhysRevD.75.105022; Y. Sasai and N. Sasakura, Prog. Theor. Phys. 118, 785 (2007)PTPKAV0033-068X10.1143/PTP.118.785]. The twisted spectra of their free Hamiltonians has been found earlier by Carmona et al. [J. M. Carmona, J. L. Cortes, J. Gamboa, and F. Mendez, Phys. Lett. B 565, 222 (2003)PYLBAJ0370-269310.1016/S0370-2693(03)00728-7; J. M. Carmona, J. L. Cortes, J. Gamboa, and F. Mendez, J. High Energy Phys.JHEPFG1029-8479 03 (2003) 05810.1088/1126-6708/2003/03/058]. We review their derivation and then compute the partition function of one such typical theory. It leads to a deformed blackbody spectrum, which is analyzed in detail. The difference between the usual and the deformed blackbody spectrum appears in the region of high frequencies. Therefore we expect that the deformed blackbody radiation may potentially be used to compute a
Noncommutative anisotropic oscillator in a homogeneous magnetic field
NASA Astrophysics Data System (ADS)
Nath, D.; Roy, P.
2017-02-01
We study anisotropic oscillator in the presence of a homogeneous magnetic field and other related systems in the noncommutative plane. Energy values as function of the noncommutative parameter θ and the magnetic field B have been obtained. Some features of the spectrum, for example, formation of energy bands etc. have been examined. The effect of anisotropy on the energy levels has also been discussed.
Noncommutative correction to Aharonov-Bohm scattering: A field theory approach
Anacleto, M.A.; Gomes, M.; Silva, A.J. da; Spehler, D.
2004-10-15
We study a noncommutative nonrelativistic theory in 2+1 dimensions of a scalar field coupled to the Chern-Simons field. In the commutative situation this model has been used to simulate the Aharonov-Bohm effect in the field theory context. We verified that, contrary to the commutative result, the inclusion of a quartic self-interaction of the scalar field is not necessary to secure the ultraviolet renormalizability of the model. However, to obtain a smooth commutative limit the presence of a quartic gauge invariant self-interaction is required. For small noncommutativity we fix the corrections to the Aharonov-Bohm scattering and prove that up to one loop the model is free from dangerous infrared/ultraviolet divergences.
NASA Astrophysics Data System (ADS)
Naka, S.; Toyoda, H.; Takanashi, T.; Umezawa, E.
2014-04-01
In kappa -Minkowski spacetime, the coordinates are Lie algebraic elements such that time and space coordinates do not commute, whereas space coordinates commute with each other. The noncommutativity is proportional to a Planck-length-scale constant kappa ^{-1}, which is a universal constant other than the velocity of light, under the kappa -Poincaré transformation. In this sense, the spacetime has a structure called "doubly special relativity." Such a noncommutative structure is known to be realized by SO(1,4) generators in 4-dimensional de Sitter space. In this paper, we try to construct a noncommutative spacetime having a commutative n-dimensional Minkowski spacetime based on AdS_{n+1} space with SO(2,n) symmetry. We also study an invariant wave equation corresponding to the first Casimir invariant of this symmetry as a nonlocal field equation expected to yield finite loop amplitudes.
Expanding and collapsing scalar field thin shell
NASA Astrophysics Data System (ADS)
Sharif, M.; Abbas, G.
2012-09-01
This paper deals with the dynamics of scalar field thin shell in the Reissner-Nordstr öm geometry. The Israel junction conditions between Reissner-Nordstr öm spacetimes are derived, which lead to the equation of motion of scalar field shell and Klien-Gordon equation. These equations are solved numerically by taking scalar field model with the quadratic scalar potential. It is found that solution represents the expanding and collapsing scalar field shell. For the better understanding of this problem, we investigate the case of massless scalar field (by taking the scalar field potential zero). Also, we evaluate the scalar field potential when p is an explicit function of R. We conclude that both massless as well as massive scalar field shell can expand to infinity at constant rate or collapse to zero size forming a curvature singularity or bounce under suitable conditions.
Scalar fields and particle accelerators
NASA Astrophysics Data System (ADS)
Sultana, Joseph; Bose, Benjamin
2015-06-01
The phenomenon discovered in 2009 by Bañados, Silk and West where particle collisions can achieve arbitrary high center-of-mass (c.m.) energies close to the event horizon of an extreme Kerr black hole, has generated a lot of interest. Although rotation seemed to be an essential requirement, it was later shown that arbitrary high energies can also be achieved for collisions between radially moving particles near the horizon of the electrically charged extreme Reissner-Nordström black hole. Recently Patil and Joshi claimed that instead of spinning up the black hole one can also crank up the c.m. energy of particle collisions by "charging up" a static black hole with a massless scalar field. In this regard they showed that infinite energies can be attained in the vicinity of the naked singularity of the Janis-Newman-Wincour (JNW) spacetime, which contains a massless scalar field that also becomes infinite at the position of the curvature singularity. In this study we show that Patil and Joshi's claim does not apply for other static black hole systems endowed with a massless scalar field. In particular we consider the well-known Bekenstein black hole and the recently discovered Martínez-Troncoso-Zanelli black hole, and show that the expression of the c.m. energy for particle collisions near the event horizons of these black holes is no different than the corresponding case with vanishing scalar field represented by the Schwarzschild solution. Moreover by studying the motion of scalar test charges that interact with the background scalar field in these black hole spacetimes we show that the resulting c.m. energies are even smaller than in the case of free particles. This shows that the infinite energies obtained by Patil and Joshi may not be due to the fact that the black hole contains a massless scalar field, but may be instead related to the geometry of the naked singularity in the JNW spacetime. An analogous case of infinite c.m. energy in the vicinity of a naked
Entropic quantization of scalar fields
Ipek, Selman; Caticha, Ariel
2015-01-13
Entropic Dynamics is an information-based framework that seeks to derive the laws of physics as an application of the methods of entropic inference. The dynamics is derived by maximizing an entropy subject to constraints that represent the physically relevant information that the motion is continuous and non-dissipative. Here we focus on the quantum theory of scalar fields. We provide an entropic derivation of Hamiltonian dynamics and using concepts from information geometry derive the standard quantum field theory in the Schrödinger representation.
3D quantum gravity and effective noncommutative quantum field theory.
Freidel, Laurent; Livine, Etera R
2006-06-09
We show that the effective dynamics of matter fields coupled to 3D quantum gravity is described after integration over the gravitational degrees of freedom by a braided noncommutative quantum field theory symmetric under a kappa deformation of the Poincaré group.
Thermodynamics of a Charged Particle in a Noncommutative Plane in a Background Magnetic Field
NASA Astrophysics Data System (ADS)
Halder, Aslam; Gangopadhyay, Sunandan
2017-03-01
Landau system in noncommutative space has been considered. To take into account the issue of gauge invariance in noncommutative space, we incorporate the Seiberg-Witten map in our analysis. Generalised Bopp-shift transformation is then used to map the noncommutative system to its commutative equivalent system. In particular we have computed the partition function of the system and from this we obtained the susceptibility of the Landau system and found that the result gets modified by the spatial noncommutative parameter θ. We also investigate the de Hass-van Alphen effect in noncommutative space and observe that the oscillation of the magnetization and the susceptibility gets noncommutative corrections. Interestingly, the susceptibility in the noncommutative scenario is non-zero in the range of the magnetic field greater than the threshold value which is in contrast to its commutative counterpart. The results obtained are valid upto all orders in the noncommutative parameter θ.
Operator Algebras and Noncommutative Geometric Aspects in Conformal Field Theory
NASA Astrophysics Data System (ADS)
Longo, Roberto
2010-03-01
The Operator Algebraic approach to Conformal Field Theory has been particularly fruitful in recent years (leading for example to the classification of all local conformal nets on the circle with central charge c < 1, jointly with Y. Kawahigashi). On the other hand the Operator Algebraic viewpoint offers a natural perspective for a Noncommutative Geometric context within Conformal Field Theory. One basic point here is to uncover the relevant structures. In this talk I will explain some of the basic steps in this "Noncommutative Geometrization program" up to the recent construction of a spectral triple associated with certain Ramond representations of the Supersymmetric Virasoro net. So Alain Connes framework enters into play. This is a joint work with S. Carpi, Y. Kawahigashi, and R. Hillier.
Cross Sections From Scalar Field Theory
NASA Technical Reports Server (NTRS)
Norbury, John W.; Dick, Frank; Norman, Ryan B.; Nasto, Rachel
2008-01-01
A one pion exchange scalar model is used to calculate differential and total cross sections for pion production through nucleon- nucleon collisions. The collisions involve intermediate delta particle production and decay to nucleons and a pion. The model provides the basic theoretical framework for scalar field theory and can be applied to particle production processes where the effects of spin can be neglected.
Mexican contributions to Noncommutative Theories
Vergara, J. David; Garcia-Compean, H.
2006-09-25
In this paper we summarize the Mexican contributions to the subject of Noncommutative theories. These contributions span several areas: Quantum Groups, Noncommutative Field Theories, Hopf algebra of renormalization, Deformation Quantization, Noncommutative Gravity, and Noncommutative Quantum Mechanics.
Stabilization of Internal Space in Noncommutative Multidimensional Cosmology
NASA Astrophysics Data System (ADS)
Khosravi, N.; Jalalzadeh, S.; Sepangi, H. R.
We study the cosmological aspects of a noncommutative, multidimensional universe where the matter source is assumed to be a scalar field which does not commute with the internal scale factor. We show that such noncommutativity results in the internal dimensions being stabilized.
Helmholtz Hodge decomposition of scalar optical fields.
Bahl, Monika; Senthilkumaran, P
2012-11-01
It is shown that the vector field decomposition method, namely, the Helmholtz Hodge decomposition, can also be applied to analyze scalar optical fields that are ubiquitously present in interference and diffraction optics. A phase gradient field that depicts the propagation and Poynting vector directions can hence be separated into solenoidal and irrotational components.
Noncommutative Geometry in M-Theory and Conformal Field Theory
Morariu, Bogdan
1999-05-01
In the first part of the thesis I will investigate in the Matrix theory framework, the subgroup of dualities of the Discrete Light Cone Quantization of M-theory compactified on tori, which corresponds to T-duality in the auxiliary Type II string theory. After a review of matrix theory compactification leading to noncommutative supersymmetric Yang-Mills gauge theory, I will present solutions for the fundamental and adjoint sections on a two-dimensional twisted quantum torus and generalize to three-dimensional twisted quantum tori. After showing how M-theory T-duality is realized in supersymmetric Yang-Mills gauge theories on dual noncommutative tori I will relate this to the mathematical concept of Morita equivalence of C*-algebras. As a further generalization, I consider arbitrary Ramond-Ramond backgrounds. I will also discuss the spectrum of the toroidally compactified Matrix theory corresponding to quantized electric fluxes on two and three tori. In the second part of the thesis I will present an application to conformal field theory involving quantum groups, another important example of a noncommutative space. First, I will give an introduction to Poisson-Lie groups and arrive at quantum groups using the Feynman path integral. I will quantize the symplectic leaves of the Poisson-Lie group SU(2)*. In this way we obtain the unitary representations of U_{q}(SU(2)). I discuss the X-structure of SU(2)* and give a detailed description of its leaves using various parametrizations. Then, I will introduce a new reality structure on the Heisenberg double of Fun_{q} (SL(N,C)) for q phase, which can be interpreted as the quantum phase space of a particle on the q-deformed mass-hyperboloid. I also present evidence that the above real form describes zero modes of certain non-compact WZNW-models.
Intermediate inflation driven by DBI scalar field
NASA Astrophysics Data System (ADS)
Nazavari, N.; Mohammadi, A.; Ossoulian, Z.; Saaidi, Kh.
2016-06-01
Picking out a DBI scalar field as inflation, the slow-rolling inflationary scenario is studied by attributing an exponential time function to scale factor, known as intermediate inflation. The perturbation parameters of the model are estimated numerically for two different cases, and the final result is compared with Planck data. The diagram of tensor-to-scalar ratio r versus scalar spectra index ns is illustrated, and it is found that they are within an acceptable range as suggested by Planck. In addition, the acquired values for amplitude of scalar perturbation reveal the ability of the model to depict a good picture of the Universe in one of its earliest stages. As a further argument, the non-Gaussianity is investigated, displaying that the model prediction stands in a 68% C.L. regime according to the latest Planck data.
Scalar field, nonminimal coupling, and cosmology
Demianski, M. International Center for Relativistic Astrophysics, Dipartimento di Fisica, Universita di Roma La Sapienza,'' Rome ); de Ritis, R.; Marmo, G.; Platania, G.; Rubano, C.; Scudellaro, P.; Stornaiolo, C. Istituto Nazionale di Fisica Nucleare, Sezione di Napoli, Mostra d'Oltremare, pad. 19, 80125 Napoli )
1991-11-15
We study the dynamics of a flat Friedmann-Robertson-Walker universe filled with a self-interacting scalar field nonminimally coupled to the gravitational field. Dynamical equations for the system can be derived from a pointlike Lagrangian. For this system an additional Noether symmetry exists provided that the coupling constant {xi} is equal to 0 or 1/6. When {xi}=1/6 the scalar potential has to be constant. In this case we obtain an exact solution. We also analyze the behavior of the scalar field when {xi}{ne}0, 1/6. Most of the considered solutions are unphysical but there exists a very interesting case in which the effective cosmological constant is rapidly changing, which might lead to inflation.
Exploring scalar field dynamics with Gaussian processes
Nair, Remya; Jhingan, Sanjay; Jain, Deepak E-mail: sanjay.jhingan@gmail.com
2014-01-01
The origin of the accelerated expansion of the Universe remains an unsolved mystery in Cosmology. In this work we consider a spatially flat Friedmann-Robertson-Walker (FRW) Universe with non-relativistic matter and a single scalar field contributing to the energy density of the Universe. Properties of this scalar field, like potential, kinetic energy, equation of state etc. are reconstructed from Supernovae and BAO data using Gaussian processes. We also reconstruct energy conditions and kinematic variables of expansion, such as the jerk and the slow roll parameter. We find that the reconstructed scalar field variables and the kinematic quantities are consistent with a flat ΛCDM Universe. Further, we find that the null energy condition is satisfied for the redshift range of the Supernovae data considered in the paper, but the strong energy condition is violated.
Halos of unified dark matter scalar field
Bertacca, Daniele; Bartolo, Nicola; Matarrese, Sabino E-mail: nicola.bartolo@pd.infn.it
2008-05-15
We investigate the static and spherically symmetric solutions of Einstein's equations for a scalar field with a non-canonical kinetic term, assumed to provide both the dark matter and dark energy components of the Universe. In particular, we give a prescription to obtain solutions (dark halos) whose rotation curve v{sub c}(r) is in good agreement with observational data. We show that there exist suitable scalar field Lagrangians that allow us to describe the cosmological background evolution and the static solutions with a single dark fluid.
Generalized gravitational entropy of interacting scalar field and Maxwell field
NASA Astrophysics Data System (ADS)
Huang, Wung-Hong
2014-12-01
The generalized gravitational entropy proposed recently by Lewkowycz and Maldacena is extended to the interacting real scalar field and Maxwell field system. Using the BTZ geometry we first investigate the case of free real scalar field and then show a possible way to calculate the entropy of the interacting scalar field. Next, we investigate the Maxwell field system. We exactly solve the wave equation and calculate the analytic value of the generalized gravitational entropy. We also use the Einstein equation to find the effect of backreaction of the Maxwell field on the area of horizon. The associated modified area law is consistent with the generalized gravitational entropy.
Photon-neutrino interaction in θ-exact covariant noncommutative field theory
NASA Astrophysics Data System (ADS)
Horvat, R.; Kekez, D.; Schupp, P.; Trampetić, J.; You, J.
2011-08-01
Photon-neutrino interactions arise quite naturally in noncommutative field theories. Such couplings are absent in ordinary field theory and imply experimental lower bounds on the energy scale ΛNC˜|θ|-2 of noncommutativity. Using nonperturbative methods and a Seiberg-Witten map based covariant approach to noncommutative gauge theory, we obtain θ-exact expressions for the interactions, thereby eliminating previous restrictions to low-energy phenomena. We discuss implications for plasmon decay, neutrino charge radii, big bang nucleosynthesis, and ultrahigh energy cosmic rays. Our results behave reasonably throughout all interaction energy scales, thus facilitating further phenomenological applications.
Noncommutative minisuperspace, gravity-driven acceleration, and kinetic inflation
NASA Astrophysics Data System (ADS)
Rasouli, S. M. M.; Moniz, Paulo Vargas
2014-10-01
In this paper, we introduce a noncommutative version of the Brans-Dicke (BD) theory and obtain the Hamiltonian equations of motion for a spatially flat Friedmann-Lemaître-Robertson-Walker universe filled with a perfect fluid. We focus on the case where the scalar potential as well as the ordinary matter sector are absent. Then, we investigate gravity-driven acceleration and kinetic inflation in this noncommutative BD cosmology. In contrast to the commutative case, in which the scale factor and BD scalar field are in a power-law form, in the noncommutative case the power-law scalar factor is multiplied by a dynamical exponential warp factor. This warp factor depends on the noncommutative parameter as well as the momentum conjugate associated to the BD scalar field. We show that the BD scalar field and the scale factor effectively depend on the noncommutative parameter. For very small values of this parameter, we obtain an appropriate inflationary solution, which can overcome problems within BD standard cosmology in a more efficient manner. Furthermore, a graceful exit from an early acceleration epoch towards a decelerating radiation epoch is provided. For late times, due to the presence of the noncommutative parameter, we obtain a zero acceleration epoch, which can be interpreted as the coarse-grained explanation.
Scattering matrix theory for stochastic scalar fields.
Korotkova, Olga; Wolf, Emil
2007-05-01
We consider scattering of stochastic scalar fields on deterministic as well as on random media, occupying a finite domain. The scattering is characterized by a generalized scattering matrix which transforms the angular correlation function of the incident field into the angular correlation function of the scattered field. Within the accuracy of the first Born approximation this matrix can be expressed in a simple manner in terms of the scattering potential of the scatterer. Apart from determining the angular distribution of the spectral intensity of the scattered field, the scattering matrix makes it possible also to determine the changes in the state of coherence of the field produced on scattering.
Singularities in a scalar field quantum cosmology
NASA Astrophysics Data System (ADS)
Lemos, Nivaldo A.
1996-04-01
The quantum theory of a spatially flat Friedmann-Robertson-Walker universe with a massless scalar field as the source is further investigated. The classical model is singular and in the framework of a genuine canonical quantization (Arnowitt-Deser-Misner formalism) a discussion is made of the cosmic evolution, particularly of the quantum gravitational collapse problem. It is shown that in a matter-time gauge such that time is identified with the scalar field the classical model is singular either at t=-∞ or at t=+∞, but the quantum model is nonsingular. The latter behavior disproves a conjecture according to which quantum cosmological singularities are predetermined on the classical level by the choice of time.
Scalar field cosmologies with inverted potentials
Boisseau, B.; Giacomini, H.
2015-10-01
Regular bouncing solutions in the framework of a scalar-tensor gravity model were found in a recent work. We reconsider the problem in the Einstein frame (EF) in the present work. Singularities arising at the limit of physical viability of the model in the Jordan frame (JF) are either of the Big Bang or of the Big Crunch type in the EF. As a result we obtain integrable scalar field cosmological models in general relativity (GR) with inverted double-well potentials unbounded from below which possess solutions regular in the future, tending to a de Sitter space, and starting with a Big Bang. The existence of the two fixed points for the field dynamics at late times found earlier in the JF becomes transparent in the EF.
Self-similar scalar field collapse
NASA Astrophysics Data System (ADS)
Banerjee, Narayan; Chakrabarti, Soumya
2017-01-01
A spherically symmetric collapsing scalar field model is discussed with a dissipative fluid which includes a heat flux. This vastly general matter distribution is analyzed at the expense of a high degree of symmetry in the space-time, that of conformal flatness and self-similarity. Indeed collapsing models terminating into a curvature singularity can be obtained. The formation of black holes or the occurrence of naked singularities depends on the initial collapsing profiles.
Noncommutative Common Cause Principles in algebraic quantum field theory
Hofer-Szabo, Gabor; Vecsernyes, Peter
2013-04-15
States in algebraic quantum field theory 'typically' establish correlation between spacelike separated events. Reichenbach's Common Cause Principle, generalized to the quantum field theoretical setting, offers an apt tool to causally account for these superluminal correlations. In the paper we motivate first why commutativity between the common cause and the correlating events should be abandoned in the definition of the common cause. Then we show that the Noncommutative Weak Common Cause Principle holds in algebraic quantum field theory with locally finite degrees of freedom. Namely, for any pair of projections A, B supported in spacelike separated regions V{sub A} and V{sub B}, respectively, there is a local projection C not necessarily commuting with A and B such that C is supported within the union of the backward light cones of V{sub A} and V{sub B} and the set {l_brace}C, C{sup Up-Tack }{r_brace} screens off the correlation between A and B.
Structure formation with scalar field dark matter: the field approach
Magaña, Juan; Sánchez-Salcedo, F.J.; Matos, Tonatiuh; Suárez, Abril E-mail: tmatos@fis.cinvestav.mx E-mail: jsanchez@astro.unam.mx
2012-10-01
We study the formation of structure in the Universe assuming that dark matter can be described by a scalar field Φ-tilde with a potential V(Φ) = −m{sup 2}Φ-tilde {sup 2}/2+λΦ-tilde {sup 4}/4. We derive the evolution equations of the scalar field in the linear regime of perturbations. We investigate the symmetry breaking and possibly a phase transition of this scalar field in the early Universe. At low temperatures, the scalar perturbations have an oscillating growing mode and therefore, this kind of dark matter could lead to the formation of gravitational structures. In order to study the nonlinear regime, we use the spherical collapse model and show that, in the quadratic potential limit, this kind of dark matter can form virialized structures. The main difference with the traditional Cold Dark Matter paradigm is that the formation of structure in the scalar field model can occur at earlier times. Thus, if the dark matter behaves as a scalar field, large galaxies are expected to be formed already at high redshifts.
Physics on noncommutative spacetimes
NASA Astrophysics Data System (ADS)
Padmanabhan, Pramod
The structure of spacetime at the Planck scale remains a mystery to this date with a lot of insightful attempts to unravel this puzzle. One such attempt is the proposition of a 'pointless' structure for spacetime at this scale. This is done by studying the geometry of the spacetime through a noncommutative algebra of functions defined on it. We call such spacetimes 'noncommutative spacetimes'. This dissertation probes physics on several such spacetimes. These include compact noncommutative spaces called fuzzy spaces and noncompact spacetimes. The compact examples we look at are the fuzzy sphere and the fuzzy Higg's manifold. The noncompact spacetimes we study are the Groenewold-Moyal plane and the Bcn⃗ plane. A broad range of physical effects are studied on these exotic spacetimes. We study spin systems on the fuzzy sphere. The construction of Dirac and chirality operators for an arbitrary spin j is studied on both S2F and S2 in detail. We compute the spectrums of the spin 1 and spin 32 Dirac operators on S2F . These systems have novel thermodynamical properties which have no higher dimensional analogs, making them interesting models. The fuzzy Higg's manifold is found to exhibit topology change, an important property for any theory attempting to quantize gravity. We study how this change occurs in the classical setting and how quantizing this manifold smoothens the classical conical singularity. We also show the construction of the star product on this manifold using coherent states on the noncommutative algebra describing this noncommutative space. On the Moyal plane we develop the LSZ formulation of scalar quantum field theory. We compute scattering amplitudes and remark on renormalization of this theory. We show that the LSZ formalism is equivalent to the interaction representation formalism for computing scattering amplitudes on the Moyal plane. This result is true for on-shell Green's functions and fails to hold for off-shell Green's functions. With the
Phase space quantization, noncommutativity, and the gravitational field
NASA Astrophysics Data System (ADS)
Chatzistavrakidis, Athanasios
2014-07-01
In this paper we study the structure of the phase space in noncommutative geometry in the presence of a nontrivial frame. Our basic assumptions are that the underlying space is a symplectic and parallelizable manifold. Furthermore, we assume the validity of the Leibniz rule and the Jacobi identities. We consider noncommutative spaces due to the quantization of the symplectic structure and determine the momentum operators that guarantee a set of canonical commutation relations, appropriately extended to include the nontrivial frame. We stress the important role of left vs right acting operators and of symplectic duality. This enables us to write down the form of the full phase space algebra on these noncommutative spaces, both in the noncompact and in the compact case. We test our results against the class of four-dimensional and six-dimensional symplectic nilmanifolds, thus presenting a large set of nontrivial examples that realizes the general formalism.
Scalar field dark matter and the Higgs field
NASA Astrophysics Data System (ADS)
Bertolami, O.; Cosme, Catarina; Rosa, João G.
2016-08-01
We discuss the possibility that dark matter corresponds to an oscillating scalar field coupled to the Higgs boson. We argue that the initial field amplitude should generically be of the order of the Hubble parameter during inflation, as a result of its quasi-de Sitter fluctuations. This implies that such a field may account for the present dark matter abundance for masses in the range 10-6-10-4eV, if the tensor-to-scalar ratio is within the range of planned CMB experiments. We show that such mass values can naturally be obtained through either Planck-suppressed non-renormalizable interactions with the Higgs boson or, alternatively, through renormalizable interactions within the Randall-Sundrum scenario, where the dark matter scalar resides in the bulk of the warped extra-dimension and the Higgs is confined to the infrared brane.
Searching for Chameleon-Like Scalar Fields
NASA Astrophysics Data System (ADS)
Levshakov, S. A.; Molaro, P.; Kozlov, M. G.; Lapinov, A. V.; Henkel, Ch.; Reimersi, D.; Sakai, T.; Agafonova, I. I.
Using the 32-m Medicina, 45-m Nobeyama, and 100-m Effelsberg telescopes we found a statistically significant velocity offset ΔV ≈ 27 ± 3 m s - 1 (1σ) between the inversion transition in NH3(1,1) and low-J rotational transitions in N2H + (1-0) and HC3N(2-1) arising in cold and dense molecular cores in the Milky Way. Systematic shifts of the line centers caused by turbulent motions and velocity gradients, possible non-thermal hyperfine structure populations, pressure and optical depth effects are shown to be lower than or about 1 m s - 1 and thus can be neglected in the total error budget. The reproducibility of ΔV at the same facility (Effelsberg telescope) on a year-to-year basis is found to be very good. Since the frequencies of the inversion and rotational transitions have different sensitivities to variations in μ ≡ m e / m p, the revealed non-zero ΔV may imply that μ changes when measured at high (terrestrial) and low (interstellar) matter densities as predicted by chameleon-like scalar field models - candidates to the dark energy carrier. Thus we are testing whether scalar field models have chameleon-type interactions with ordinary matter. The measured velocity offset corresponds to the ratio Δμ / μ ≡ (μspace - μlab) / μlab of (26 ± 3) ×10 - 9 (1σ).
Study of Several Potentials as Scalar Field Dark Matter Candidates
Matos, Tonatiuh; Vazquez-Gonzalez, Alberto; Magan a, Juan
2008-12-04
In this work we study several scalar field potentials as a plausible candidate to be the dark matter in the universe. The main idea is the following; if the scalar field is an ultralight boson particle, it condensates like a Bose-Einstein system at very early times and forms the basic structure of the Universe. Real scalar fields collapse in equilibrium configurations which oscillate in space-time (oscillatons). The cosmological behavior of the field equations are solved using the dynamical system formalism. We use the current cosmological parameters as constraints for the free parameters of the scalar field potentials. We are able to reproduce very well the cosmological predictions of the standard {lambda}CDM model with some scalar field potentials. Therefore, scalar field dark matter seems to be a good alternative to be the nature of the dark matter of the universe.
Towards Noncommutative Topological Quantum Field Theory: New invariants for 3-manifolds
NASA Astrophysics Data System (ADS)
Zois, I. P.
2016-08-01
We present some ideas for a possible Noncommutative Topological Quantum Field Theory (NCTQFT for short) and Noncommutative Floer Homology (NCFH for short). Our motivation is two-fold and it comes both from physics and mathematics: On the one hand we argue that NCTQFT is the correct mathematical framework for a quantum field theory of all known interactions in nature (including gravity). On the other hand we hope that a possible NCFH will apply to practically every 3-manifold (and not only to homology 3-spheres as ordinary Floer Homology currently does). The two motivations are closely related since, at least in the commutative case, Floer Homology Groups constitute the space of quantum observables of (3+1)-dim Topological Quantum Field Theory. Towards this goal we define some new invariants for 3-manifolds using the space of taut codim-1 foliations modulo coarse isotopy along with various techniques from noncommutative geometry.
Electromagnetic fields with vanishing scalar invariants
NASA Astrophysics Data System (ADS)
Ortaggio, Marcello; Pravda, Vojtěch
2016-06-01
We determine the class of p-forms {\\boldsymbol{F}} that possess vanishing scalar invariants (VSIs) at arbitrary order in an n-dimensional spacetime. Namely, we prove that {\\boldsymbol{F}} is a VSI if and only if if it is of type N, its multiple null direction {\\boldsymbol{\\ell }} is ‘degenerate Kundt’, and {\\pounds }{\\boldsymbol{\\ell }}{\\boldsymbol{F}}=0. The result is theory-independent. Next, we discuss the special case of Maxwell fields, both at the level of test fields and of the full Einstein-Maxwell equations. These describe electromagnetic non-expanding waves propagating in various Kundt spacetimes. We further point out that a subset of these solutions possesses a universal property, i.e. they also solve (virtually) any generalized (non-linear and with higher derivatives) electrodynamics, possibly also coupled to Einstein’s gravity.
Massive basketball diagram for a thermal scalar field theory
NASA Astrophysics Data System (ADS)
Andersen, Jens O.; Braaten, Eric; Strickland, Michael
2000-08-01
The ``basketball diagram'' is a three-loop vacuum diagram for a scalar field theory that cannot be expressed in terms of one-loop diagrams. We calculate this diagram for a massive scalar field at nonzero temperature, reducing it to expressions involving three-dimensional integrals that can be easily evaluated numerically. We use this result to calculate the free energy for a massive scalar field with a φ4 interaction to three-loop order.
Self-interacting complex scalar field as dark matter
Briscese, F.
2011-10-14
We study the viability of a a complex scalar field {chi} with self-interacting potential V = m{sub 0}{sup {chi}/}2|{chi}|{sup 2}+h|{chi}|{sup 4} as dark matter. Due to the self interaction, the scalar field forms a Bose-Einstein condensate at early times that represents dark matter. The self interaction is also responsible of quantum corrections to the scalar field mass that naturally give the dark matter domination at late times without any fine tuning on the energy density of the scalar field at early times. Finally the properties of the spherically symmetric dark matter halos are also discussed.
Chameleon scalar fields in relativistic gravitational backgrounds
Tsujikawa, Shinji; Tamaki, Takashi; Tavakol, Reza E-mail: tamaki@gravity.phys.waseda.ac.jp
2009-05-15
We study the field profile of a scalar field {phi} that couples to a matter fluid (dubbed a chameleon field) in the relativistic gravitational background of a spherically symmetric spacetime. Employing a linear expansion in terms of the gravitational potential {Phi}{sub c} at the surface of a compact object with a constant density, we derive the thin-shell field profile both inside and outside the object, as well as the resulting effective coupling with matter, analytically. We also carry out numerical simulations for the class of inverse power-law potentials V({phi}) = M{sup 4+n}{phi}{sup -n} by employing the information provided by our analytical solutions to set the boundary conditions around the centre of the object and show that thin-shell solutions in fact exist if the gravitational potential {Phi}{sub c} is smaller than 0.3, which marginally covers the case of neutron stars. Thus the chameleon mechanism is present in the relativistic gravitational backgrounds, capable of reducing the effective coupling. Since thin-shell solutions are sensitive to the choice of boundary conditions, our analytic field profile is very helpful to provide appropriate boundary conditions for {Phi}{sub c}{approx}
Free □ k scalar conformal field theory
NASA Astrophysics Data System (ADS)
Brust, Christopher; Hinterbichler, Kurt
2017-02-01
We consider the generalizations of the free U( N ) and O( N ) scalar conformal field theories to actions with higher powers of the Laplacian □ k , in general dimension d. We study the spectra, Verma modules, anomalies and OPE of these theories. We argue that in certain d and k, the spectrum contains zero norm operators which are both primary and descendant, as well as extension operators which are neither primary nor descendant. In addition, we argue that in even dimensions d ≤ 2 k, there are well-defined operator algebras which are related to the □ k theories and are novel in that they have a finite number of single-trace states.
Bose-Einstein condensates from scalar field dark matter
Urena-Lopez, L. Arturo
2010-12-07
We review the properties of astrophysical and cosmological relevance that may arise from the bosonic nature of scalar field dark matter models. The key property is the formation of Bose-Einstein condensates, but we also consider the presence of non-empty excited states that may be relevant for the description of scalar field galaxy halos and the properties of rotation curves.
Gravitational collapse of massless scalar field in f (R ) gravity
NASA Astrophysics Data System (ADS)
Zhang, Cheng-Yong; Tang, Zi-Yu; Wang, Bin
2016-11-01
We study the spherically symmetric gravitational collapse of massless scalar matter field in asymptotic flat spacetime in the Starobinsky R2 gravity, one specific model in the f (R ) gravity. In the Einstein frame of f (R ) gravity, an additional scalar field arises due to the conformal transformation. We find that in addition to the usual competition between gravitational energy and kinetic energy in the process of gravitational collapse, the new scalar field brought by the conformal transformation adds one more competing force in the dynamical system. The dynamical competition can be controlled by tuning the amplitudes of the initial perturbations of the new scalar field and the matter field. To understand the physical reasons behind these phenomena, we analyze the gravitational potential behavior and calculate the Ricci scalar at center with the change of initial amplitudes of perturbations. We find rich physics on the formation of black holes through gravitational collapse in f (R ) gravity.
Modified f( R, T) gravity theory and scalar field cosmology
NASA Astrophysics Data System (ADS)
Singh, Vijay; Singh, C. P.
2015-03-01
In this paper, we explore the behaviors of scalar field in modified f( R, T) gravity theory within the framework of a flat Friedmann-Robertson-Walker cosmological model. The universe is assumed to be filled with two non-interacting matter sources, scalar field (normal or phantom) with scalar potential and matter contribution due to f( R, T) action. We first explore a model where the potential is a constant, and the universe evolves as a de Sitter type. This model is compatible with phantom scalar field only which gives fine tuning with the recent observations. The model exhibits a wide variety of early time physical phenomena that eventually behaves like a cosmological constant at late times. The model shows transition from decelerated to accelerated expansion of the universe. We also explore a model where the scalar field potential and the scale factor evolve exponentially as a scalar field. This model is compatible with normal scalar field only and describes transition from inflationary to the decelerated phase at early times and quintessence to phantom phase at late times. We constraint our results with the recent observational data and find that some values of parameters are consistent with SNe Ia and H( z)+SNe Ia data to describe accelerated expansion only whereas some one give decelerated and accelerated expansions with H( z), WMAP7 and WMAP7+BAO+ H( z) observational data.
Massive basketball diagram for a thermal scalar field theory
Andersen, Jens O.; Braaten, Eric; Strickland, Michael
2000-08-15
The ''basketball diagram'' is a three-loop vacuum diagram for a scalar field theory that cannot be expressed in terms of one-loop diagrams. We calculate this diagram for a massive scalar field at nonzero temperature, reducing it to expressions involving three-dimensional integrals that can be easily evaluated numerically. We use this result to calculate the free energy for a massive scalar field with a {phi}{sup 4} interaction to three-loop order. (c) 2000 The American Physical Society.
Black holes and a scalar field in an expanding universe
NASA Astrophysics Data System (ADS)
Saida, Hiromi; Soda, Jiro
2000-12-01
We consider a model of an inhomogeneous universe with the presence of a massless scalar field, where the inhomogeneity is assumed to consist of many black holes. This model can be constructed by following Lindquist and Wheeler, which has already been investigated without the presence of a scalar field to show that an averaged scale factor coincides with that of the Friedmann model in Einstein gravity. In this paper we construct the inhomogeneous universe with a massless scalar field, where it is assumed that the averaged scale factor and scalar field are given by those of the Friedmann model including the scalar field. All of our calculations are carried out within the framework of Brans-Dicke gravity. In constructing the model of an inhomogeneous universe, we define the mass of a black hole in the Brans-Dicke expanding universe which is equivalent to the ADM mass in the epoch of the adiabatic time evolution of the mass, and obtain an equation relating our mass with the averaged scalar field and scale factor. We find that the mass has an adiabatic time dependence in a sufficiently late stage of the expansion of the universe; that is our mass is equivalent to the ADM mass. The other result is that its time dependence is qualitatively different according to the sign of the curvature of the universe: the mass increases (decelerating) in the closed universe case, is constant in the flat case and decreases (decelerating) in the open case. It is also noted that the mass in the Einstein frame depends on time. Our results that the mass has a time dependence should be retained even in the general scalar-tensor gravities with a scalar field potential. Furthermore, we discuss the relation of our model of the inhomogeneous universe to the uniqueness theorem of black hole spacetime and the gravitational memory effect of black holes in scalar-tensor gravities.
Bianchi type-I models with conformally invariant scalar field
Accioly, A.J.; Vaidya, A.N.; Som, M.M.
1983-05-15
The solutions of the Einstein equations with the trace-free energy-momentum tensor of conformally invariant scalar field as source are obtained in a spatially homogeneous anisotropic space-time. Some interesting features of the solutions are discussed.
A nonlinear dynamics for the scalar field in Randers spacetime
NASA Astrophysics Data System (ADS)
Silva, J. E. G.; Maluf, R. V.; Almeida, C. A. S.
2017-03-01
We investigate the properties of a real scalar field in the Finslerian Randers spacetime, where the local Lorentz violation is driven by a geometrical background vector. We propose a dynamics for the scalar field by a minimal coupling of the scalar field and the Finsler metric. The coupling is intrinsically defined on the Randers spacetime, and it leads to a non-canonical kinetic term for the scalar field. The nonlinear dynamics can be split into a linear and nonlinear regimes, which depend perturbatively on the even and odd powers of the Lorentz-violating parameter, respectively. We analyze the plane-waves solutions and the modified dispersion relations, and it turns out that the spectrum is free of tachyons up to second-order.
Nonlinear scalar field equations involving the fractional Laplacian
NASA Astrophysics Data System (ADS)
Byeon, Jaeyoung; Kwon, Ohsang; Seok, Jinmyoung
2017-04-01
In this paper we study the existence, regularity, radial symmetry and decay property of a mountain pass solution for nonlinear scalar field equations involving the fractional Laplacian under an almost optimal class of continuous nonlinearities.
Dynamics of a scalar field in Robertson-Walker spacetimes
NASA Astrophysics Data System (ADS)
Copeland, Edmund J.; Mizuno, Shuntaro; Shaeri, Maryam
2009-05-01
We analyze the dynamics of a single scalar field in Friedmann-Robertson-Walker universes with spatial curvature. We obtain the fixed point solutions which are shown to be late time attractors. In particular, we determine the corresponding scalar field potentials which correspond to these stable solutions. The analysis is quite general and incorporates expanding and contracting universes with both positive and negative scalar potentials. We demonstrate that the known power law, exponential, and de Sitter solutions are certain limits of our general set of solutions.
Scalar Field Theory on κ-MINKOWSKI Space-Time and Translation and Lorentz Invariance
NASA Astrophysics Data System (ADS)
Meljanac, S.; Samsarov, A.
We investigate the properties of κ-Minkowski space-time by using representations of the corresponding deformed algebra in terms of undeformed Heisenberg-Weyl algebra. The deformed algebra consists of κ-Poincaré algebra extended with the generators of the deformed Weyl algebra. The part of deformed algebra, generated by rotation, boost and momentum generators, is described by the Hopf algebra structure. The approach used in our considerations is completely Lorentz covariant. We further use an advantage of this approach to consistently construct a star product, which has a property that under integration sign, it can be replaced by a standard pointwise multiplication, a property that was since known to hold for Moyal but not for κ-Minkowski space-time. This star product also has generalized trace and cyclic properties, and the construction alone is accomplished by considering a classical Dirac operator representation of deformed algebra and requiring it to be Hermitian. We find that the obtained star product is not translationally invariant, leading to a conclusion that the classical Dirac operator representation is the one where translation invariance cannot simultaneously be implemented along with hermiticity. However, due to the integral property satisfied by the star product, noncommutative free scalar field theory does not have a problem with translation symmetry breaking and can be shown to reduce to an ordinary free scalar field theory without nonlocal features and tachyonic modes and basically of the very same form. The issue of Lorentz invariance of the theory is also discussed.
Perfect focusing of scalar wave fields in three dimensions.
Benítez, Pablo; Miñano, Juan C; González, Juan C
2010-04-12
A method to design isotropic inhomogeneous refractive index distribution is presented, in which the scalar wave field solutions propagate exactly on an eikonal function (i.e., remaining constant on the Geometrical Optics wavefronts). This method is applied to the design of "dipole lenses", which perfectly focus a scalar wave field emitted from a point source onto a point absorber, in both two and three dimensions. Also, the Maxwell fish-eye lens in two and three dimensions is analysed.
Primordial magnetic fields from self-ordering scalar fields
Horiguchi, Kouichirou; Ichiki, Kiyotomo; Sugiyama, Naoshi; Sekiguchi, Toyokazu E-mail: ichiki@a.phys.nagoya-u.ac.jp E-mail: naoshi@nagoya-u.jp
2015-04-01
A symmetry-breaking phase transition in the early universe could have led to the formation of cosmic defects. Because these defects dynamically excite not only scalar and tensor type cosmological perturbations but also vector type ones, they may serve as a source of primordial magnetic fields. In this study, we calculate the time evolution and the spectrum of magnetic fields that are generated by a type of cosmic defects, called global textures, using the non-linear sigma (NLSM) model. Based on the standard cosmological perturbation theory, we show, both analytically and numerically, that a vector-mode relative velocity between photon and baryon fluids is induced by textures, which inevitably leads to the generation of magnetic fields over a wide range of scales. We find that the amplitude of the magnetic fields is given by B∼10{sup −9}((1+z)/10{sup 3}){sup −2.5}(v/m{sub pl}){sup 2}(k/Mpc{sup −1}){sup 3.5}/√N Gauss in the radiation dominated era for k∼< 1 Mpc{sup −1}, with v being the vacuum expectation value of the O(N) symmetric scalar fields. By extrapolating our numerical result toward smaller scales, we expect that B∼ 10{sup −14.5}((1+z)/10{sup 3}){sup 1/2}(v/m{sub pl}){sup 2}(k/Mpc{sup −1}){sup 1/2}/√N Gauss on scales of k∼> 1 Mpc{sup −1} at redshift 0z∼> 110. This might be a seed of the magnetic fields observed on large scales today.
Alternate Light Front Quantization Procedure for Scalar Fields
NASA Astrophysics Data System (ADS)
Przeszowski, Jerzy A.
2017-03-01
The novel procedure for the light-front (LF) quantization is formulated and applied for models of free scalar fields. The expected well-known results are rediscovered for a single field and new results are obtained for the two fields model. We use fields smeared with a test function on the LF hypersurface as the basic ingredient of our novel quantization procedure.
Gravity quantized: Loop quantum gravity with a scalar field
Domagala, Marcin; Kaminski, Wojciech; Giesel, Kristina; Lewandowski, Jerzy
2010-11-15
...''but we do not have quantum gravity.'' This phrase is often used when analysis of a physical problem enters the regime in which quantum gravity effects should be taken into account. In fact, there are several models of the gravitational field coupled to (scalar) fields for which the quantization procedure can be completed using loop quantum gravity techniques. The model we present in this paper consists of the gravitational field coupled to a scalar field. The result has similar structure to the loop quantum cosmology models, except that it involves all the local degrees of freedom of the gravitational field because no symmetry reduction has been performed at the classical level.
NASA Astrophysics Data System (ADS)
Berberian, John Edwin
1999-01-01
A new framework is presented for analysing the spherically symmetric Einstein field equations for a zero-mass scalar field. The framework consists of a coordinate system (p, q), where the coordinate p is the scalar field, and q is a coordinate chosen to be orthogonal to p. This idea allows for a reduction of the field equations into a system of two first order partial differential equations for the areal metric function gqq and a mass function m . The metric coefficients in this coordinate system then take on values which are simply related to the scalars of the problem: 1->f˙1 ->f,gq q and-via the field equations-the scalar curvature R as well. The scalar field coordinate system is shown to have many advantages. Many of the known exact solutions (e.g. static, Roberts) are represented simply, and new self- similar solutions are derived. The framework is then applied to the problem of matching spherically symmetric scalar-tensor vacuum solutions to a homogeneous and isotropic dust solution (e.g. scalar- tensor Einstein-Straus swiss cheese solutions, scalar- tensor Oppenheimer-Snyder dust ball collapse). Scalar field coordinates are shown to be ideal for such an application. We derive the necessary matching conditions in scalar field coordinates, and show how they imply a natural extension of the Schücking condition for spherically symmetric vacuum in general relativity. The problem of finding a vacuum solution which matches a given homogeneous and isotropic solution is examined. It is found that the matching conditions are sufficient to guarantee local existence and uniqueness of the vacuum solution if it is assumed that the scalar field has neither maxima nor minima on the matching interface. In order to find explicit matched solutions, criteria are developed to screen known exact vacuum solutions for matchability, and procedures are given for determining the details of the homogeneous and isotropic solution (curvature constant, comoving radial coordinate of the
Unified description of the dynamics of quintessential scalar fields
Ureña-López, L. Arturo
2012-03-01
Using the dynamical system approach, we describe the general dynamics of cosmological scalar fields in terms of critical points and heteroclinic lines. It is found that critical points describe the initial and final states of the scalar field dynamics, but that heteroclinic lines give a more complete description of the evolution in between the critical points. In particular, the heteroclinic line that departs from the (saddle) critical point of perfect fluid-domination is the representative path in phase space of quintessence fields that may be viable dark energy candidates. We also discuss the attractor properties of the heteroclinic lines, and their importance for the description of thawing and freezing fields.
Minimally coupled scalar field cosmology in anisotropic cosmological model
NASA Astrophysics Data System (ADS)
Singh, C. P.; Srivastava, Milan
2017-02-01
We study a spatially homogeneous and anisotropic cosmological model in the Einstein gravitational theory with a minimally coupled scalar field. We consider a non-interacting combination of scalar field and perfect fluid as the source of matter components which are separately conserved. The dynamics of cosmic scalar fields with a zero rest mass and an exponential potential are studied, respectively. We find that both assumptions of potential along with the average scale factor as an exponential function of scalar field lead to the logarithmic form of scalar field in each case which further gives power-law form of the average scale factor. Using these forms of the average scale factor, exact solutions of the field equations are obtained to the metric functions which represent a power-law and a hybrid expansion, respectively. We find that the zero-rest-mass model expands with decelerated rate and behaves like a stiff matter. In the case of exponential potential function, the model decelerates, accelerates or shows the transition depending on the parameters. The isotropization is observed at late-time evolution of the Universe in the exponential potential model.
Critical behavior in black hole scalar field interaction
NASA Astrophysics Data System (ADS)
Crespo, J. A.; de Oliveira, H. P.
2015-09-01
We study the critical behavior at the threshold of black hole formation in a model consisting of a scalar field incident to a reflector barrier enclosing a Schwarzschild black hole. Weak incident scalar field waves disturb slightly the black hole spacetime and are completely radiated by the reflector, like water waves striking against the wall of a dam. Strong incident waves produce the formation of an apparent horizon outside the barrier. In this case, a fraction of scalar field crosses the horizon together with the barrier, whereas another fraction escapes to infinity. We have integrated the field equations using a Galerkin collocation code that allowed the necessary accuracy to investigate the behavior of the black hole masses for a broad range of scalar field initial amplitude. We have shown that a scaling law describes the black hole masses for amplitudes very close to the critical value. In the limit of very strong scalar fields, the black hole masses either scale linearly with the initial amplitude or saturate depending on the existence of the initial monopole moment.
Inflation with an extra light scalar field after Planck
Vennin, Vincent; Koyama, Kazuya; Wands, David E-mail: kazuya.koyama@port.ac.uk
2016-03-01
Bayesian inference techniques are used to investigate situations where an additional light scalar field is present during inflation and reheating. This includes (but is not limited to) curvaton-type models. We design a numerical pipeline where ≅ 200 inflaton setups × 10 reheating scenarios = 2000 models are implemented and we present the results for a few prototypical potentials. We find that single-field models are remarkably robust under the introduction of light scalar degrees of freedom. Models that are ruled out at the single-field level are not improved in general, because good values of the spectral index and the tensor-to-scalar ratio can only be obtained for very fine-tuned values of the extra field parameters and/or when large non-Gaussianities are produced. The only exception is quartic large-field inflation, so that the best models after Planck are of two kinds: plateau potentials, regardless of whether an extra field is added or not, and quartic large-field inflation with an extra light scalar field, in some specific reheating scenarios. Using Bayesian complexity, we also find that more parameters are constrained for the models we study than for their single-field versions. This is because the added parameters not only contribute to the reheating kinematics but also to the cosmological perturbations themselves, to which the added field contributes. The interplay between these two effects lead to a suppression of degeneracies that is responsible for having more constrained parameters.
Inflation with an extra light scalar field after Planck
NASA Astrophysics Data System (ADS)
Vennin, Vincent; Koyama, Kazuya; Wands, David
2016-03-01
Bayesian inference techniques are used to investigate situations where an additional light scalar field is present during inflation and reheating. This includes (but is not limited to) curvaton-type models. We design a numerical pipeline where simeq 200 inflaton setups × 10 reheating scenarios = 2000 models are implemented and we present the results for a few prototypical potentials. We find that single-field models are remarkably robust under the introduction of light scalar degrees of freedom. Models that are ruled out at the single-field level are not improved in general, because good values of the spectral index and the tensor-to-scalar ratio can only be obtained for very fine-tuned values of the extra field parameters and/or when large non-Gaussianities are produced. The only exception is quartic large-field inflation, so that the best models after Planck are of two kinds: plateau potentials, regardless of whether an extra field is added or not, and quartic large-field inflation with an extra light scalar field, in some specific reheating scenarios. Using Bayesian complexity, we also find that more parameters are constrained for the models we study than for their single-field versions. This is because the added parameters not only contribute to the reheating kinematics but also to the cosmological perturbations themselves, to which the added field contributes. The interplay between these two effects lead to a suppression of degeneracies that is responsible for having more constrained parameters.
N-body simulations for coupled scalar-field cosmology
Li Baojiu; Barrow, John D.
2011-01-15
We describe in detail the general methodology and numerical implementation of consistent N-body simulations for coupled-scalar-field models, including background cosmology and the generation of initial conditions (with the different couplings to different matter species taken into account). We perform fully consistent simulations for a class of coupled-scalar-field models with an inverse power-law potential and negative coupling constant, for which the chameleon mechanism does not work. We find that in such cosmological models the scalar-field potential plays a negligible role except in the background expansion, and the fifth force that is produced is proportional to gravity in magnitude, justifying the use of a rescaled gravitational constant G in some earlier N-body simulation works for similar models. We then study the effects of the scalar coupling on the nonlinear matter power spectra and compare with linear perturbation calculations to see the agreement and places where the nonlinear treatment deviates from the linear approximation. We also propose an algorithm to identify gravitationally virialized matter halos, trying to take account of the fact that the virialization itself is also modified by the scalar-field coupling. We use the algorithm to measure the mass function and study the properties of dark-matter halos. We find that the net effect of the scalar coupling helps produce more heavy halos in our simulation boxes and suppresses the inner (but not the outer) density profile of halos compared with the {Lambda}CDM prediction, while the suppression weakens as the coupling between the scalar field and dark-matter particles increases in strength.
Very light cosmological scalar fields from a tiny cosmological constant
Calmet, Xavier
2007-10-15
I discuss a mechanism which generates a mass term for a scalar field in an expanding universe. The mass of this field turns out to be generated by the cosmological constant and can be naturally small if protected by a conformal symmetry which is, however, broken in the gravitational sector. The mass is comparable today to the Hubble time. This scalar field could thus impact our Universe today and, for example, be at the origin of a time variation of the couplings and masses of the parameters of the standard model.
Finite temperature scalar field theory in the early universe
Leutwyler, H.; Mallik, S. )
1991-01-01
The authors study a scalar Higgs field in an expanding Robertson-Walker geometry, using the real time formulation of Semenoff and Weiss. It is shown that the density matrix associated with the Hamiltonian at a sharp time describes a state for which perturbation theory is not renormalizable and an alternative, renormalizable characterization of thermal equilibrium is given. They calculate the thermal quantum fluctuations surrounding a classical field and discuss the characteristic time scales occurring in the evolution of a scalar field from an initial radiation dominated phase of thermal equilibrium to an unstable, inflationary de Sitter phase.
Symmetry breaking in noncommutative finite temperature λphi4 theory with a nonuniform ground state
NASA Astrophysics Data System (ADS)
Hernández, J. M.; Ramírez, C.; Sánchez, M.
2014-05-01
We consider the CJT effective action at finite temperature for a noncommutative real scalar field theory, with noncommutativity among space and time variables. We study the solutions of a stripe type nonuniform background, which depends on space and time. The analysis in the first approximation shows that such solutions appear in the planar limit, but also under normal anisotropic noncommutativity. Further we show that the transition from the uniform ordered phase to the non uniform one is first order and that the critical temperature depends on the nonuniformity of the ground state.
Impact of other scalar fields on oscillons after hilltop inflation
Antusch, Stefan; Orani, Stefano E-mail: stefano.orani@unibas.ch
2016-03-01
Oscillons are spatially localized and relatively stable field fluctuations which can form after inflation under suitable conditions. In order to reheat the universe, the fields which dominate the energy density after inflation have to couple to other degrees of freedom and finally produce the matter particles present in the universe today. In this study, we use lattice simulations in 2+1 dimensions to investigate how such couplings can affect the formation and stability of oscillons. We focus on models of hilltop inflation, where we have recently shown that hill crossing oscillons generically form, and consider the coupling to an additional scalar field which, depending on the value of the coupling parameter, can get resonantly enhanced from the inhomogeneous inflaton field. We find that three cases are realized: without a parametric resonance, the additional scalar field has no effects on the oscillons. For a fast and strong parametric resonance of the other scalar field, oscillons are strongly suppressed. For a delayed parametric resonance, on the other hand, the oscillons get imprinted on the other scalar field and their stability is even enhanced compared to the single-field oscillons.
Running of scalar spectral index in multi-field inflation
Gong, Jinn-Ouk
2015-05-01
We compute the running of the scalar spectral index in general multi-field slow-roll inflation. By incorporating explicit momentum dependence at the moment of horizon crossing, we can find the running straightforwardly. At the same time, we can distinguish the contributions from the quasi de Sitter background and the super-horizon evolution of the field fluctuations.
Bose-Einstein condensates and scalar fields; exploring the similitudes
NASA Astrophysics Data System (ADS)
Castellanos, E.; Macías, A.; Núñez, D.
2014-01-01
We analyze the the remarkable analogy between the classical Klein-Gordon equation for a test scalar field in a flat and also in a curved background, and the Gross-Pitaevskii equation for a Bose-Einstein condensate trapped by an external potential. We stress here that the solution associated with the Klein-Gordon equation (KG) in a flat space time has the same mathematical structure, under certain circumstances, to those obtained for the Gross-Pitaevskii equation, that is, a static soliton solution. Additionally, Thomas-Fermi approximation is applied to the 3-dimensional version of this equation, in order to calculate some thermodynamical properties of the system in curved a space-time back ground. Finally, we stress the fact that a gravitational background provides, in some cases, a kind of confining potential for the scalar field, allowing us to remarks even more the possible connection between scalar fields and the phenomenon of Bose-Einstein condensation.
A scalar field dark energy model: Noether symmetry approach
NASA Astrophysics Data System (ADS)
Dutta, Sourav; Panja, Madan Mohan; Chakraborty, Subenoy
2016-04-01
Scalar field dark energy cosmology has been investigated in the present paper in the frame work of Einstein gravity. In the context of Friedmann-Lemaitre-Robertson-Walker space time minimally coupled scalar field with self interacting potential and non-interacting perfect fluid with barotropic equation of state (dark matter) is chosen as the matter context. By imposing Noether symmetry on the Lagrangian of the system the symmetry vector is obtained and the self interacting potential for the scalar field is determined. Then we choose a point transformation (a, φ )→ (u, v) such that one of the transformation variable (say u) is cyclic for the Lagrangian. Subsequently, using conserved charge (corresponding to the cyclic co-ordinate) and the constant of motion, solutions are obtained. Finally, the cosmological implication of the solutions in the perspective of recent observation has been examined.
Bose–Einstein condensates and scalar fields; exploring the similitudes
Castellanos, E.; Macías, A.; Núñez, D.
2014-01-14
We analyze the the remarkable analogy between the classical Klein–Gordon equation for a test scalar field in a flat and also in a curved background, and the Gross–Pitaevskii equation for a Bose–Einstein condensate trapped by an external potential. We stress here that the solution associated with the Klein–Gordon equation (KG) in a flat space time has the same mathematical structure, under certain circumstances, to those obtained for the Gross–Pitaevskii equation, that is, a static soliton solution. Additionally, Thomas–Fermi approximation is applied to the 3–dimensional version of this equation, in order to calculate some thermodynamical properties of the system in curved a space–time back ground. Finally, we stress the fact that a gravitational background provides, in some cases, a kind of confining potential for the scalar field, allowing us to remarks even more the possible connection between scalar fields and the phenomenon of Bose–Einstein condensation.
Screening of scalar fields in Dirac-Born-Infeld theory
NASA Astrophysics Data System (ADS)
Burrage, Clare; Khoury, Justin
2014-07-01
We study a new screening mechanism which is present in Dirac-Born-Infeld (DBI)-like theories. A scalar field with a DBI-like Lagrangian is minimally coupled to matter. In the vicinity of sufficiently dense sources, nonlinearities in the scalar dominate and result in an approximately constant acceleration on a test particle, thereby suppressing the scalar force relative to gravity. Unlike generic P(X) or chameleon theories, screening happens within the regime of validity of the effective field theory thanks to the DBI symmetry. We derive an exact form for the field profile around multiple sources and determine the constraints on the theory parameters from tests of gravity. Perturbations around the spherically-symmetric background propagate superluminally, but we argue for a chronology protection analogous to Galileons. This is the first example of a screening mechanism for which quantum corrections to the theory are under control and exact solutions to cosmological N-body problems can be found.
Detecting chameleons: The astronomical polarization produced by chameleonlike scalar fields
Burrage, Clare; Davis, Anne-Christine; Shaw, Douglas J.
2009-02-15
We show that a coupling between chameleonlike scalar fields and photons induces linear and circular polarization in the light from astrophysical sources. In this context chameleonlike scalar fields include those of the Olive-Pospelov (OP) model, which describes a varying fine structure constant. We determine the form of this polarization numerically and give analytic expressions in two useful limits. By comparing the predicted signal with current observations we are able to improve the constraints on the chameleon-photon coupling and the coupling in the OP model by over 2 orders of magnitude. It is argued that, if observed, the distinctive form of the chameleon induced circular polarization would represent a smoking gun for the presence of a chameleon. We also report a tentative statistical detection of a chameleonlike scalar field from observations of starlight polarization in our galaxy.
Behavior of Phantom Scalar Fields near Black Holes
Lora-Clavijo, F. D.; Gonzalez, J. A.; Guzman, F. S.
2010-07-12
We present the accretion of a phantom scalar field into a black hole for various scalar field potentials in the full non-linear regime. Our results are based on the use of numerical methods and show that for all the cases studied the black hole's apparent horizon mass decreases. We explore a particular subset of the parameter space and from our results we conclude that this is a very efficient black hole shrinking process because the time scales of the area reduction of the horizon are short. We show that the radial equation of state of the scalar field depends strongly on the space and time, with the condition {omega} = p/{rho}>-1, as opposed to a phantom fluid at cosmic scales that allows {omega}<-1.
Towards Noncommutative Supersymmetric Quantum Cosmology
Sabido, M.; Socorro, J.; Guzman, W.
2010-12-07
In this work a construction of supersymmetric noncommutative cosmology is presented. We start with a ''noncommutative'' deformation of the minisuperspace variables, and by using the time reparametrization invariance of the noncommutative bosonic model we proceed to construct a super field description of the model.
Dark energy parametrization motivated by scalar field dynamics
NASA Astrophysics Data System (ADS)
de la Macorra, Axel
2016-05-01
We propose a new dark energy (DE) parametrization motivated by the dynamics of a scalar field ϕ. We use an equation of state w parametrized in terms of two functions L and y, closely related to the dynamics of scalar fields, which is exact and has no approximation. By choosing an appropriate ansatz for L we obtain a wide class of behavior for the evolution of DE without the need to specify the scalar potential V. We parametrize L and y in terms of only four parameters, giving w a rich structure and allowing for a wide class of DE dynamics. Our w can either grow and later decrease, or it can happen the other way around; the steepness of the transition is not fixed and it contains the ansatz w={w}o+{w}a(1-a). Our parametrization follows closely the dynamics of a scalar field, and the function L allows us to connect it with the scalar potential V(φ ). While the Universe is accelerating and the slow roll approximation is valid, we get L≃ {({V}\\prime /V)}2. To determine the dynamics of DE we also calculate the background evolution and its perturbations, since they are important to discriminate between different DE models.
DBI scalar field theory for QGP hydrodynamics
NASA Astrophysics Data System (ADS)
Nastase, Horatiu
2016-07-01
A way to describe the hydrodynamics of the quark-gluon plasma using a Dirac-Born-Infeld (DBI) action is proposed, based on the model found by Heisenberg for high energy scattering of nucleons. The expanding plasma is described as a shockwave in a DBI model for a real scalar standing in for the pion, and I show that one obtains a fluid description in terms of a relativistic fluid that near the shock is approximately ideal (η ≃0 ) and conformal. One can introduce an extra term inside the square root of the DBI action that generates a shear viscosity term in the energy-momentum tensor near the shock, as well as a bulk viscosity, and regulates the behavior of the energy density at the shock, making it finite. The resulting fluid satisfies the relativistic Navier-Stokes equation with uμ,ρ ,P ,η defined in terms of ϕ and its derivatives. One finds a relation between the parameters of the theory and the quark-gluon plasma thermodynamics, α /β2=η /(s T ), and by fixing α and β from usual (low multiplicity) particle scattering, one finds T ∝mπ.
Can a spectator scalar field enhance inflationary tensor mode?
NASA Astrophysics Data System (ADS)
Fujita, Tomohiro; Yokoyama, Jun'ichi; Yokoyama, Shuichiro
2015-04-01
We consider the possibility of enhancing the inflationary tensor mode by introducing a spectator scalar field with a small sound speed which induces gravitational waves as a second-order effect. We analytically obtain the power spectra of gravitational waves and curvature perturbation induced by the spectator scalar field. We find that the small sound speed amplifies the curvature perturbation much more than the tensor mode and the current observational constraint forces the induced gravitational waves to be negligible compared with those from the vacuum fluctuation during inflation.
An Asymmetric Noncommutative Torus
NASA Astrophysics Data System (ADS)
Dąbrowski, Ludwik; Sitarz, Andrzej
2015-09-01
We introduce a family of spectral triples that describe the curved noncommutative two-torus. The relevant family of new Dirac operators is given by rescaling one of two terms in the flat Dirac operator. We compute the dressed scalar curvature and show that the Gauss-Bonnet theorem holds (which is not covered by the general result of Connes and Moscovici).
Quantum Theory of a Strongly-Dissipative Scalar Field
NASA Astrophysics Data System (ADS)
Jafari, Marjan; Kheirandish, Fardin
2017-04-01
The properties of a quantum dissipative scalar field is analyzed by Caldeira-Leggett model in strong-coupling regime. The Lagrangian of the total system is canonically quantized and the full Hamiltonian is diagonalized using Fano technique. A mode-dependent probability density is introduced. The steady state energy and correlation functions at finite temperature are calculated in terms of the probability density.
Remarks on the spherical scalar field halo in galaxies
Nandi, Kamal K.; Valitov, Ildar; Migranov, Nail G.
2009-08-15
Matos, Guzman, and Nunez proposed a model for the galactic halo within the framework of scalar field theory. We argue that an analysis involving the full metric can reveal the true physical nature of the halo only when a certain condition is maintained. We fix that condition and also calculate its impact on observable parameters of the model.
Propagation of Scalar Fields in a Plane Symmetric Spacetime
NASA Astrophysics Data System (ADS)
Celestino, Juliana; Alves, Márcio E. S.; Barone, F. A.
2016-12-01
The present article deals with solutions for a minimally coupled scalar field propagating in a static plane symmetric spacetime. The considered metric describes the curvature outside a massive infinity plate and exhibits an intrinsic naked singularity (a singular plane) that makes the accessible universe finite in extension. This solution can be interpreted as describing the spacetime of static domain walls. In this context, a first solution is given in terms of zero order Bessel functions of the first and second kind and presents a stationary pattern which is interpreted as a result of the reflection of the scalar waves at the singular plane. This is an evidence, at least for the massless scalar field, of an old interpretation given by Amundsen and Grøn regarding the behaviour of test particles near the singularity. A second solution is obtained in the limit of a weak gravitational field which is valid only far from the singularity. In this limit, it was possible to find out an analytic solution for the scalar field in terms of the Kummer and Tricomi confluent hypergeometric functions.
Collapse of charged scalar field in dilaton gravity
Borkowska, Anna; Rogatko, Marek; Moderski, Rafal
2011-04-15
We elaborated the gravitational collapse of a self-gravitating complex charged scalar field in the context of the low-energy limit of the string theory, the so-called dilaton gravity. We begin with the regular spacetime and follow the evolution through the formation of an apparent horizon and the final central singularity.
Brans-Dicke scalar field as a chameleon
Das, Sudipta; Banerjee, Narayan
2008-08-15
In this paper it is shown that in Brans-Dicke theory, if one considers a nonminimal coupling between the matter and the scalar field, it can give rise to a late time accelerated expansion for the Universe preceded by a decelerated expansion for very high values of the Brans-Dicke parameter {omega}.
Effects of a scalar scaling field on quantum mechanics
Benioff, Paul
2016-04-18
This paper describes the effects of a complex scalar scaling field on quantum mechanics. The field origin is an extension of the gauge freedom for basis choice in gauge theories to the underlying scalar field. The extension is based on the idea that the value of a number at one space time point does not determine the value at another point. This, combined with the description of mathematical systems as structures of different types, results in the presence of separate number fields and vector spaces as structures, at different space time locations. Complex number structures and vector spaces at each location are scaled by a complex space time dependent scaling factor. The effect of this scaling factor on several physical and geometric quantities has been described in other work. Here the emphasis is on quantum mechanics of one and two particles, their states and properties. Multiparticle states are also briefly described. The effect shows as a complex, nonunitary, scalar field connection on a fiber bundle description of nonrelativistic quantum mechanics. Here, the lack of physical evidence for the presence of this field so far means that the coupling constant of this field to fermions is very small. It also means that the gradient of the field must be very small in a local region of cosmological space and time. Outside this region, there are no restrictions on the field gradient.
Effects of a scalar scaling field on quantum mechanics
Benioff, Paul
2016-04-18
This paper describes the effects of a complex scalar scaling field on quantum mechanics. The field origin is an extension of the gauge freedom for basis choice in gauge theories to the underlying scalar field. The extension is based on the idea that the value of a number at one space time point does not determine the value at another point. This, combined with the description of mathematical systems as structures of different types, results in the presence of separate number fields and vector spaces as structures, at different space time locations. Complex number structures and vector spaces at eachmore » location are scaled by a complex space time dependent scaling factor. The effect of this scaling factor on several physical and geometric quantities has been described in other work. Here the emphasis is on quantum mechanics of one and two particles, their states and properties. Multiparticle states are also briefly described. The effect shows as a complex, nonunitary, scalar field connection on a fiber bundle description of nonrelativistic quantum mechanics. Here, the lack of physical evidence for the presence of this field so far means that the coupling constant of this field to fermions is very small. It also means that the gradient of the field must be very small in a local region of cosmological space and time. Outside this region, there are no restrictions on the field gradient.« less
Time-dependent scalar fields as candidates for dark matter
NASA Astrophysics Data System (ADS)
Malakolkalami, B.; Mahmoodzadeh, A.
2016-11-01
In this paper, we study some properties of what is called the oscillaton, a spherically symmetric object made of a real time-dependent scalar field. Using an exponential scalar potential instead of a quadratic one discussed in previous works, as a new choice, we investigate the oscillaton properties with this potential. Solving the differential equation system resulting from the Einstein-Klein-Gordon equations reveals the importance of the oscillatons as candidates for dark matter. Meanwhile, a simplification called the stationary limit procedure is also carried out.
Effective Hamiltonian for non-minimally coupled scalar fields
NASA Astrophysics Data System (ADS)
Meşe, Emine; Pirinççiog˜Lu, Nurettin; Açıkgöz, Irfan; Binbay, Figen
2009-01-01
In the post Newtonian limit, a non-relativistic Hamiltonian is derived for scalar fields with quartic self-interaction and non-minimal coupling to the curvature scalar of the background spacetime. These effects are found to contribute to the non-relativistic Hamiltonian by adding nonlinearities and by modifying the gravitational Darwin term. As we discuss briefly in the text, the impact of these novel structures can be sizable in dense media like neutron star core, and can have observable signatures in phase transitions, for example.
Thick branes from self-gravitating scalar fields
Novikov, Oleg O.; Andrianov, Vladimir A.; Andrianov, Alexander A.
2014-07-23
The formation of a domain wall ('thick brane') induced by scalar matter dynamics and triggered by a thin brane defect is considered in noncompact five-dimensional space-time with warped AdS type geometry. The scalar matter is composed of two fields with softly broken O(2) symmetry and minimal coupling to gravity. The nonperturbative effects in the invariant mass spectrum of light localized scalar states are investigated for different values of the tension of the thin brane defect. Especially interesting is the case of the thin brane with negative tension when the singular barriers form a potential well with two infinitely tall walls and the discrete spectrum of localized states arises completely isolated from the bulk.
Brane models with a Ricci-coupled scalar field
Bogdanos, C.; Dimitriadis, A.; Tamvakis, K.
2006-08-15
We consider the problem of a scalar field, nonminimally coupled to gravity through a -{xi}{phi}{sup 2}R term, in the presence of a brane. Exact solutions, for a wide range of values of the coupling parameter {xi}, for both {phi}-dependent and {phi}-independent brane tension, are derived and their behavior is studied. In the case of a Randall-Sundrum geometry, a class of the resulting scalar field solutions exhibits a folded-kink profile. We go beyond the Randall-Sundrum geometry studying general warp factor solutions in the presence of a kink scalar. Analytic and numerical results are provided for the case of a brane or for smooth geometries, where the scalar field acts as a thick brane. It is shown that finite geometries with warp factors that asymptotically decrease exponentially are realizable for a wide range of parameter values. We also study graviton localization in our setup and find that the localizing potential for gravitons with the characteristic volcanolike profile develops a local maximum located at the origin for high values of the coupling {xi}.
Unification of gravity and quantum field theory from extended noncommutative geometry
NASA Astrophysics Data System (ADS)
Yu, Hefu; Ma, Bo-Qiang
2017-02-01
We make biframe and quaternion extensions on the noncommutative geometry, and construct the biframe spacetime for the unification of gravity and quantum field theory (QFT). The extended geometry distinguishes between the ordinary spacetime based on the frame bundle and an extra non-coordinate spacetime based on the biframe bundle constructed by our extensions. The ordinary spacetime frame is globally flat and plays the role as the spacetime frame in which the fields of the Standard Model are defined. The non-coordinate frame is locally flat and is the gravity spacetime frame. The field defined in both frames of such “flat” biframe spacetime can be quantized and plays the role as the gravity field which couples with all the fields to connect the gravity effect with the Standard Model. Thus, we provide a geometric paradigm in which gravity and QFT can be unified.
Diagrammar in classical scalar field theory
Cattaruzza, E.; Gozzi, E.; Francisco Neto, A.
2011-09-15
In this paper we analyze perturbatively a g{phi}{sup 4}classical field theory with and without temperature. In order to do that, we make use of a path-integral approach developed some time ago for classical theories. It turns out that the diagrams appearing at the classical level are many more than at the quantum level due to the presence of extra auxiliary fields in the classical formalism. We shall show that a universal supersymmetry present in the classical path-integral mentioned above is responsible for the cancelation of various diagrams. The same supersymmetry allows the introduction of super-fields and super-diagrams which considerably simplify the calculations and make the classical perturbative calculations almost 'identical' formally to the quantum ones. Using the super-diagrams technique, we develop the classical perturbation theory up to third order. We conclude the paper with a perturbative check of the fluctuation-dissipation theorem. - Highlights: > We provide the Feynman diagrams of perturbation theory for a classical field theory. > We give a super-formalism which links the quantum diagrams to the classical ones. > We check perturbatively the fluctuation-dissipation theorem.
Semi-Classical Dirac Vacuum Polarisation in a Scalar Field
NASA Astrophysics Data System (ADS)
Lampart, Jonas; Lewin, Mathieu
2016-08-01
We study vacuum polarisation effects of a Dirac field coupled to an external scalar field and derive a semi-classical expansion of the regu-larised vacuum energy. The leading order of this expansion is given by a classical formula due to Chin, Lee-Wick and Walecka, for which our result provides the first rigorous proof. We then discuss applications to the non-relativistic large-coupling limit of an interacting system, and to the stability of homogeneous systems.
GravitoMagnetic Field in Tensor-Vector-Scalar Theory
Exirifard, Qasem
2013-04-01
We study the gravitomagnetism in the TeVeS theory. We compute the gravitomagnetic field that a slow moving mass distribution produces in its Newtonian regime. We report that the consistency between the TeVeS gravitomagnetic field and that predicted by the Einstein-Hilbert theory leads to a relation between the vector and scalar coupling constants of the theory. We translate the Lunar Laser Ranging measurement's data into a constraint on the deviation from this relation.
Charged Renyi entropies for free scalar fields
NASA Astrophysics Data System (ADS)
Dowker, J. S.
2017-04-01
I first calculate the charged spherical Rényi entropy by a numerical method that does not require knowledge of any eigenvalue degeneracies, and applies to all odd dimensions. An image method is used to relate the full sphere values to those for an integer covering, n. It is shown to be equivalent to a ‘transformation’ property of the zeta-function. The n\\to ∞ limit is explicitly constructed analytically and a relation deduced between the limits of corner coefficients and the effective action (free energy) which generalises, for free fields, a result of Bueno, Myers and Witczak-Krempa and Elvang and Hadjiantonis to any dimension. Finally, the known polynomial expressions for the Rényi entropy on even spheres at zero chemical potential are re–derived in a different form and a simple formula for the conformal anomaly given purely in terms of central factorials is obtained.
Entanglement entropy for free scalar fields in AdS
NASA Astrophysics Data System (ADS)
Sugishita, Sotaro
2016-09-01
We compute entanglement entropy for free massive scalar fields in anti-de Sitter (AdS) space. The entangling surface is a minimal surface whose boundary is a sphere at the boundary of AdS. The entropy can be evaluated from the thermal free energy of the fields on a topological black hole by using the replica method. In odd-dimensional AdS, exact expressions of the Rényi entropy S n are obtained for arbitrary n. We also evaluate 1-loop corrections coming from the scalar fields to holographic entanglement entropy. Applying the results, we compute the leading difference of entanglement entropy between two holographic CFTs related by a renormalization group flow triggered by a double trace deformation. The difference is proportional to the shift of a central charge under the flow.
Singular cosmological evolution using canonical and ghost scalar fields
Nojiri, Shin'ichi; Odintsov, S.D.; Oikonomou, V.K.; Saridakis, Emmanuel N. E-mail: odintsov@ieec.uab.es E-mail: Emmanuel_Saridakis@baylor.edu
2015-09-01
We demonstrate that finite time singularities of Type IV can be consistently incorporated in the Universe's cosmological evolution, either appearing in the inflationary era, or in the late-time regime. While using only one scalar field instabilities can in principle occur at the time of the phantom-divide crossing, when two fields are involved we are able to avoid such instabilities. Additionally, the two-field scalar-tensor theories prove to be able to offer a plethora of possible viable cosmological scenarios, at which various types of cosmological singularities can be realized. Amongst others, it is possible to describe inflation with the appearance of a Type IV singularity, and phantom late-time acceleration which ends in a Big Rip. Finally, for completeness, we also present the Type IV realization in the context of suitably reconstructed F(R) gravity.
On the stability of the asymptotically free scalar field theories
Shalaby, A M.
2015-03-30
Asymptotic freedom plays a vital role in our understanding of the theory of particle interactions. To have this property, one has to resort to a Non-abelian gauge theory with the number of colors equal to or greater than three (QCD). However, recent studies have shown that simple scalar field theories can possess this interesting property. These theories have non-Hermitian effective field forms but their classical potentials are bounded from above. In this work, we shall address the stability of the vacua of the bounded from above (−Φ{sup 4+n}) scalar field theories. Moreover, we shall cover the effect of the distribution of the Stokes wedges in the complex Φ-plane on the features of the vacuum condensate within these theories.
Quantum entanglement in three accelerating qubits coupled to scalar fields
NASA Astrophysics Data System (ADS)
Dai, Yue; Shen, Zhejun; Shi, Yu
2016-07-01
We consider quantum entanglement of three accelerating qubits, each of which is locally coupled with a real scalar field, without causal influence among the qubits or among the fields. The initial states are assumed to be the GHZ and W states, which are the two representative three-partite entangled states. For each initial state, we study how various kinds of entanglement depend on the accelerations of the three qubits. All kinds of entanglement eventually suddenly die if at least two of three qubits have large enough accelerations. This result implies the eventual sudden death of all kinds of entanglement among three particles coupled with scalar fields when they are sufficiently close to the horizon of a black hole.
Feynman propagator for a free scalar field on a causal set.
Johnston, Steven
2009-10-30
The Feynman propagator for a free bosonic scalar field on the discrete spacetime of a causal set is presented. The formalism includes scalar field operators and a vacuum state which define a scalar quantum field theory on a causal set. This work can be viewed as a novel regularization of quantum field theory based on a Lorentz invariant discretization of spacetime.
Non-Gaussianity from self-ordering scalar fields
Figueroa, Daniel G.; Kamionkowski, Marc
2010-06-15
The Universe may harbor relics of the post-inflationary epoch in the form of a network of self-ordered scalar fields. Such fossils, while consistent with current cosmological data at trace levels, may leave too weak an imprint on the cosmic microwave background and the large-scale distribution of matter to allow for direct detection. The non-Gaussian statistics of the density perturbations induced by these fields, however, permit a direct means to probe for these relics. Here we calculate the bispectrum that arises in models of self-ordered scalar fields. We find a compact analytic expression for the bispectrum, evaluate it numerically, and provide a simple approximation that may be useful for data analysis. The bispectrum is largest for triangles that are aligned (have edges k{sub 1{approx_equal}}2k{sub 2{approx_equal}}2k{sub 3}) as opposed to the local-model bispectrum, which peaks for squeezed triangles (k{sub 1{approx_equal}}k{sub 2}>>k{sub 3}), and the equilateral bispectrum, which peaks at k{sub 1{approx_equal}}k{sub 2{approx_equal}}k{sub 3}. We estimate that this non-Gaussianity should be detectable by the Planck satellite if the contribution from self-ordering scalar fields to primordial perturbations is near the current upper limit.
On the late-time cosmology of a condensed scalar field
NASA Astrophysics Data System (ADS)
Ghalee, Amir
2016-04-01
We study the late-time cosmology of a scalar field with a kinetic term non-minimally coupled to gravity. It is demonstrated that the scalar field dominate the radiation matter and the cold dark matter (CDM). Moreover, we show that eventually the scalar field will be condensed and results in an accelerated expansion. The metric perturbations around the condensed phase of the scalar field are investigated and it has been shown that the ghost instability and gradient instability do not exist.
Scalar field as a Bose-Einstein condensate?
Castellanos, Elías; Escamilla-Rivera, Celia; Macías, Alfredo; Núñez, Darío E-mail: cescamilla@mctp.mx E-mail: nunez@nucleares.unam.mx
2014-11-01
We discuss the analogy between a classical scalar field with a self-interacting potential, in a curved spacetime described by a quasi-bounded state, and a trapped Bose-Einstein condensate. In this context, we compare the Klein-Gordon equation with the Gross-Pitaevskii equation. Moreover, the introduction of a curved background spacetime endows, in a natural way, an equivalence to the Gross-Pitaevskii equation with an explicit confinement potential. The curvature also induces a position dependent self-interaction parameter. We exploit this analogy by means of the Thomas-Fermi approximation, commonly used to describe the Bose-Einstein condensate, in order to analyze the quasi bound scalar field distribution surrounding a black hole.
New techniques in 3D scalar and vector field visualization
Max, N.; Crawfis, R.; Becker, B.
1993-05-05
At Lawrence Livermore National Laboratory (LLNL) we have recently developed several techniques for volume visualization of scalar and vector fields, all of which use back-to-front compositing. The first renders volume density clouds by compositing polyhedral volume cells or their faces. The second is a ``splatting`` scheme which composites textures used to reconstruct the scalar or vector fields. One version calculates the necessary texture values in software, and another takes advantage of hardware texture mapping. The next technique renders contour surface polygons using semi-transparent textures, which adjust appropriately when the surfaces deform in a flow, or change topology. The final one renders the ``flow volume`` of smoke or dye tracer swept out by a fluid flowing through a small generating polygon. All of these techniques are applied to a climate model data set, to visualize cloud density and wind velocity.
Dynamical dark energy: Scalar fields and running vacuum
NASA Astrophysics Data System (ADS)
Solà, Joan; Gómez-Valent, Adrià; de Cruz Pérez, Javier
2017-03-01
Recent analyses in the literature suggest that the concordance ΛCDM model with rigid cosmological term, Λ = const. may not be the best description of the cosmic acceleration. The class of “running vacuum models”, in which Λ = Λ(H) evolves with the Hubble rate, has been shown to fit the string of SNIa + BAO + H(z) + LSS + CMB data significantly better than the ΛCDM. Here, we provide further evidence on the time-evolving nature of the dark energy (DE) by fitting the same cosmological data in terms of scalar fields. As a representative model, we use the original Peebles and Ratra potential, V ∝ ϕ‑α. We find clear signs of dynamical DE at ˜ 4σ c.l., thus reconfirming through a nontrivial scalar field approach the strong hints formerly found with other models and parametrizations.
NASA Astrophysics Data System (ADS)
Bochicchio, Marco
2015-03-01
We review a number of old and new concepts in quantum gauge theories, some of which are well-established but not widely appreciated, some are most recent, that may have analogs in gauge formulations of quantum gravity, loop quantum gravity, and their topological versions, and may be of general interest. Such concepts involve noncommutative gauge theories and their relation to the large-N limit, loop equations and the change to the anti-selfdual (ASD) variables also known as Nicolai map, topological field theory (TFT) and its relation to localization and Morse-Smale-Floer homology, with an emphasis both on the mathematical aspects and the physical meaning. These concepts, assembled in a new way, enter a line of attack to the problem of the mass gap in large-NSU(N) Yang-Mills (YM), that is reviewed as well. Algebraic considerations furnish a measure of the mathematical complexity of a complete solution of large-NSU(N) YM: In the large-N limit of pure SU(N) YM the ambient algebra of Wilson loops is known to be a type II1 nonhyperfinite factor. Nevertheless, for the mass gap problem at the leading 1/N order, only the subalgebra of local gauge-invariant single-trace operators matters. The connected two-point correlators in this subalgebra must be an infinite sum of propagators of free massive fields, since the interaction is subleading in (1)/(N), a vast simplification. It is an open problem, determined by the growth of the degeneracy of the spectrum, whether the aforementioned local subalgebra is in fact hyperfinite. Moreover, the sum of free propagators that occurs in the two-point correlators in the aforementioned local subalgebra must be asymptotic for large momentum to the result implied by the asymptotic freedom and the renormalization group: This fundamental constraint fixes asymptotically the residues of the poles of the propagators in terms of the mass spectrum and of the anomalous dimensions of the local operators. For the mass gap problem, in the search of a
Cosmology and Structure Formation with Scalar Field Dark Matter
NASA Astrophysics Data System (ADS)
Rindler-Daller, Tanja; Li, Bohua; Shapiro, Paul R.
2013-04-01
The exploration of the nature of the cosmological dark matter is an ongoing hot topic in modern cosmology and particle physics. Suggested candidates include ultra-light particles which are described by a real or complex scalar field. Previous literature has revealed the richness of this candidate in terms of its power to explain astrophysical and cosmological observations, from the background cosmological evolution to galactic rotation curves. However, a lot of research remains to be done to find out which parts of the parameter space of this kind of dark matter is able to explain observations on all scales consistently. In this talk, we will present our current and ongoing work on the study of complex scalar field dark matter (SFDM). We find that this SFDM underwent three distinctive states in the early Universe, a scalar-field dominated, a radiation-dominated and a matter-dominated phase. The timing and longevity of each phase places important first constraints on the parameters of the model. For this SFDM model, we revisit classical problems of structure formation theory, like the tophat collapse, the problem of virial shocks, and the cosmological infall problem for an isolated halo, in order to find viable model parameters which match the constraints from cosmology.
Three-dimensional noncommutative Yukawa theory: Induced effective action and propagating modes
NASA Astrophysics Data System (ADS)
Bufalo, R.; Ghasemkhani, M.
2017-02-01
In this paper, we establish the analysis of noncommutative Yukawa theory, encompassing neutral and charged scalar fields. We approach the analysis by considering carefully the derivation of the respective effective actions. Hence, based on the obtained results, we compute the one-loop contributions to the neutral and charged scalar field self-energy, as well as to the Chern-Simons polarization tensor. In order to properly define the behavior of the quantum fields, the known UV/IR mixing due to radiative corrections is analyzed in the one-loop physical dispersion relation of the scalar and gauge fields.
Pointwise analysis of scalar fields: A nonstandard approach
Yamashita, Hideyasu
2006-09-15
A new nonstandard-analytical approach to quantum fields is presented, which gives a mathematical foundation for manipulating pointwise-defined quantum fields. In our approach, a field operator {phi}(x) is not a standard operator-valued distribution, but a nonstandard operator-valued function. Then formal expressions containing, e.g., {phi}(x){sup 2} can be understood literally, and shown to be well defined. In the free field cases, we show that the Wightman functions are explicitly calculated with the pointwise field, without any regularization, e.g., Wick product. Our notion of pointwise fields is applied also to the path integral formalisms of scalar fields. We show that some of physicists' naive expressions of Lagrangian path integral formulas can be rigorously justified.
M-flation: inflation from matrix valued scalar fields
Ashoorioon, Amjad; Firouzjahi, Hassan; Sheikh-Jabbari, M.M. E-mail: firouz@physics.mcgill.ca
2009-06-01
We propose an inflationary scenario, M-flation, in which inflation is driven by three N × N hermitian matrices Φ{sub i}, i = 1, 2, 3. The inflation potential of our model, which is strongly motivated from string theory, is constructed from Φ{sub i} and their commutators. We show that one can consistently restrict the classical dynamics to a sector in which the Φ{sub i} are proportional to the N × N irreducible representations of SU(2). In this sector our model effectively behaves as an N-flation model with 3N{sup 2} number of fields and the effective inflaton field has a super-Planckian field value. Furthermore, the fine-tunings associated with unnaturally small couplings in the chaotic type inflationary scenarios are removed. Due to the matrix nature of the inflaton fields there are 3N{sup 2}−1 extra scalar fields in the dynamics. These have the observational effects such as production of iso-curvature perturbations on cosmic microwave background. Moreover, the existence of these extra scalars provides us with a natural preheating mechanism and exit from inflation. As the effective inflaton field can traverse super-Planckian distances in the field space, the model is capable of producing a considerable amount of gravity waves that can be probed by future CMB polarization experiments such as PLANCK, QUIET and CMBPOL.
Scalar field evolution in Gauss-Bonnet black holes
Abdalla, E.; Konoplya, R.A.; Molina, C.
2005-10-15
It is presented a thorough analysis of scalar perturbations in the background of Gauss-Bonnet, Gauss-Bonnet-de Sitter and Gauss-Bonnet-anti-de Sitter black hole spacetimes. The perturbations are considered both in frequency and time domain. The dependence of the scalar field evolution on the values of the cosmological constant {lambda} and the Gauss-Bonnet coupling {alpha} is investigated. For Gauss-Bonnet and Gauss-Bonnet-de Sitter black holes, at asymptotically late times either power-law or exponential tails dominate, while for Gauss-Bonnet-anti-de Sitter black hole, the quasinormal modes govern the scalar field decay at all times. The power-law tails at asymptotically late times for odd-dimensional Gauss-Bonnet black holes does not depend on {alpha}, even though the black hole metric contains {alpha} as a new parameter. The corrections to quasinormal spectrum due to Gauss-Bonnet coupling is not small and should not be neglected. For the limit of near extremal value of the (positive) cosmological constant and pure de Sitter and anti-de Sitter modes in Gauss-Bonnet gravity we have found analytical expressions.
Scalar-tensor cosmologies: Fixed points of the Jordan frame scalar field
Jaerv, Laur; Kuusk, Piret; Saal, Margus
2008-10-15
We study the evolution of homogeneous and isotropic, flat cosmological models within the general scalar-tensor theory of gravity with arbitrary coupling function and potential. After introducing the limit of general relativity we describe the details of the phase space geometry. Using the methods of dynamical systems for the decoupled equation of the Jordan frame scalar field we find the fixed points of flows in two cases: potential domination and matter domination. We present the conditions on the mathematical form of the coupling function and potential which determine the nature of the fixed points (attractor or other). There are two types of fixed points, both are characterized by cosmological evolution mimicking general relativity, but only one of the types is compatible with the Solar System parametrized post-Newtonian (PPN) constraints. The phase space structure should also carry over to the Einstein frame as long as the transformation between the frames is regular which however is not the case for the latter (PPN compatible) fixed point.
Galilean-invariant scalar fields can strengthen gravitational lensing.
Wyman, Mark
2011-05-20
The mystery of dark energy suggests that there is new gravitational physics on long length scales. Yet light degrees of freedom in gravity are strictly limited by Solar System observations. We can resolve this apparent contradiction by adding a Galilean-invariant scalar field to gravity. Called Galileons, these scalars have strong self-interactions near overdensities, like the Solar System, that suppress their dynamical effect. These nonlinearities are weak on cosmological scales, permitting new physics to operate. In this Letter, we point out that a massive-gravity-inspired coupling of Galileons to stress energy can enhance gravitational lensing. Because the enhancement appears at a fixed scaled location for dark matter halos of a wide range of masses, stacked cluster analysis of weak lensing data should be able to detect or constrain this effect.
Averaged energy inequalities for the nonminimally coupled classical scalar field
Fewster, Christopher J.; Osterbrink, Lutz W.
2006-08-15
The stress-energy tensor for the classical nonminimally coupled scalar field is known not to satisfy the pointwise energy conditions of general relativity. In this paper we show, however, that local averages of the classical stress-energy tensor satisfy certain inequalities. We give bounds for averages along causal geodesics and show, e.g., that in Ricci-flat background spacetimes, ANEC and AWEC are satisfied. Furthermore we use our result to show that in the classical situation we have an analogue to the phenomenon of quantum interest. These results lay the foundations for analogous energy inequalities for the quantized nonminimally coupled fields, which will be discussed elsewhere.
Massless scalar field vacuum in de Sitter spacetime
Page, Don N.; Wu, Xing E-mail: xwu5@ualberta.ca
2012-11-01
As a spacetime with compact spatial sections, de Sitter spacetime does not have a de Sitter-invariant ground state for a minimally-coupled massless scalar field that gives definite expectation values for any observables not invariant under constant shifts of the field. However, if one restricts to observables that are shift invariant, as the action is, then there is a unique vacuum state. Here we calculate the shift-invariant four-point function that is the vacuum expectation value of the product of the difference of the field values at one pair of points and of the difference of the field values at a second pair of points. We show that this vacuum expectation value obeys a cluster-decomposition property of vanishing in the limit that the one pair of points is moved arbitrarily far from the other pair. We also calculate the shift-invariant correlation of the gradient of the scalar field at two different points and show that it also obeys a cluster-decomposition property. Possible relevance to a putative de Sitter-invariant quantum state for gravity is discussed.
Search for strongly coupled Chameleon scalar field with neutron interferometry
NASA Astrophysics Data System (ADS)
Li, K.; Arif, M.; Cory, D.; Haun, R.; Heacock, B.; Huber, M.; Nsofini, J.; Pushin, D. A.; Saggu, P.; Sarenac, D.; Shahi, C.; Skavysh, V.; Snow, M.; Young, A.
2015-04-01
The dark energy proposed to explain the observed accelerated expansion of the universe is not understood. A chameleon scalar field proposed as a dark energy candidate can explain the accelerated expansion and evade all current gravity experimental bounds. It features an effective range of the chameleon scalar field that depends on the local mass density. Hence a perfect crystal neutron interferometer, that measures relative phase shift between two paths, is a prefect tool to search for the chameleon field. We are preparing a two-chamber helium gas cell for the neutron interferometer. We can lower the pressure in one cell so low that the chameleon field range expands into the cell and causes a measurable neutron phase shift while keeping the pressure difference constant. We expect to set a new upper limit of the Chameleon field by at least one order of magnitude. This work is supported by NSF Grant 1205977, DOE Grant DE-FG02-97ER41042, Canadian Excellence Research Chairs program, Natural Sciences and Engineering Research Council of Canada and Collaborative Research and Training Experience Program
Bose-Einstein condensation of relativistic Scalar Field Dark Matter
Urena-Lopez, L. Arturo
2009-01-15
Standard thermodynamical results of ideal Bose gases are used to study the possible formation of a cosmological Bose-Einstein condensate in Scalar Field Dark Matter models; the main hypothesis is that the boson particles were in thermal equilibrium in the early Universe. It is then shown that the only relevant case needs the presence of both particles and anti-particles, and that it corresponds to models in which the bosonic particle is very light. Contrary to common wisdom, the condensate should be a relativistic phenomenon. Some cosmological implications are discussed in turn.
Slowly rotating scalar field wormholes: The second order approximation
Kashargin, P. E.; Sushkov, S. V.
2008-09-15
We discuss rotating wormholes in general relativity with a scalar field with negative kinetic energy. To solve the problem, we use the assumption about slow rotation. The role of a small dimensionless parameter plays the ratio of the linear velocity of rotation of the wormhole's throat and the velocity of light. We construct the rotating wormhole solution in the second-order approximation with respect to the small parameter. The analysis shows that the asymptotical mass of the rotating wormhole is greater than that of the nonrotating one, and the null energy condition violation in the rotating wormhole spacetime is weaker than that in the nonrotating one.
Self tuning scalar fields in spherically symmetric spacetimes
Appleby, Stephen
2015-05-01
We search for self tuning solutions to the Einstein-scalar field equations for the simplest class of 'Fab-Four' models with constant potentials. We first review the conditions under which self tuning occurs in a cosmological spacetime, and by introducing a small modification to the original theory—introducing the second and third Galileon terms—show how one can obtain de Sitter states where the expansion rate is independent of the vacuum energy. We then consider whether the same self tuning mechanism can persist in a spherically symmetric inhomogeneous spacetime. We show that there are no asymptotically flat solutions to the field equations in which the vacuum energy is screened, other than the trivial one (Minkowski space). We then consider the possibility of constructing Schwarzschild de Sitter spacetimes for the modified Fab Four plus Galileon theory. We argue that the only model that can successfully screen the vacuum energy in both an FLRW and Schwarzschild de Sitter spacetime is one containing 'John' ∼ G{sup μ}{sub ν} ∂{sub μ}φ∂{sup ν}φ and a canonical kinetic term ∼ ∂{sub α}φ ∂{sup α}φ. This behaviour was first observed in [1]. The screening mechanism, which requires redundancy of the scalar field equation in the 'vacuum', fails for the 'Paul' term in an inhomogeneous spacetime.
On static solutions of the Einstein-Scalar Field equations
NASA Astrophysics Data System (ADS)
Reiris, Martín
2017-03-01
In this article we study self-gravitating static solutions of the Einstein-Scalar Field system in arbitrary dimensions. We discuss the existence of geodesically complete solutions depending on the form of the scalar field potential V(φ ), and provide full global geometric estimates when the solutions exist. The most complete results are obtained for the physically important Klein-Gordon field and are summarised as follows. When V(φ )=m2|φ |2, it is proved that geodesically complete solutions have Ricci-flat spatial metric, have constant lapse and are vacuum, (that is φ is constant and equal to zero if m≠ 0). In particular, when the spatial dimension is three, the only such solutions are either Minkowski or a quotient thereof (no nontrivial solutions exist). When V(φ )=m2|φ |2+2Λ , that is, when a vacuum energy or a cosmological constant is included, it is proved that no geodesically complete solution exists when Λ >0, whereas when Λ <0 it is proved that no non-vacuum geodesically complete solution exists unless m2<-2Λ /(n-1), ( n is the spatial dimension) and the spatial manifold is non-compact. The proofs are based on novel techniques in comparison geometry á la Bakry-Émery that have their own interest.
Massless scalar field and solar-system experiments
Formiga, J. B.
2011-04-15
The solution of Einstein's field equations with the energy-momentum tensor of a massless scalar field is known as the Fisher solution. It is well known that this solution has a naked singularity due to the ''charge''{Sigma} of the massless scalar field. Here I obtain the radial null geodesic of the Fisher solution and use it to confirm that there is no black hole. In addition, I use the parametrized post-Newtonian formalism to show that the Fisher spacetime predicts the same effects on solar-system experiments as the Schwarzschild one does, as long as we impose a limit on {Sigma}. I show that this limit is not a strong constraint and we can even take values of {Sigma} bigger than M. By using the exact formula of the redshift and some assumptions, I evaluate this limit for the experiment of Pound and Snider [Phys. Rev. 140, B788 (1965)]. It turns out that this limit is {Sigma}<5.8x10{sup 3} m.
Instability of charged wormholes supported by a ghost scalar field
Gonzalez, J. A.; Guzman, F. S.; Sarbach, O.
2009-07-15
In previous work, we analyzed the linear and nonlinear stability of static, spherically symmetric wormhole solutions to Einstein's field equations coupled to a massless ghost scalar field. Our analysis revealed that all these solutions are unstable with respect to linear and nonlinear spherically symmetric perturbations and showed that the perturbation causes the wormholes to either decay to a Schwarzschild black hole or undergo a rapid expansion. Here, we consider charged generalization of the previous models by adding to the gravitational and ghost scalar field an electromagnetic one. We first derive the most general static, spherically symmetric wormholes in this theory and show that they give rise to a four-parameter family of solutions. This family can be naturally divided into subcritical, critical and supercritical solutions depending on the sign of the sum of the asymptotic masses. Then, we analyze the linear stability of these solutions. We prove that all subcritical and all critical solutions possess one exponentially in time growing mode. It follows that all subcritical and critical wormholes are linearly unstable. In the supercritical case we provide numerical evidence for the existence of a similar unstable mode.
Scalar self-force on a static particle in Schwarzschild spacetime using the massive field approach
NASA Astrophysics Data System (ADS)
Rosenthal, Eran
2004-12-01
I use the recently developed massive field approach to calculate the scalar self-force on a static particle in a Schwarzschild spacetime. In this approach the scalar self-force is obtained from the difference between the (massless) scalar field, and an auxiliary massive scalar field combined with a certain limiting process. By applying this approach to a static particle in Schwarzschild I show that the scalar self-force vanishes in this case. This result conforms with a previous analysis [A. G. Wiseman, Phys. Rev. D612000084014].
Weak scattering of scalar and electromagnetic random fields
NASA Astrophysics Data System (ADS)
Tong, Zhisong
This dissertation encompasses several studies relating to the theory of weak potential scattering of scalar and electromagnetic random, wide-sense statistically stationary fields from various types of deterministic or random linear media. The proposed theory is largely based on the first Born approximation for potential scattering and on the angular spectrum representation of fields. The main focus of the scalar counterpart of the theory is made on calculation of the second-order statistics of scattered light fields in cases when the scattering medium consists of several types of discrete particles with deterministic or random potentials. It is shown that the knowledge of the correlation properties for the particles of the same and different types, described with the newly introduced pair-scattering matrix, is crucial for determining the spectral and coherence states of the scattered radiation. The approach based on the pair-scattering matrix is then used for solving an inverse problem of determining the location of an "alien" particle within the scattering collection of "normal" particles, from several measurements of the spectral density of scattered light. Weak scalar scattering of light from a particulate medium in the presence of optical turbulence existing between the scattering centers is then approached using the combination of the Born's theory for treating the light interaction with discrete particles and the Rytov's theory for light propagation in extended turbulent medium. It is demonstrated how the statistics of scattered radiation depend on scattering potentials of particles and the power spectra of the refractive index fluctuations of turbulence. This theory is of utmost importance for applications involving atmospheric and oceanic light transmission. The second part of the dissertation includes the theoretical procedure developed for predicting the second-order statistics of the electromagnetic random fields, such as polarization and linear momentum
Casimir effect for a scalar field via Krein quantization
Pejhan, H.; Tanhayi, M.R.; Takook, M.V.
2014-02-15
In this work, we present a rather simple method to study the Casimir effect on a spherical shell for a massless scalar field with Dirichlet boundary condition by applying the indefinite metric field (Krein) quantization technique. In this technique, the field operators are constructed from both negative and positive norm states. Having understood that negative norm states are un-physical, they are only used as a mathematical tool for renormalizing the theory and then one can get rid of them by imposing some proper physical conditions. -- Highlights: • A modification of QFT is considered to address the vacuum energy divergence problem. • Casimir energy of a spherical shell is calculated, through this approach. • In this technique, it is shown, the theory is automatically regularized.
Gravitational waves and scalar perturbations from spectator fields
NASA Astrophysics Data System (ADS)
Biagetti, Matteo; Dimastrogiovanni, Emanuela; Fasiello, Matteo; Peloso, Marco
2015-04-01
The most conventional mechanism for gravitational waves (gw) production during inflation is the amplification of vacuum metric fluctuations. In this case the gw production can be uniquely related to the inflationary expansion rate H. For example, a gw detection close to the present experimental limit (tensor-to-scalar ratio r ~ 0.1) would indicate an inflationary expansion rate close to 1014 GeV. This conclusion, however, would be invalid if the observed gw originated from a different source. We construct and study one of the possible covariant formulations of the mechanism suggested in [1], where a spectator field σ with a sound speed cs ll 1 acts as a source for gw during inflation. In our formulation σ is described by a so-called P(X) Lagrangian and a non-minimal coupling to gravity. This field interacts only gravitationally with the inflaton, which has a standard action. We compute the amount of scalar and tensor density fluctuations produced by σ and find that, in our realization, r is not enhanced with respect to the standard result but it is strongly sensitive to cs, thus breaking the direct r leftrightarrow H connection.
Unified Dark Matter scalar field models with fast transition
Bertacca, Daniele; Bruni, Marco; Piattella, Oliver F.; Pietrobon, Davide E-mail: marco.bruni@port.ac.uk E-mail: davide.pietrobon@jpl.nasa.gov
2011-02-01
We investigate the general properties of Unified Dark Matter (UDM) scalar field models with Lagrangians with a non-canonical kinetic term, looking specifically for models that can produce a fast transition between an early Einstein-de Sitter CDM-like era and a later Dark Energy like phase, similarly to the barotropic fluid UDM models in JCAP01(2010)014. However, while the background evolution can be very similar in the two cases, the perturbations are naturally adiabatic in fluid models, while in the scalar field case they are necessarily non-adiabatic. The new approach to building UDM Lagrangians proposed here allows to escape the common problem of the fine-tuning of the parameters which plague many UDM models. We analyse the properties of perturbations in our model, focusing on the the evolution of the effective speed of sound and that of the Jeans length. With this insight, we can set theoretical constraints on the parameters of the model, predicting sufficient conditions for the model to be viable. An interesting feature of our models is that what can be interpreted as w{sub DE} can be < −1 without violating the null energy conditions.
Gravitational waves and scalar perturbations from spectator fields
Biagetti, Matteo; Dimastrogiovanni, Emanuela; Peloso, Marco; Fasiello, Matteo E-mail: emanuela1573@gmail.com E-mail: peloso@physics.umn.edu
2015-04-01
The most conventional mechanism for gravitational waves (gw) production during inflation is the amplification of vacuum metric fluctuations. In this case the gw production can be uniquely related to the inflationary expansion rate H. For example, a gw detection close to the present experimental limit (tensor-to-scalar ratio r ∼ 0.1) would indicate an inflationary expansion rate close to 10{sup 14} GeV. This conclusion, however, would be invalid if the observed gw originated from a different source. We construct and study one of the possible covariant formulations of the mechanism suggested in [1], where a spectator field σ with a sound speed c{sub s} || 1 acts as a source for gw during inflation. In our formulation σ is described by a so-called P(X) Lagrangian and a non-minimal coupling to gravity. This field interacts only gravitationally with the inflaton, which has a standard action. We compute the amount of scalar and tensor density fluctuations produced by σ and find that, in our realization, r is not enhanced with respect to the standard result but it is strongly sensitive to c{sub s}, thus breaking the direct r ↔ H connection.
Spikes and matter inhomogeneities in massless scalar field models
NASA Astrophysics Data System (ADS)
Coley, A. A.; Lim, W. C.
2016-01-01
We shall discuss the general relativistic generation of spikes in a massless scalar field or stiff perfect fluid model. We first investigate orthogonally transitive (OT) G 2 stiff fluid spike models both heuristically and numerically, and give a new exact OT G 2 stiff fluid spike solution. We then present a new two-parameter family of non-OT G 2 stiff fluid spike solutions, obtained by the generalization of non-OT G 2 vacuum spike solutions to the stiff fluid case by applying Geroch's transformation on a Jacobs seed. The dynamics of these new stiff fluid spike solutions is qualitatively different from that of the vacuum spike solutions in that the matter (stiff fluid) feels the spike directly and the stiff fluid spike solution can end up with a permanent spike. We then derive the evolution equations of non-OT G 2 stiff fluid models, including a second perfect fluid, in full generality, and briefly discuss some of their qualitative properties and their potential numerical analysis. Finally, we discuss how a fluid, and especially a stiff fluid or massless scalar field, affects the physics of the generation of spikes.
Local approximations for effective scalar field equations of motion
NASA Astrophysics Data System (ADS)
Berera, Arjun; Moss, Ian G.; Ramos, Rudnei O.
2007-10-01
Fluctuation and dissipation dynamics is examined at all temperature ranges for the general case of a background time evolving scalar field coupled to heavy intermediate quantum fields which in turn are coupled to light quantum fields. The evolution of the background field induces particle production from the light fields through the action of the intermediate catalyzing heavy fields. Such field configurations are generically present in most particle physics models, including grand unified and supersymmetry theories, with application of this mechanism possible in inflation, heavy ion collision, and phase transition dynamics. The effective evolution equation for the background field is obtained and a fluctuation-dissipation theorem is derived for this system. The effective evolution, in general, is nonlocal in time. Appropriate conditions are found for when these time nonlocal effects can be approximated by local terms. Here careful distinction is made between a local expansion and the special case of a derivative expansion to all orders, which requires analytic behavior of the evolution equation in Fourier space.
Noncommutative via closed star product
NASA Astrophysics Data System (ADS)
Kupriyanov, V. G.; Vitale, P.
2015-08-01
We consider linear star products on of Lie algebra type. First we derive the closed formula for the polydifferential representation of the corresponding Lie algebra generators. Using this representation we define the Weyl star product on the dual of the Lie algebra. Then we construct a gauge operator relating the Weyl star product with the one which is closed with respect to some trace functional, Tr ( f ⋆ g) = Tr ( f · g). We introduce the derivative operator on the algebra of the closed star product and show that the corresponding Leibniz rule holds true up to a total derivative. As a particular example we study the space R {/θ 3} with type noncommutativity and show that in this case the closed star product is the one obtained from the Duflo quantization map. As a result a Laplacian can be defined such that its commutative limit reproduces the ordinary commutative one. The deformed Leibniz rule is applied to scalar field theory to derive conservation laws and the corresponding noncommutative currents.
Locally smeared operator product expansions in scalar field theory
Monahan, Christopher; Orginos, Kostas
2015-04-01
We propose a new locally smeared operator product expansion to decompose non-local operators in terms of a basis of smeared operators. The smeared operator product expansion formally connects nonperturbative matrix elements determined numerically using lattice field theory to matrix elements of non-local operators in the continuum. These nonperturbative matrix elements do not suffer from power-divergent mixing on the lattice, which significantly complicates calculations of quantities such as the moments of parton distribution functions, provided the smearing scale is kept fixed in the continuum limit. The presence of this smearing scale complicates the connection to the Wilson coefficients of the standardmore » operator product expansion and requires the construction of a suitable formalism. We demonstrate the feasibility of our approach with examples in real scalar field theory.« less
Locally smeared operator product expansions in scalar field theory
Monahan, Christopher; Orginos, Kostas
2015-04-01
We propose a new locally smeared operator product expansion to decompose non-local operators in terms of a basis of smeared operators. The smeared operator product expansion formally connects nonperturbative matrix elements determined numerically using lattice field theory to matrix elements of non-local operators in the continuum. These nonperturbative matrix elements do not suffer from power-divergent mixing on the lattice, which significantly complicates calculations of quantities such as the moments of parton distribution functions, provided the smearing scale is kept fixed in the continuum limit. The presence of this smearing scale complicates the connection to the Wilson coefficients of the standard operator product expansion and requires the construction of a suitable formalism. We demonstrate the feasibility of our approach with examples in real scalar field theory.
Accretion of phantom scalar field into a black hole
Gonzalez, J. A.; Guzman, F. S.
2009-06-15
Using numerical methods we present the first full nonlinear study of a phantom scalar field accreted into a black hole. We study different initial configurations and find that the accretion of the field into the black hole can reduce its area down to 50 percent within time scales of the order of few masses of the initial horizon. The analysis includes the cases where the total energy of the space-time is positive or negative. The confirmation of this effect in full nonlinear general relativity implies that the accretion of exotic matter could be considered an evaporation process. We speculate that if this sort of exotic matter has some cosmological significance, this black hole area reduction process might have played a crucial role in black hole formation and population.
Optimization of Geometries for Experimental Searches of Chameleon Scalar Fields
NASA Astrophysics Data System (ADS)
Skavysh, Vladimir; Arif, Muhammad; Shahi, Chandra; Haun, Robert; Snow, Mike; Li, Ke; Heacock, Benjamin; Young, Albert; Indiana Univeristy Team; National Institute of Standards; Technology Team; North Carolina State University Team
2015-04-01
The chameleon scalar field theory is a dynamic model of dark energy. This model is unique in that it gives predictions which can be tested in terrestrial experiments. Here, we consider the prediction that the chameleon field exacts a force on objects in vacuum. Due to symmetry of typical objects, this force is usually miniscule. However, the chameleon force on a single surface can be surprisingly large, which is why we investigate whether there exist geometries for which the net chameleon force on an object is large enough to be measured. Moreover, we consider multi-body systems, such as the setup of the high-frequency short-range gravity experiment at Indiana University (arXiv:hep-ph/0303057v2), which consists of three oscillating parallel plates.
Stability and quasinormal modes of the massive scalar field around Kerr black holes
NASA Astrophysics Data System (ADS)
Konoplya, R. A.; Zhidenko, A. V.
2006-06-01
In this paper, we find quasinormal spectrum of the massive scalar field in the background of the Kerr black holes. We show that all found modes are damped under the quasinormal modes boundary conditions when μM≲1, thereby implying stability of the massive scalar field. This complements the region of stability determined by the Beyer inequality for large masses of the field. We show that, similar to the case of a nonrotating black hole, the massive term of the scalar field does not contribute in the regime of high damping. Therefore, the high damping asymptotic should be the same as for the massless scalar field.
NASA Astrophysics Data System (ADS)
Nandi, Debottam; Shankaranarayanan, S.
2016-10-01
In this work, we present a consistent Hamiltonian analysis of cosmological perturbations for generalized non-canonical scalar fields. In order to do so, we introduce a new phase-space variable that is uniquely defined for different non-canonical scalar fields. We also show that this is the simplest and efficient way of expressing the Hamiltonian. We extend the Hamiltonian approach of [1] to non-canonical scalar field and obtain an unique expression of speed of sound in terms of phase-space variable. In order to invert generalized phase-space Hamilton's equations to Euler-Lagrange equations of motion, we prescribe a general inversion formulae and show that our approach for non-canonical scalar field is consistent. We also obtain the third and fourth order interaction Hamiltonian for generalized non-canonical scalar fields and briefly discuss the extension of our method to generalized Galilean scalar fields.
NASA Astrophysics Data System (ADS)
Huang, Wung-Hong; Du, Yi-Hsien
2017-02-01
We apply the transformation of mixing azimuthal and internal coordinate or mixing time and internal coordinate to a stack of N black M-branes to find the Melvin spacetime of a stack of N black D-branes with magnetic or electric flux in string theory, after the Kaluza-Klein reduction. We slightly extend previous formulas to investigate the external magnetic and electric effects on the butterfly effect and holographic mutual information. It shows that the Melvin fields do not modify the scrambling time and will enhance the mutual information. In addition, we also T-dualize and twist a stack of N black D-branes to find a Melvin Universe supported by the flux of the NSNS b-field, which describes a non-comutative spacetime. It also shows that the spatial noncommutativity does not modify the scrambling time and will enhance the mutual information. We also study the corrected mutual information in the backreaction geometry due to the shock wave in our three model spacetimes.
Bianchi type I Universe and interacting ghost scalar fields models of dark energy
NASA Astrophysics Data System (ADS)
Hossienkhani, H.
2016-04-01
We suggest a correspondence between interacting ghost dark energy model with the quintessence, tachyon and K-essence scalar field in a non-isotropic universe. This correspondence allows to reconstruct the potential and the dynamics for the scalar field of the interacting ghost dark energy model, which describe accelerated expansion of the universe. Our numerical result show the effects of the interaction and anisotropic on the evolutionary behavior the ghost scalar field models.
Neutron Star Structure in the Presence of Conformally Coupled Scalar Fields
NASA Technical Reports Server (NTRS)
Sultana, Joseph; Bose, Benjamin; Kazanas, Demosthenes
2014-01-01
Neutron star models are studied in the context of scalar-tensor theories of gravity in the presence of a conformally coupled scalar field, using two different numerical equations of state (EoS) representing different degrees of stiffness. In both cases we obtain a complete solution by matching the interior numerical solution of the coupled Einstein-scalar field hydrostatic equations, with an exact metric on the surface of the star. These are then used to find the effect of the scalar field and its coupling to geometry, on the neutron star structure, particularly the maximum neutron star mass and radius. We show that in the presence of a conformally coupled scalar field, neutron stars are less dense and have smaller masses and radii than their counterparts in the minimally coupled case, and the effect increases with the magnitude of the scalar field at the center of the star.
Polymer-Fourier quantization of the scalar field revisited
NASA Astrophysics Data System (ADS)
Garcia-Chung, Angel; Vergara, J. David
2016-10-01
The polymer quantization of the Fourier modes of the real scalar field is studied within algebraic scheme. We replace the positive linear functional of the standard Poincaré invariant quantization by a singular one. This singular positive linear functional is constructed as mimicking the singular limit of the complex structure of the Poincaré invariant Fock quantization. The resulting symmetry group of such polymer quantization is the subgroup SDiff(ℝ4) which is a subgroup of Diff(ℝ4) formed by spatial volume preserving diffeomorphisms. In consequence, this yields an entirely different irreducible representation of the canonical commutation relations, nonunitary equivalent to the standard Fock representation. We also compared the Poincaré invariant Fock vacuum with the polymer Fourier vacuum.
The real scalar field in extreme RNdS space
NASA Astrophysics Data System (ADS)
Guo, Guanghai; Gui, Yuanxing; Tian, Jianxiang
2005-07-01
The real scalar field equation between the outer black hole horizon and the cosmological horizon is solved in the extreme Reissner-Nordström de Sitter (RNdS) space. We use an accurate approximation, the polynomial approximation, to approximate the tortoise coordinate x(r) in order to get the inverse function r = r(x) and then to solve the wave equation. The case where the two horizons are very close to each other is discussed in detail. We find that the wave function is harmonic only in the very small regions near the horizons, and the amplitude decreases remarkably near the potential peak because of the effect of the potential. Furthermore, it is found that the height of the potential increases as the cosmological constant Λ decreases, and the wave amplitude will decrease more remarkably with less Λ.
Scalar field critical collapse in 2 +1 dimensions
NASA Astrophysics Data System (ADS)
JałmuŻna, Joanna; Gundlach, Carsten; Chmaj, Tadeusz
2015-12-01
We carry out numerical experiments in the critical collapse of a spherically symmetric massless scalar field in 2 +1 spacetime dimensions in the presence of a negative cosmological constant and compare them against a new theoretical model. We approximate the true critical solution as the n =4 Garfinkle solution, matched at the light cone to a Vaidya-like solution, and corrected to leading order for the effect of Λ <0 . This approximation is only C3 at the light cone and has three growing modes. We conjecture that pointwise it is a good approximation to a yet unknown true critical solution that is analytic with only one growing mode (itself approximated by the top mode of our amended Garfinkle solution). With this conjecture, we predict a Ricci-scaling exponent of γ =8 /7 and a mass-scaling exponent of δ =16 /23 , compatible with our numerical experiments.
Gravitomagnetic effects in quadratic gravity with a scalar field
NASA Astrophysics Data System (ADS)
Finch, Andrew; Said, Jackson Levi
2016-10-01
The two gravitomagnetic effects which influence bodies orbiting around a gravitational source are the geodetic effect and the Lense-Thirring effect. The former describes the precession angle of the axis of a spinning gyroscope while in orbit around a nonrotating gravitational source whereas the latter provides a correction for this angle in the case of a spinning source. In this paper we derive the relevant equations in quadratic gravity and relate them to their equivalents in general relativity. Starting with an investigation into Kepler's third law in quadratic gravity with a scalar field, the effects of an axisymmetric and rotating gravitational source on an orbiting body in a circular, equatorial orbit are introduced.
Space-time symmetries of noncommutative spaces
Calmet, Xavier
2005-04-15
We define a noncommutative Lorentz symmetry for canonical noncommutative spaces. The noncommutative vector fields and the derivatives transform under a deformed Lorentz transformation. We show that the star product is invariant under noncommutative Lorentz transformations. We then apply our idea to the case of actions obtained by expanding the star product and the fields taken in the enveloping algebra via the Seiberg-Witten maps and verify that these actions are invariant under these new noncommutative Lorentz transformations. We finally consider general coordinate transformations and show that the metric is undeformed.
Vacuum polarization of a quantized scalar field in the thermal state in a long throat
NASA Astrophysics Data System (ADS)
Popov, Arkady A.
2016-12-01
Vacuum polarization of scalar fields in the background of a long throat is investigated. The field is assumed to be both massive or massless, with arbitrary coupling to the scalar curvature, and in a thermal state at an arbitrary temperature. Analytical approximation for ⟨φ2⟩ren is obtained.
Casimir force for a scalar field in warped brane worlds
Linares, Roman; Morales-Tecotl, Hugo A.; Pedraza, Omar
2008-03-15
In looking for imprints of extra dimensions in braneworld models one usually builds these so that they are compatible with known low energy physics and thus focuses on high energy effects. Nevertheless, just as submillimeter Newton's law tests probe the mode structure of gravity other low energy tests might apply to matter. As a model example, in this work we determine the 4D Casimir force corresponding to a scalar field subject to Dirichlet boundary conditions on two parallel planes lying within the single brane of a Randall-Sundrum scenario extended by one compact extra dimension. Using the Green's function method such a force picks the contribution of each field mode as if it acted individually but with a weight given by the square of the mode wave functions on the brane. In the low energy regime one regains the standard 4D Casimir force that is associated to a zero mode in the massless case or to a quasilocalized or resonant mode in the massive one while the effect of the extra dimensions gets encoded as an additional term.
Thermalization process after inflation and effective potential of scalar field
Mukaida, Kyohei; Yamada, Masaki E-mail: yamadam@icrr.u-tokyo.ac.jp
2016-02-01
We investigate the thermalization process of the Universe after inflation to determine the evolution of the effective temperature. The time scale of thermalization is found to be so long that it delays the evolution of the effective temperature, and the resulting maximal temperature of the Universe can be significantly lower than the one obtained in the literature. Our results clarify the finite density corrections to the effective potential of a scalar field and also processes of heavy particle production. In particular, we find that the maximum temperature of the Universe may be at most electroweak scale if the reheating temperature is as low as O (1) MeV, which implies that the electroweak symmetry may be marginally restored. In addition, it is noticeable that the dark matter may not be produced from thermal plasma in such a low reheating scenario, since the maximum temperature can be smaller than the conventional estimation by five orders of magnitude. We also give implications to the Peccei-Quinn mechanism and the Affleck-Dine baryogenesis.
Intermediate inflation from a non-canonical scalar field
Rezazadeh, K.; Karami, K.; Karimi, P. E-mail: KKarami@uok.ac.ir
2015-09-01
We study the intermediate inflation in a non-canonical scalar field framework with a power-like Lagrangian. We show that in contrast with the standard canonical intermediate inflation, our non-canonical model is compatible with the observational results of Planck 2015. Also, we estimate the equilateral non-Gaussianity parameter which is in well agreement with the prediction of Planck 2015. Then, we obtain an approximation for the energy scale at the initial time of inflation and show that it can be of order of the Planck energy scale, i.e. M{sub P} ∼ 10{sup 18}GeV. We will see that after a short period of time, inflation enters in the slow-roll regime that its energy scale is of order M{sub P}/100 ∼ 10{sup 16}GeV and the horizon exit takes place in this energy scale. We also examine an idea in our non-canonical model to overcome the central drawback of intermediate inflation which is the fact that inflation never ends. We solve this problem without disturbing significantly the nature of the intermediate inflation until the time of horizon exit.
Thermalization process after inflation and effective potential of scalar field
NASA Astrophysics Data System (ADS)
Mukaida, Kyohei; Yamada, Masaki
2016-02-01
We investigate the thermalization process of the Universe after inflation to determine the evolution of the effective temperature. The time scale of thermalization is found to be so long that it delays the evolution of the effective temperature, and the resulting maximal temperature of the Universe can be significantly lower than the one obtained in the literature. Our results clarify the finite density corrections to the effective potential of a scalar field and also processes of heavy particle production. In particular, we find that the maximum temperature of the Universe may be at most electroweak scale if the reheating temperature is as low as Script O (1) MeV, which implies that the electroweak symmetry may be marginally restored. In addition, it is noticeable that the dark matter may not be produced from thermal plasma in such a low reheating scenario, since the maximum temperature can be smaller than the conventional estimation by five orders of magnitude. We also give implications to the Peccei-Quinn mechanism and the Affleck-Dine baryogenesis.
Instability of coherent states of a real scalar field
Koutvitsky, Vladimir A.; Maslov, Eugene M.
2006-02-15
We investigate stability of both localized time-periodic coherent states (pulsons) and uniformly distributed coherent states (oscillating condensate) of a real scalar field satisfying the Klein-Gordon equation with a logarithmic nonlinearity. The linear analysis of time-dependent parts of perturbations leads to the Hill equation with a singular coefficient. To evaluate the characteristic exponent we extend the Lindemann-Stieltjes method, usually applied to the Mathieu and Lame equations, to the case that the periodic coefficient in the general Hill equation is an unbounded function of time. As a result, we derive the formula for the characteristic exponent and calculate the stability-instability chart. Then we analyze the spatial structure of the perturbations. Using these results we show that the pulsons of any amplitudes, remaining well-localized objects, lose their coherence with time. This means that, strictly speaking, all pulsons of the model considered are unstable. Nevertheless, for the nodeless pulsons the rate of the coherence breaking in narrow ranges of amplitudes is found to be very small, so that such pulsons can be long-lived. Further, we use the obtained stability-instability chart to examine the Affleck-Dine-type condensate. We conclude the oscillating condensate can decay into an ensemble of the nodeless pulsons.
Rapid topography mapping of scalar fields: Large molecular clusters
NASA Astrophysics Data System (ADS)
Yeole, Sachin D.; López, Rafael; Gadre, Shridhar R.
2012-08-01
An efficient and rapid algorithm for topography mapping of scalar fields, molecular electron density (MED) and molecular electrostatic potential (MESP) is presented. The highlight of the work is the use of fast function evaluation by Deformed-atoms-in-molecules (DAM) method. The DAM method provides very rapid as well as sufficiently accurate function and gradient evaluation. For mapping the topography of large systems, the molecular tailoring approach (MTA) is invoked. This new code is tested out for mapping the MED and MESP critical points (CP's) of small systems. It is further applied to large molecular clusters viz. (H2O)25, (C6H6)8 and also to a unit cell of valine crystal at MP2/6-31+G(d) level of theory. The completeness of the topography is checked by extensive search as well as applying the Poincaré-Hopf relation. The results obtained show that the DAM method in combination with MTA provides a rapid and efficient route for mapping the topography of large molecular systems.
Three-dimensional Casimir piston for massive scalar fields
Lim, S.C. Teo, L.P.
2009-08-15
We consider Casimir force acting on a three-dimensional rectangular piston due to a massive scalar field subject to periodic, Dirichlet and Neumann boundary conditions. Exponential cut-off method is used to derive the Casimir energy. It is shown that the divergent terms do not contribute to the Casimir force acting on the piston, thus render a finite well-defined Casimir force acting on the piston. Explicit expressions for the total Casimir force acting on the piston is derived, which show that the Casimir force is always attractive for all the different boundary conditions considered. As a function of a - the distance from the piston to the opposite wall, it is found that the magnitude of the Casimir force behaves like 1/a{sup 4} when a{yields}0{sup +} and decays exponentially when a{yields}{infinity}. Moreover, the magnitude of the Casimir force is always a decreasing function of a. On the other hand, passing from massless to massive, we find that the effect of the mass is insignificant when a is small, but the magnitude of the force is decreased for large a in the massive case.
Intermediate inflation from a non-canonical scalar field
NASA Astrophysics Data System (ADS)
Rezazadeh, K.; Karami, K.; Karimi, P.
2015-09-01
We study the intermediate inflation in a non-canonical scalar field framework with a power-like Lagrangian. We show that in contrast with the standard canonical intermediate inflation, our non-canonical model is compatible with the observational results of Planck 2015. Also, we estimate the equilateral non-Gaussianity parameter which is in well agreement with the prediction of Planck 2015. Then, we obtain an approximation for the energy scale at the initial time of inflation and show that it can be of order of the Planck energy scale, i.e. MP ~ 1018GeV. We will see that after a short period of time, inflation enters in the slow-roll regime that its energy scale is of order MP/100 ~ 1016GeV and the horizon exit takes place in this energy scale. We also examine an idea in our non-canonical model to overcome the central drawback of intermediate inflation which is the fact that inflation never ends. We solve this problem without disturbing significantly the nature of the intermediate inflation until the time of horizon exit.
Braneworld cosmology and noncommutative inflation
NASA Astrophysics Data System (ADS)
Calcagni, Gianluca
2005-03-01
In this work we develop the patch formalism, an approach providing a very simple and compact description of braneworld-motivated cosmologies with nonstandard effective Friedmann equations. In particular, the Hubble parameter is assumed to depend on some power of the brane energy density, H^2 propto rho^q. The high-energy limit of Randall-Sundrum (q=2) and Gauss-Bonnet (q=2/3) braneworlds are considered, during an accelerating era triggered by a single ordinary or tachyonic scalar field. The inflationary dynamics, solutions, and spectra are provided. Using the latest results from WMAP and other experiments for estimates of cosmological observables, it is shown that future data and missions can in principle discriminate between standard four-dimensional and braneworld scenarios. The issue of non-Gaussianity is also studied within nonlinear perturbation theory. The introduction of a fundamental energy scale reinforces these results. Several classes of noncommutative inflationary models are considered and their features analyzed in a number of ways and energy regimes. Finally, we establish dual relations between inflationary, cyclic/ekpyrotic and phantom cosmologies, as well as between scalar-driven and tachyon-driven cosmologies. The exact dualities relating the four-dimensional spectra are broken in favour of their braneworld counterparts. The dual solutions display new interesting features because of the modification of the effective Friedmann equation on the brane.
NASA Astrophysics Data System (ADS)
Antunes, V.; Novello, M.
2017-04-01
In the present work we revisit a model consisting of a scalar field with a quartic self-interaction potential non-minimally (conformally) coupled to gravity (Novello in Phys Lett 90A:347 1980). When the scalar field vacuum is in a broken symmetry state, an effective gravitational constant emerges which, in certain regimes, can lead to gravitational repulsive effects when only ordinary radiation is coupled to gravity. In this case, a bouncing universe is shown to be the only cosmological solution admissible by the field equations when the scalar field is in such broken symmetry state.
NASA Astrophysics Data System (ADS)
Kim, Nakwoo
2015-03-01
We consider scalar fields which are coupled to Einstein gravity with a negative cosmological constant, and construct periodic solutions perturbatively. In particular, we study tachyonic scalar fields whose mass is at or above the Breitenlohner-Freedman bound in four, five, and seven spacetime dimensions. The critical amplitude of the leading order perturbation, for which the perturbative expansion breaks down, increases as we consider less massive fields. We present various examples including a model with a self-interacting scalar field which is derived from a consistent truncation of IIB supergravity.
Noncommutative geometry, Grand Symmetry and twisted spectral triple
NASA Astrophysics Data System (ADS)
Devastato, Agostino
2015-08-01
In the noncommutative geometry approach to the standard model we discuss the possibility to derive the extra scalar field sv - initially suggested by particle physicist to stabilize the electroweak vacuum - from a “grand algebra” that contains the usual standard model algebra. We introduce the Connes-Moscovici twisted spectral triples for the Grand Symmetry model, to cure a technical problem, that is the appearance, together with the field sv, of unbounded vectorial terms. The twist makes these terms bounded, and also permits to understand the breaking making the computation of the Higgs mass compatible with the 126 GeV experimental value.
Signature change in p-adic and noncommutative FRW cosmology
NASA Astrophysics Data System (ADS)
Djordjevic, Goran S.; Nesic, Ljubisa; Radovancevic, Darko
2014-10-01
The significant matter for the construction of the so-called no-boundary proposal is the assumption of signature transition, which has been a way to deal with the problem of initial conditions of the universe. On the other hand, results of Loop Quantum Gravity indicate that the signature change is related to the discrete nature of space at the Planck scale. Motivated by possibility of non-Archimedean and/or noncommutative structure of space-time at the Planck scale, in this work we consider the classical, p-adic and (spatial) noncommutative form of a cosmological model with Friedmann-Robertson-Walker (FRW) metric coupled with a self-interacting scalar field.
Effects of a scalar field on the thermodynamics of interuniversal entanglement
NASA Astrophysics Data System (ADS)
Garay, Iñaki; Robles-Pérez, Salvador
2014-03-01
We consider a multiverse scenario made up of classically disconnected regions of the spacetime that are, nevertheless, in a quantum entangled state. The addition of a scalar field enriches the model and allows us to treat both the inflationary and the "oscillatory stage" of the universe on the same basis. Imposing suitable boundary conditions on the state of the multiverse, two different representations are constructed related by a Bogoliubov transformation. We compute the thermodynamic magnitudes of the entanglement, such as entropy and energy, explore the effects introduced by the presence of the scalar field and compare with previous results in the absence of scalar field.
Laser intensity effects in noncommutative QED
Heinzl, Thomas; Ilderton, Anton; Marklund, Mattias
2010-03-01
We discuss a twofold extension of QED assuming the presence of strong external fields provided by an ultraintense laser and noncommutativity of spacetime. While noncommutative effects leave the electron's intensity induced mass shift unchanged, photons change significantly in character: they acquire a quasimomentum that is no longer lightlike. We study the consequences of this combined noncommutative strong-field effect for the basic lepton-photon interactions.
Slow-roll suppression of adiabatic instabilities in coupled scalar field-dark matter models
Corasaniti, Pier Stefano
2008-10-15
We study the evolution of linear density perturbations in the context of interacting scalar field-dark matter cosmologies, where the presence of the coupling acts as a stabilization mechanism for the runaway behavior of the scalar self-interaction potential as in the case of the chameleon model. We show that, in the 'adiabatic' background regime of the system, the rise of unstable growing modes of the perturbations is suppressed by the slow-roll dynamics of the field. Furthermore, the coupled system behaves as an inhomogeneous adiabatic fluid. In contrast, instabilities may develop for large values of the coupling constant, or along nonadiabatic solutions, characterized by a period of high-frequency dumped oscillations of the scalar field. In the latter case, the dynamical instabilities of the field fluctuations, which are typical of oscillatory scalar field regimes, are amplified and transmitted by the coupling to dark matter perturbations.
Morita equivalence of noncommutative supertori
NASA Astrophysics Data System (ADS)
Chang-Young, Ee; Kim, Hoil; Nakajima, Hiroaki
2010-06-01
In this paper we study the extension of Morita equivalence of noncommutative tori to the supersymmetric case. The structure of the symmetry group yielding Morita equivalence appears to be intact but its parameter field becomes supersymmetrized having both body and soul parts. Our result is mainly in the two dimensional case in which noncommutative supertori have been constructed recently: The group SO(2,2,VZ0), where VZ0 denotes Grassmann even number whose body part belongs to Z, yields Morita equivalent noncommutative supertori in two dimensions.
Morita equivalence of noncommutative supertori
Chang-Young, Ee; Kim, Hoil; Nakajima, Hiroaki
2010-06-15
In this paper we study the extension of Morita equivalence of noncommutative tori to the supersymmetric case. The structure of the symmetry group yielding Morita equivalence appears to be intact but its parameter field becomes supersymmetrized having both body and soul parts. Our result is mainly in the two dimensional case in which noncommutative supertori have been constructed recently: The group SO(2,2,V{sub Z}{sup 0}), where V{sub Z}{sup 0} denotes Grassmann even number whose body part belongs to Z, yields Morita equivalent noncommutative supertori in two dimensions.
A late time accelerated FRW model with scalar and vector fields via Noether symmetry
NASA Astrophysics Data System (ADS)
Vakili, Babak
2014-11-01
We study the evolution of a three-dimensional minisuperspace cosmological model by the Noether symmetry approach. The phase space variables turn out to correspond to the scale factor of a flat Friedmann-Robertson-Walker (FRW) model, a scalar field with potential function V (ϕ) with which the gravity part of the action is minimally coupled and a vector field of its kinetic energy is coupled with the scalar field by a coupling function f (ϕ). Then, the Noether symmetry of such a cosmological model is investigated by utilizing the behavior of the corresponding Lagrangian under the infinitesimal generator of the desired symmetry. We explicitly calculate the form of the coupling function between the scalar and the vector fields and also the scalar field potential function for which such symmetry exists. Finally, by means of the corresponding Noether current, we integrate the equations of motion and obtain exact solutions for the scale factor, scalar and vector fields. It is shown that the resulting cosmology is an accelerated expansion universe for which its expansion is due to the presence of the vector field in the early times, while the scalar field is responsible of its late time expansion.
Noncommutative geometry and arithmetics
NASA Astrophysics Data System (ADS)
Almeida, P.
2009-09-01
We intend to illustrate how the methods of noncommutative geometry are currently used to tackle problems in class field theory. Noncommutative geometry enables one to think geometrically in situations in which the classical notion of space formed of points is no longer adequate, and thus a “noncommutative space” is needed; a full account of this approach is given in [3] by its main contributor, Alain Connes. The class field theory, i.e., number theory within the realm of Galois theory, is undoubtedly one of the main achievements in arithmetics, leading to an important algebraic machinery; for a modern overview, see [23]. The relationship between noncommutative geometry and number theory is one of the many themes treated in [22, 7-9, 11], a small part of which we will try to put in a more down-to-earth perspective, illustrating through an example what should be called an “application of physics to mathematics,” and our only purpose is to introduce nonspecialists to this beautiful area.
Landau levels of scalar QED in time-dependent magnetic fields
Kim, Sang Pyo
2014-05-15
The Landau levels of scalar QED undergo continuous transitions under a homogeneous, time-dependent magnetic field. We analytically formulate the Klein–Gordon equation for a charged spinless scalar as a Cauchy initial value problem in the two-component first order formalism and then put forth a measure that classifies the quantum motions into the adiabatic change, the nonadiabatic change, and the sudden change. We find the exact quantum motion and calculate the pair-production rate when the magnetic field suddenly changes as a step function. -- Highlights: •We study the Landau levels of scalar QED in time-dependent magnetic fields. •Instantaneous Landau levels make continuous transitions but keep parity. •The Klein–Gordon equation is expressed in the two-component first order formalism. •A measure is advanced that characterizes the quantum motions into three categories. •A suddenly changing magnetic field produces pairs of charged scalars from vacuum.
NASA Astrophysics Data System (ADS)
Hod, Shahar
2016-12-01
The physical properties of bound-state charged massive scalar field configurations linearly coupled to a spherically symmetric charged reflecting shell are studied analytically. To that end, we solve the Klein-Gordon wave equation for a static scalar field of proper mass μ, charge coupling constant q, and spherical harmonic index l in the background of a charged shell of radius R and electric charge Q. It is proved that the dimensionless inequality μR <√{(qQ) 2 -(l + 1 / 2) 2 } provides an upper bound on the regime of existence of the composed charged-spherical-shell-charged-massive-scalar-field configurations. Interestingly, we explicitly show that the discrete spectrum of shell radii {Rn(μ,qQ,l)}n = 0 n = ∞ which can support the static bound-state charged massive scalar field configurations can be determined analytically. We confirm our analytical results by numerical computations.
How the scalar field of unified dark matter models can cluster
Bertacca, Daniele; Bartolo, Nicola; Matarrese, Sabino; Diaferio, Antonaldo E-mail: nicola.bartolo@pd.infn.it E-mail: sabino.matarrese@pd.infn.it
2008-10-15
We use scalar field Lagrangians with a non-canonical kinetic term to obtain unified dark matter models where both the dark matter and the dark energy, the latter mimicking a cosmological constant, are described by the scalar field itself. In this framework, we propose a technique for reconstructing models where the effective speed of sound is small enough that the scalar field can cluster. These models avoid the strong time evolution of the gravitational potential and the large integrated Sachs-Wolfe effect which have been serious drawbacks of models considered previously. Moreover, these unified dark matter scalar field models can be easily generalized to behave as dark matter plus a dark energy component behaving like any type of quintessence fluid.
Farakos, K.; Koutsoumbas, G.; Pasipoularides, P.
2007-09-15
Brane world models with a nonminimally coupled bulk scalar field have been studied recently. In this paper we consider metric fluctuations around an arbitrary gravity-scalar background solution, and we show that the corresponding spectrum includes a localized zero mode which strongly depends on the profile of the background scalar field. For a special class of solutions, with a warp factor of the RS form, we solve the linearized Einstein equations, for a pointlike mass source on the brane, by using the brane bending formalism. We see that general relativity on the brane is recovered only if we impose restrictions on the parameter space of the models under consideration.
Wheeler-DeWitt equation and Lie symmetries in Bianchi scalar-field cosmology
NASA Astrophysics Data System (ADS)
Paliathanasis, A.; Karpathopoulos, L.; Wojnar, A.; Capozziello, S.
2016-04-01
Lie symmetries are discussed for the Wheeler-De Witt equation in Bianchi Class A cosmologies. In particular, we consider general relativity, minimally coupled scalar-field gravity and hybrid gravity as paradigmatic examples of the approach. Several invariant solutions are determined and classified according to the form of the scalar-field potential. The approach gives rise to a suitable method to select classical solutions and it is based on the first principle of the existence of symmetries.
Optical design of inhomogeneous media to perfectly focus scalar wave fields
NASA Astrophysics Data System (ADS)
Benítez, Pablo; Miñano, Juan C.; González, Juan C.
2010-08-01
A method to design isotropic inhomogeneous refractive index distribution is presented, in which the scalar wave field solutions propagate exactly on an eikonal function (i.e., remaining constant on the Geometrical Optics wavefronts). This method is applied to the design of "dipole lenses", which perfectly focus a scalar wave field emitted from a point source onto a point absorber, in both two and three dimensions. Also, the Maxwell fish-eye lens in two and three dimensions is analyzed.
SO(2, 3) noncommutative gravity model
NASA Astrophysics Data System (ADS)
Dimitrijević, M.; Radovanović, V.
2014-12-01
In this paper the noncommutative gravity is treated as a gauge theory of the non-commutative SO(2, 3)★ group, while the noncommutativity is canonical. The Seiberg-Witten (SW) map is used to express noncommutative fields in terms of the corresponding commutative fields. The commutative limit of the model is the Einstein-Hilbert action plus the cosmological term and the topological Gauss-Bonnet term. We calculate the second order correction to this model and obtain terms that are zeroth, first, ... and fourth power of the curvature tensor. Finally, we discuss physical consequences of those correction terms in the limit of big cosmological constant.
Properties and uncertainties of scalar field models of dark energy with barotropic equation of state
Novosyadlyj, Bohdan; Sergijenko, Olga; Apunevych, Stepan; Pelykh, Volodymyr
2010-11-15
The dynamics of expansion and large scale structure formation in the multicomponent Universe with dark energy modeled by the minimally coupled scalar field with generalized linear barotropic equation of state are analyzed. It is shown that the past dynamics of expansion and future of the Universe - eternal accelerated expansion or turnaround and collapse - are completely defined by the current energy density of a scalar field and relation between its current and early equation of state parameters. The clustering properties of such models of dark energy and their imprints in the power spectrum of matter density perturbations depend on the same relation and, additionally, on the 'effective sound speed' of a scalar field, defined by its Lagrangian. It is concluded that such scalar fields with different values of these parameters are distinguishable in principle. This gives the possibility to constrain them by confronting the theoretical predictions with the corresponding observational data. For that we have used the 7-year Wilkinson Microwave Anisotropy Probe data on cosmic microwave background anisotropies, the Union2 data set on Supernovae Ia and the seventh data release of the Sloan Digital Sky Survey data on luminous red galaxies space distribution. Using the Markov Chain Monte Carlo technique the marginalized posterior and mean likelihood distributions are computed for the scalar fields with two different Lagrangians: Klein-Gordon and Dirac-Born-Infeld ones. The properties of such scalar field models of dark energy with best fitting parameters and uncertainties of their determination are also analyzed in the paper.
The Geometry of Noncommutative Space-Time
NASA Astrophysics Data System (ADS)
Mendes, R. Vilela
2016-10-01
Stabilization, by deformation, of the Poincaré-Heisenberg algebra requires both the introduction of a fundamental lentgh and the noncommutativity of translations which is associated to the gravitational field. The noncommutative geometry structure that follows from the deformed algebra is studied both for the non-commutative tangent space and the full space with gravity. The contact points of this approach with the work of David Finkelstein are emphasized.
Twisted covariant noncommutative self-dual gravity
Estrada-Jimenez, S.; Garcia-Compean, H.; Obregon, O.; Ramirez, C.
2008-12-15
A twisted covariant formulation of noncommutative self-dual gravity is presented. The formulation for constructing twisted noncommutative Yang-Mills theories is used. It is shown that the noncommutative torsion is solved at any order of the {theta} expansion in terms of the tetrad and some extra fields of the theory. In the process the first order expansion in {theta} for the Plebanski action is explicitly obtained.
Dark sector impact on gravitational collapse of an electrically charged scalar field
NASA Astrophysics Data System (ADS)
Nakonieczna, Anna; Rogatko, Marek; Nakonieczny, Łukasz
2015-11-01
Dark matter and dark energy are dominating components of the Universe. Their presence affects the course and results of processes, which are driven by the gravitational interaction. The objective of the paper was to examine the influence of the dark sector on the gravitational collapse of an electrically charged scalar field. A phantom scalar field was used as a model of dark energy in the system. Dark matter was modeled by a complex scalar field with a quartic potential, charged under a U(1)-gauge field. The dark components were coupled to the electrically charged scalar field via the exponential coupling and the gauge field-Maxwell field kinetic mixing, respectively. Complete non-linear simulations of the investigated process were performed. They were conducted from regular initial data to the end state, which was the matter dispersal or a singularity formation in a spacetime. During the collapse in the presence of dark energy dynamical wormholes and naked singularities were formed in emerging spacetimes. The wormhole throats were stabilized by the violation of the null energy condition, which occurred due to a significant increase of a value of the phantom scalar field function in its vicinity. The square of mass parameter of the dark matter scalar field potential controlled the formation of a Cauchy horizon or wormhole throats in the spacetime. The joint impact of dark energy and dark matter on the examined process indicated that the former decides what type of an object forms, while the latter controls the amount of time needed for the object to form. Additionally, the dark sector suppresses the natural tendency of an electrically charged scalar field to form a dynamical Reissner-Nordström spacetime during the gravitational collapse.
Cosmic Evolution of Scalar Fields with Multiple Vacua: Generalized DBI and Quintessence
NASA Astrophysics Data System (ADS)
Gao, Changjun; Shen, You-Gen
2016-10-01
We find a method to rewrite the equations of motion of scalar fields, generalized DBI field and quintessence, in the autonomous form for arbitrary scalar potentials. With the aid of this method, we explore the cosmic evolution of generalized DBI field and quintessence with the potential of multiple vacua. Then we find that the scalars are always frozen in the false or true vacuum in the end. Compared to the evolution of quintessence, the generalized DBI field has more times of oscillations around the vacuum of the potential. The reason for this point is that, with the increasing of speed dot {φ }, the friction term of generalized DBI field is greatly decreased. Thus the generalized DBI field acquires more times of oscillations.
The statistics of a passive scalar in field-guided magnetohydrodynamic turbulence
NASA Astrophysics Data System (ADS)
Mason, J.; Boldyrev, S.; Cattaneo, F.; Perez, J. C.
2014-11-01
A variety of studies of magnetised plasma turbulence invoke theories for the advection of a passive scalar by turbulent fluctuations. Examples include modelling the electron density fluctuations in the interstellar medium, understanding the chemical composition of galaxy clusters and the intergalactic medium, and testing the prevailing phenomenological theories of magnetohydrodynamic turbulence. While passive scalar turbulence has been extensively studied in the hydrodynamic case, its counterpart in MHD turbulence is significantly less well understood. Herein we conduct a series of high-resolution direct numerical simulations of incompressible, field-guided, MHD turbulence in order to establish the fundamental properties of passive scalar evolution. We study the scalar anisotropy, establish the scaling relation analogous to Yaglom's law, and measure the intermittency of the passive scalar statistics. We also assess to what extent the pseudo Alfven fluctuations in strong MHD turbulence can be modelled as a passive scalar. The results suggest that the dynamics of a passive scalar in MHD turbulence is considerably more complicated than in the hydrodynamic case.
Rothschild, Freda; Bishop, Alexis I; Kitchen, Marcus J; Paganin, David M
2014-03-24
The Cornu spiral is, in essence, the image resulting from an Argand-plane map associated with monochromatic complex scalar plane waves diffracting from an infinite edge. Argand-plane maps can be useful in the analysis of more general optical fields. We experimentally study particular features of Argand-plane mappings known as "vorticity singularities" that are associated with mapping continuous single-valued complex scalar speckle fields to the Argand plane. Vorticity singularities possess a hierarchy of Argand-plane catastrophes including the fold, cusp and elliptic umbilic. We also confirm their connection to vortices in two-dimensional complex scalar waves. The study of vorticity singularities may also have implications for higher-dimensional fields such as coherence functions and multi-component fields such as vector and spinor fields.
Noncommutative accelerated multidimensional universe dominated by quintessence
NASA Astrophysics Data System (ADS)
El-Nabulsi, Ahmad Rami
2010-04-01
Noncommutative Geometry recently attracted growing interest of cosmologists, mainly after the greatest success of unifying the forces of nature into a single gravitational spectral action in a purely algebraic way, rather than as being an entirely new formalism. In the present work, we discuss a multidimensional Friedmann-Robertson-Walker flat universe in which the perfect fluid has a Gaussian profile in time and depends on a fundamental minimal length sqrt{θ} like ρ= ρ(0)exp (- t 2/4 θ) for some positive constant ρ(0). This special form is motivated by a more recent noncommutative inflationary cosmological model, which was found to be able to drive the universe through a bounce without the need of any scalar field. Furthermore, we conjecture that the generalized equation of state has the special form p= ω a m ρ- ρ,( ω, m)∈ℝ where a( t) is the scale factor. It was found that the expansion of the multidimensional universe accelerates in time and is dominated for very large time by quintessence. Many additional consequences are revealed and discussed in some detail.
Dirac equation on coordinate dependent noncommutative space-time
NASA Astrophysics Data System (ADS)
Kupriyanov, V. G.
2014-05-01
In this paper we discuss classical aspects of spinor field theory on the coordinate dependent noncommutative space-time. The noncommutative Dirac equation describing spinning particle in an external vector field and the corresponding action principle are proposed. The specific choice of a star product allows us to derive a conserved noncommutative probability current and to obtain the energy-momentum tensor for free noncommutative spinor field. Finally, we consider a free noncommutative Dirac fermion and show that if the Poisson structure is Lorentz-covariant, the standard energy-momentum dispersion relation remains valid.
Chaplygin gas inspired scalar fields inflation via well-known potentials
NASA Astrophysics Data System (ADS)
Jawad, Abdul; Butt, Sadaf; Rani, Shamaila
2016-08-01
Brane inflationary universe models in the context of modified Chaplygin gas and generalized cosmic Chaplygin gas are being studied. We develop these models in view of standard scalar and tachyon fields. In both models, the implemented inflationary parameters such as scalar and tensor power spectra, scalar spectral index and tensor to scalar ratio are derived under slow roll approximations. We also use chaotic and exponential potential in high energy limits and discuss the characteristics of inflationary parameters for both potentials. These models are compatible with recent astronomical observations provided by WMAP7{+}9 and Planck data, i.e., ηs=1.027±0.051, 1.009±0.049, 0.096±0.025 and r<0.38, 0.36, 0.11.
Dynamical system of scalar field from 2-dimension to 3-D and its cosmological implications
NASA Astrophysics Data System (ADS)
Fang, Wei; Tu, Hong; Huang, Jiasheng; Shu, Chenggang
2016-09-01
We give the three-dimensional dynamical autonomous systems for most of the popular scalar field dark energy models including (phantom) quintessence, (phantom) tachyon, K-essence, and general non-canonical scalar field models, change the dynamical variables from variables (x, y, λ ) to observable related variables (w_{φ }, Ω _{φ }, λ ), and show the intimate relationships between those scalar fields that the three-dimensional system of K-essence can reduce to (phantom) tachyon, general non-canonical scalar field can reduce to (phantom) quintessence and K-essence can also reduce to (phantom) quintessence for some special cases. For the applications of the three-dimensional dynamical systems, we investigate several special cases and give the exactly dynamical solutions in detail. In the end of this paper, we argue that it is more convenient and also has more physical meaning to express the differential equations of dynamical systems in (w_{φ }, Ω _{φ }, λ ) instead of variables (x, y, λ ) and to investigate the dynamical system in three dimensions instead of two dimensions. We also raise a question about the possibility of the chaotic behavior in the spatially flat single scalar field FRW cosmological models in the presence of ordinary matter.
Can a particle interacting with a scalar field reach the speed of light\\?
NASA Astrophysics Data System (ADS)
Vollick, Dan N.
1995-09-01
The motion of a particle interacting with a scalar field is examined. It is shown that the effective mass of the particle is a linear function of the scalar field and that the particle reaches the speed of light when its effective mass goes to zero if scalar field radiation is neglected. The equation of motion for the particle including radiation reaction has the same form as the Lorentz-Dirac equation. The radiation emitted diverges as the particle approaches the speed of light and prevents the particle from becoming luminal. The energy-momentum tensor for the particle and field is calculated and it is shown that there exists an interaction energy-momentum tensor which allows for violations of the weak energy condition.
Symmetry breaking and onset of cosmic acceleration in scalar field models
NASA Astrophysics Data System (ADS)
Mohseni Sadjadi, H.; Honardoost, M.; Sepangi, H. R.
2016-12-01
We propose a new scenario for the onset of positive acceleration of our Universe based on symmetry breaking in coupled dark energy scalar field model. In a symmetry breaking process where the scalar field rolls down its own potential, the potential reduction is not in favor of acceleration. In our model, when dark matter density becomes less than a critical value, the shape of the effective potential is changed and, the quintessence field climbs up along its own potential while rolls down the effective potential. We show that this procedure may establish the positivity of the potential required for the Universe to accelerate. In addition, we show that by choosing an appropriate interaction between dark sectors there is the possibility that the scalar field resides in a new vacuum giving rise to a positive cosmological constant which is responsible for a permanent late time acceleration.
Are black holes a serious threat to scalar field dark matter models?
Barranco, Juan; Degollado, Juan Carlos; Bernal, Argelia; Diez-Tejedor, Alberto; Megevand, Miguel; Alcubierre, Miguel; Nunez, Dario; Sarbach, Olivier
2011-10-15
Classical scalar fields have been proposed as possible candidates for the dark matter component of the universe. Given the fact that supermassive black holes seem to exist at the center of most galaxies, in order to be a viable candidate for the dark matter halo a scalar field configuration should be stable in the presence of a central black hole, or at least be able to survive for cosmological time scales. In the present work we consider a scalar field as a test field on a Schwarzschild background, and study under which conditions one can obtain long-lived configurations. We present a detailed study of the Klein-Gordon equation in the Schwarzschild space-time, both from an analytical and numerical point of view, and show that indeed there exist quasistationary solutions that can remain surrounding a black hole for large time scales.
Quanta of geometry: noncommutative aspects.
Chamseddine, Ali H; Connes, Alain; Mukhanov, Viatcheslav
2015-03-06
In the construction of spectral manifolds in noncommutative geometry, a higher degree Heisenberg commutation relation involving the Dirac operator and the Feynman slash of real scalar fields naturally appears and implies, by equality with the index formula, the quantization of the volume. We first show that this condition implies that the manifold decomposes into disconnected spheres, which will represent quanta of geometry. We then refine the condition by involving the real structure and two types of geometric quanta, and show that connected spin manifolds with large quantized volume are then obtained as solutions. The two algebras M_{2}(H) and M_{4}(C) are obtained, which are the exact constituents of the standard model. Using the two maps from M_{4} to S^{4} the four-manifold is built out of a very large number of the two kinds of spheres of Planckian volume. We give several physical applications of this scheme such as quantization of the cosmological constant, mimetic dark matter, and area quantization of black holes.
Superradiance of a charged scalar field coupled to the Einstein-Maxwell equations
NASA Astrophysics Data System (ADS)
Baake, Olaf; Rinne, Oliver
2016-12-01
We consider the Einstein-Maxwell-Klein-Gordon equations for a spherically symmetric scalar field scattering off a Reissner-Nordström black hole in asymptotically flat spacetime. The equations are solved numerically using a hyperboloidal evolution scheme. For suitable frequencies of the initial data, superradiance is observed, leading to a substantial decrease of mass and charge of the black hole. We also derive a Bondi mass loss formula using the Kodama vector field and investigate the late-time decay of the scalar field.
Effects of quantized scalar fields in cosmological spacetimes with big rip singularities
Bates, Jason D.; Anderson, Paul R.
2010-07-15
Effects of quantized free scalar fields in cosmological spacetimes with big rip singularities are investigated. The energy densities for these fields are computed at late times when the expansion is very rapid. For the massless minimally coupled field it is shown that an attractor state exists in the sense that, for a large class of states, the energy density of the field asymptotically approaches the energy density it would have if it was in the attractor state. Results of numerical computations of the energy density for the massless minimally coupled field and for massive fields with minimal and conformal couplings to the scalar curvature are presented. For the massive fields the energy density is seen to always asymptotically approach that of the corresponding massless field. The question of whether the energy densities of quantized fields can be large enough for backreaction effects to remove the big rip singularity is addressed.
An Exact Solution of Einstein-Maxwell Gravity Coupled to a Scalar Field
NASA Technical Reports Server (NTRS)
Turyshev, S. G.
1995-01-01
The general solution to low-energy string theory representing static spherically symmetric solution of the Einstein-Maxwell gravity with a massless scalar field has been found. Some of the partial cases appear to coincide with known solutions to black holes, naked singularities, and gravity and electromagnetic fields.
Gravitational collapse of a homogeneous scalar field coupled kinematically to Einstein tensor
NASA Astrophysics Data System (ADS)
Koutsoumbas, George; Ntrekis, Konstantinos; Papantonopoulos, Eleftherios; Tsoukalas, Minas
2017-02-01
We study the gravitational collapse of a homogeneous time-dependent scalar field that, besides its coupling to curvature, is also kinematically coupled to the Einstein tensor. This coupling is a part of the Horndeski theory and we investigate its effect on the collapsing process. We find that the time required for the scalar field to collapse depends on the value of the derivative coupling and the singularity is protected by a horizon. Matching the internal solution with an external Schwarzschild-anti-de Sitter metric we show that a black hole is formed, while the weak energy condition is satisfied during the collapsing process. The scalar field takes on a finite value at the singularity.
Non-minimally coupled scalar field cosmology on the phase plane
Hrycyna, Orest; Szydlowski, Marek E-mail: uoszydlo@cyf-kr.edu.pl
2009-04-15
In this publication we investigate dynamics of a flat FRW cosmological model with a non-minimally coupled scalar field with the coupling term {xi}R{psi}{sup 2} in the scalar field action. The quadratic potential function V({psi}) {proportional_to} {psi}{sup 2} is assumed. All the evolutional paths are visualized and classified in the phase plane, at which the parameter of non-minimal coupling {xi} plays the role of a control parameter. The fragility of global dynamics with respect to changes of the coupling constant is studied in details. We find that the future big rip singularity appearing in the phantom scalar field cosmological models can be avoided due to non-minimal coupling constant effects. We have shown the existence of a finite scale factor singular point (future or past) where the Hubble function as well as its first cosmological time derivative diverge.
NASA Astrophysics Data System (ADS)
Dutta, Sourav; Panja, Madan Mohan; Chakraborty, Subenoy
2016-06-01
Non-minimally coupled scalar field cosmology has been studied in this work within the framework of Einstein gravity. In the background of homogeneous and isotropic Friedmann-Lemaitre-Robertson-Walker (FLRW) spacetime non-minimally coupled scalar field having self-interacting potential is taken as the source of the matter content. The constraint of imposing Noether symmetry on the Lagrangian of the system not only determines the infinitesimal generator (the symmetry vector) but also the coupling function and the self-interacting potential for the scalar field. By choosing appropriately a point transformation in the augmented space, one of the transformed variables is cyclic for the Lagrangian. Finally, using constants of motion, the solutions are analyzed.
Non-minimally coupled scalar fields, Holst action and black hole mechanics
NASA Astrophysics Data System (ADS)
Chatterjee, Ayan
2011-02-01
The paper deals with the extension of the Weak Isolated Horizon (WIH) formulation of black hole horizons to the non-minimally coupled scalar fields. In the early part of the paper, we introduce an appropriate Holst type action to incorporate scalar fields non-minimally coupled to gravity and construct the covariant phase space of the theory. Using this phase space, we proceed to prove the laws of black hole mechanics. Further, we show that with a gauge fixing, the symplectic structure on the horizon reduces to that of a U(1) Chern-Simons theory. The level of the Chern-Simons theory is shown to depend on the non-minimally coupled scalar field.
Formation of caustics in Dirac-Born-Infeld type scalar field systems
Goswami, U. D.; Nandan, H.; Sami, M.
2010-11-15
We investigate the formation of caustics in the Dirac-Born-Infeld type scalar field systems for generic classes of potentials, viz., massive rolling scalar with potential, V({phi})=V{sub 0}e{sup {+-}(1/2)M2{phi}2} and inverse power-law potentials with V({phi})=V{sub 0}/{phi}{sup n}, 0
Logarithmic corrections to the entropy of scalar field in BTZ black hole spacetime
NASA Astrophysics Data System (ADS)
Singh, Dharm Veer; Sachan, Shobhit
The entanglement entropy correlates two quantum subsystems which are part of a larger system. A logarithmic divergence term present in the entanglement entropy is universal in nature and directly proportional to the conformal anomaly. We study this logarithmic divergence term of entropy for massive scalar field in (2 + 1) dimensions by applying numerical techniques to entanglement entropy approach. This (2+1)-dimensional massive theory can be obtained from the (3+1)-dimensional massless scalar field via dimensional reduction. We also calculated mass corrections to entanglement entropy for scalar field. Finally, we observe that the area law contribution to the entanglement entropy is not affected by this mass term and the universal quantities depend upon the basic properties of the system.
Radiation-like scalar field and gauge fields in cosmology for a theory with dynamical time
NASA Astrophysics Data System (ADS)
Benisty, David; Guendelman, E. I.
2016-09-01
Cosmological solutions with a scalar field behaving as radiation are obtained, in the context of gravitational theory with dynamical time. The solution requires the spacial curvature of the universe k, to be zero, unlike the standard radiation solutions, which do not impose any constraint on the spatial curvature of the universe. This is because only such k = 0 radiation solutions pose a homothetic Killing vector. This kind of theory can be used to generalize electromagnetism and other gauge theories, in curved spacetime, and there are no deviations from standard gauge field equation (like Maxwell equations) in the case there exist a conformal Killing vector. But there could be departures from Maxwell and Yang-Mills equations, for more general spacetimes.
Is Sextans dwarf galaxy in a scalar field dark matter halo?
Lora, V.; Magaña, Juan E-mail: juan.magana@uv.cl
2014-09-01
The Bose-Einstein condensate/scalar field dark matter model, considers that the dark matter is composed by spinless-ultra-light particles which can be described by a scalar field. This model is an alternative model to the Λ-cold dark matter paradigm, and therefore should be studied at galactic and cosmological scales. Dwarf spheroidal galaxies have been very useful when studying any dark matter theory, because the dark matter dominates their dynamics. In this paper we study the Sextans dwarf spheroidal galaxy, embedded in a scalar field dark matter halo. We explore how the dissolution time-scale of the stellar substructures in Sextans, constrain the mass, and the self-interacting parameter of the scalar field dark matter boson. We find that for masses in the range (0.12< m{sub φ}<8) ×10{sup -22} eV, scalar field dark halos without self-interaction would have cores large enough to explain the longevity of the stellar substructures in Sextans, and small enough mass to be compatible with dynamical limits. If the self-interacting parameter is distinct to zero, then the mass of the boson could be as high as m{sub φ}≈2×10{sup -21} eV, but it would correspond to an unrealistic low mass for the Sextans dark matter halo . Therefore, the Sextans dwarf galaxy could be embedded in a scalar field/BEC dark matter halo with a preferred self-interacting parameter equal to zero.
Dynamics of scalar field dark matter with a cosh-like potential
Matos, Tonatiuh; Vazquez, Jose Alberto; Luevano, Jose-Ruben; Quiros, Israel; Urena-Lopez, L. Arturo
2009-12-15
The dynamics of a cosmological model of dark matter and dark energy represented by a scalar field endowed with a cosh-like potential plus a cosmological constant is investigated in detail. By studying the appropriate phase space of the equations of motion, it is shown that a standard evolution of the Universe is recovered for appropriate values of the free parameters, and that the only late-time attractor is always the de Sitter solution. We also discuss the appearance of scalar field oscillations corresponding to dark matter behavior.
Absorption of a Massive Scalar Field by Wormhole Space-Times
NASA Astrophysics Data System (ADS)
Huang, Hai; Chen, Juhua; Wang, Yongjiu; Jin, Yao
2017-04-01
In this paper we consider the problem of the test massive scalar field propagating in the background of a class of wormhole space-times. Basing on the quantum scattering theory, we analyze the Schrödinger-type scalar wave equation and compute transmission coefficients for arbitrary coupling of the field to the background geometry with the WKB approximation. We numerically investigate its absorption cross section and analyze them in the high frequency regime. We find that the absorption cross section oscillates about the geometric optical value and the limit of absorption cross section is uniform in the high frequency regime.
Absorption of a Massive Scalar Field by Wormhole Space-Times
NASA Astrophysics Data System (ADS)
Huang, Hai; Chen, Juhua; Wang, Yongjiu; Jin, Yao
2017-01-01
In this paper we consider the problem of the test massive scalar field propagating in the background of a class of wormhole space-times. Basing on the quantum scattering theory, we analyze the Schrödinger-type scalar wave equation and compute transmission coefficients for arbitrary coupling of the field to the background geometry with the WKB approximation. We numerically investigate its absorption cross section and analyze them in the high frequency regime. We find that the absorption cross section oscillates about the geometric optical value and the limit of absorption cross section is uniform in the high frequency regime.
NASA Astrophysics Data System (ADS)
Pozdeeva, Ekaterina O.; Skugoreva, Maria A.; Toporensky, Alexey V.; Vernov, Sergey Yu.
2016-12-01
We explore dynamics of cosmological models with bounce solutions evolving on a spatially flat Friedmann-Lemaître-Robertson-Walker background. We consider cosmological models that contain the Hilbert-Einstein curvature term, the induced gravity term with a negative coupled constant, and even polynomial potentials of the scalar field. Bounce solutions with non-monotonic Hubble parameters have been obtained and analyzed. The case when the scalar field has the conformal coupling and the Higgs-like potential with an opposite sign is studied in detail. In this model the evolution of the Hubble parameter of the bounce solution essentially depends on the sign of the cosmological constant.
The Hamiltonian formalism for scalar fields coupled to gravity in a cosmological background
NASA Astrophysics Data System (ADS)
Bernardini, A. E.; Bertolami, O.
2013-11-01
A novel routine to investigate the scalar fields in a cosmological context is discussed in the framework of the Hamiltonian formalism. Starting from the Einstein-Hilbert action coupled to a Lagrangian density that contains two components-one corresponding to a scalar field Lagrangian, Lϕ, and another that depends on the scale parameter, La-one can identify a generalized Hamiltonian density from which first-order dynamical equations can be obtained. This set up corresponds to the dynamics of Friedmann-Robertson-Walker models in the presence of homogeneous fields embedded into a generalized cosmological background fluid in a system that evolves all together isentropically. Once the generalized Hamiltonian density is properly defined, the constraints on the gravity-matter-field system are straightforwardly obtained through the first-order Hamilton equations. The procedure is illustrated for three examples of cosmological interest for studies of the dark sector: real scalar fields, tachyonic fields and generalized Born-Infeld tachyonic fields. The inclusion of some isentropic fluid component into the Friedmann equation allows for identifying an exact correspondence between the dark sector underlying scalar field and an ordinary real scalar field dynamics. As a final issue, the Hamiltonian formulation is used to set the first-order dynamical equations through which one obtains the exact analytical description of the cosmological evolution of a generalized Chaplygin gas (GCG) with dustlike matter, radiation or curvature contributions. Model stability in terms of the square of the sound velocity, cs2, cosmic acceleration, q, and conditions for inflation are discussed.
Possible Statistics of Two Coupled Random Fields: Application to Passive Scalar
NASA Technical Reports Server (NTRS)
Dubrulle, B.; He, Guo-Wei; Bushnell, Dennis M. (Technical Monitor)
2000-01-01
We use the relativity postulate of scale invariance to derive the similarity transformations between two coupled scale-invariant random elds at different scales. We nd the equations leading to the scaling exponents. This formulation is applied to the case of passive scalars advected i) by a random Gaussian velocity field; and ii) by a turbulent velocity field. In the Gaussian case, we show that the passive scalar increments follow a log-Levy distribution generalizing Kraichnan's solution and, in an appropriate limit, a log-normal distribution. In the turbulent case, we show that when the velocity increments follow a log-Poisson statistics, the passive scalar increments follow a statistics close to log-Poisson. This result explains the experimental observations of Ruiz et al. about the temperature increments.
Boson stars in a theory of complex scalar field coupled to gravity
NASA Astrophysics Data System (ADS)
Kumar, Sanjeev; Kulshreshtha, Usha; Kulshreshtha, Daya Shankar
2015-07-01
We study boson stars in a theory of complex scalar field coupled to Einstein gravity with the potential: (where and are positive constant parameters). This could be considered either as a theory of massive complex scalar field coupled to gravity in a conical potential or as a theory in the presence of a potential which is an overlap of a parabolic and a conical potential. We study our theory with positive as well as negative values of the cosmological constant . Boson stars are found to come in two types, having either ball-like or shell-like charge density. We have studied the properties of these solutions and have also determined their domains of existence for some specific values of the parameters of the theory. Similar solutions have also been obtained by Hartmann, Kleihaus, Kunz, and Schaffer, in a V-shaped scalar potential.
Turbulent transport of a passive-scalar field by using a renormalization-group method
NASA Technical Reports Server (NTRS)
Hossain, Murshed
1992-01-01
A passive-scalar field is considered to evolve under the influence of a turbulent fluid governed by the Navier-Stokes equation. Turbulent-transport coefficients are calculated by small-scale elimination using a renormalization-group method. Turbulent processes couple both the viscosity and the diffusivity. In the absence of any correlation between the passive-scalar fluctuations and any component of the fluid velocity, the renormalized diffusivity is essentially the same as if the fluid velocity were frozen, although the renormalized equation does contain higher-order nonlinear terms involving viscosity. This arises due to the nonlinear interaction of the velocity with itself. In the presence of a finite correlation, the turbulent diffusivity becomes coupled with both the velocity field and the viscosity. There is then a dependence of the turbulent decay of the passive scalar on the turbulent Prandtl number.
Imaging of Passive Scalar Fields by Filtered Rayleigh Scattering
NASA Astrophysics Data System (ADS)
Kearney, Sean; Grasser, Thomas; Beresh, Steven; Schefer, Robert
2002-11-01
Filtered Rayleigh Scattering (FRS) is a molecular-filter-based, laser-diagnostic approach for multiparameter flowfield imaging that has been gaining popularity over the past 5-10 years [1]. Advantages of FRS for noninvasive gas-phase imaging include: (1) elimination of particle or chemical seeding requirements, (2) increased optical noise rejection allowing imaging close to walls and in "dirty" laboratory environments, (3) imaging of multiple flowfield parameters with a single diagnostic. In this work, the construction and performance of a FRS optical system for passive scalar imaging at Sandia National Laboratories is presented. Data were obtained in an open lab where no special precautions for the elimination of room particulate were made. Results from nonreacting jets and from a premixed flame are shown. Temperature imaging in a nonreacting, steady calibration jet reveals the precision of the time-averaged FRS thermometry results to be ±20 K, or 4of the characteristic temperature difference, while the single-laser-pulse precision is degraded to approximately ±40-50 K. These results are adequate for combustion thermometry purposes. Relative to the jet temperature measurements, species concentration imaging of a buoyant helium jet displays increased signal dynamic range and further improved precision. Reacting flow measurements from the combustion-product region of a methane-air Hencken-type premixed flame are also presented and a comparison of FRS and coherent anti-Stokes Raman scattering (CARS) experiments to calculated adiabatic-equilibrium product temperatures is made which validates the suitability of our FRS instrument for combustion temperature imaging. [1]G.S. Elliott, N. Glumac, and C.D. Carter, Meas. Sci. Tech., 12, 452, 2001.
Late-time evolution of a self-interacting scalar field in the spacetime of a dilaton black hole
Moderski, Rafal; Rogatko, Marek
2001-08-15
We investigate the late-time tails of self-interacting (massive) scalar fields in the spacetime of a dilaton black hole. Following the no hair theorem we examine the mechanism by which self-interacting scalar hair decays. We reveal that the intermediate asymptotic behavior of the considered field perturbations is dominated by an oscillatory inverse power-law decaying tail. The numerical simulations show that at very late time, massive self-interacting scalar hair decays slower than any power law.
NASA Astrophysics Data System (ADS)
Ebner, Dieter W.
1991-11-01
A Lorentz-invariant model of vacuum is given in the form of a 7-dimensional manifold endowed with a statistical metrical tensor. Certain scalar fields on this manifold behave then as spinor fields when viewed from their space-time projection. This paper generalizes previous work fromSO(3)-covariance to Lorentz-covariance.
A hyperboloidal study of tail decay rates for scalar and Yang Mills fields
NASA Astrophysics Data System (ADS)
Zenginoğlu, Anıl
2008-09-01
We investigate the asymptotic behavior of spherically symmetric solutions to scalar wave and Yang Mills equations on a Schwarzschild background. The studies demonstrate the astrophysical relevance of null infinity in predicting radiation signals for gravitational wave detectors and show how test fields on unbounded domains in black hole spacetimes can be simulated conveniently by numerically solving hyperboloidal initial value problems.
Brane structure from a scalar field in general covariant Horava-Lifshitz gravity
NASA Astrophysics Data System (ADS)
Bazeia, D.; Brito, F. A.; Costa, F. G.
2015-02-01
In this paper we have considered the structure of the nonprojectable Horava-Melby-Thompson gravity to find braneworld scenarios. A relativistic scalar field is considered in the matter sector and we have shown how to reduce the equations of motion to first-order differential equations. In particular, we have studied thick brane solutions of both the dilatonic and Randall-Sundrum types.
Cosmological bounces and Lorentzian wormholes in Galileon theories with an extra scalar field
NASA Astrophysics Data System (ADS)
Kolevatov, R.; Mironov, S.
2016-12-01
We study whether it is possible to design a "classical" spatially flat bouncing cosmology or a static, spherically symmetric asymptotically flat Lorentzian wormhole in cubic Galileon theories interacting with an extra scalar field. We show that bouncing models are always plagued with gradient instabilities, while there are always ghosts in wormhole backgrounds.
Langevin simulation of scalar fields: Additive and multiplicative noises and lattice renormalization
NASA Astrophysics Data System (ADS)
Cassol-Seewald, N. C.; Farias, R. L. S.; Fraga, E. S.; Krein, G.; Ramos, Rudnei O.
2012-08-01
We consider the Langevin lattice dynamics for a spontaneously broken λϕ4 scalar field theory where both additive and multiplicative noise terms are incorporated. The lattice renormalization for the corresponding stochastic Ginzburg-Landau-Langevin and the subtleties related to the multiplicative noise are investigated.
AdS collapse of a scalar field in higher dimensions
Jalmuzna, Joanna; Rostworowski, Andrzej; Bizon, Piotr
2011-10-15
We show that the weakly turbulent instability of anti-de Sitter space, recently found in P. Bizon and A. Rostworowski, Phys. Rev. Lett. 107, 031102 (2011) for 3+1-dimensional spherically symmetric Einstein-massless-scalar field equations with negative cosmological constant, is present in all dimensions d+1 for d{>=}3.
Dynamics of a scalar field in a polymer-like representation
NASA Astrophysics Data System (ADS)
Han, Muxin; Ma, Yongge
2006-04-01
In the last 20 years, loop quantum gravity, a background-independent approach to unify general relativity and quantum mechanics, has been widely investigated. We consider the quantum dynamics of a real massless scalar field coupled to gravity in this framework. A Hamiltonian operator for the scalar field can be well defined in the coupled diffeomorphism-invariant Hilbert space, which is both self-adjoint and positive. On the other hand, the Hamiltonian constraint operator for the scalar field coupled to gravity can be well defined in the coupled kinematical Hilbert space. There are one-parameter ambiguities due to scalar field in the construction of both operators. The results heighten our confidence that there is no divergence within this background-independent and diffeomorphism-invariant quantization approach of matter coupled to gravity. Moreover, to avoid possible quantum anomaly, the master constraint programme can be carried out in this coupled system by employing a self-adjoint master constraint operator on the diffeomorphism-invariant Hilbert space.
Functional evolution of scalar fields in bounded one-dimensional regions
NASA Astrophysics Data System (ADS)
Barbero G, J. Fernando; Margalef-Bentabol, Juan; Villaseñor, Eduardo J. S.
2017-03-01
We discuss the unitarity of the quantum evolution between arbitrary Cauchy surfaces of a 1 + 1 dimensional free scalar field defined on a bounded spatial region and subject to several types of boundary conditions including Dirichlet, Neumann and Robin.
Cosmological evolution of a complex scalar field with repulsive or attractive self-interaction
NASA Astrophysics Data System (ADS)
Suárez, Abril; Chavanis, Pierre-Henri
2017-03-01
We study the cosmological evolution of a complex scalar field with a self-interaction potential V (|φ |2) , possibly describing self-gravitating Bose-Einstein condensates, using a fully general relativistic treatment. We generalize the hydrodynamic representation of the Klein-Gordon-Einstein equations in the weak field approximation developed in our previous paper [A. Suárez and P.-H. Chavanis, Phys. Rev. D 92, 023510 (2015), 10.1103/PhysRevD.92.023510]. We establish the general equations governing the evolution of a spatially homogeneous complex scalar field in an expanding background. We show how they can be simplified in the fast oscillation regime (equivalent to the Thomas-Fermi, or semiclassical, approximation) and derive the equation of state of the scalar field in parametric form for an arbitrary potential V (|φ |2) . We explicitly consider the case of a quartic potential with repulsive or attractive self-interaction. For repulsive self-interaction, the scalar field undergoes a stiff matter era followed by a pressureless dark matter era in the weakly self-interacting regime and a stiff matter era followed by a radiationlike era and a pressureless dark matter era in the strongly self-interacting regime. For attractive self-interaction, the scalar field undergoes an inflation era followed by a stiff matter era and a pressureless dark matter era in the weakly self-interacting regime and an inflation era followed by a cosmic stringlike era and a pressureless dark matter era in the strongly self-interacting regime (the inflation era is suggested, not demonstrated). We also find a peculiar branch on which the scalar field emerges suddenly at a nonzero scale factor with a finite energy density. At early times, it behaves as a gas of cosmic strings. At later times, it behaves as dark energy with an almost constant energy density giving rise to a de Sitter evolution. This is due to spintessence. We derive the effective cosmological constant produced by the scalar
Barbero-Immirzi parameter as a scalar field: K-inflation from loop quantum gravity?
NASA Astrophysics Data System (ADS)
Taveras, Victor; Yunes, Nicolás
2008-09-01
We consider a loop-quantum gravity inspired modification of general relativity, where the Holst action is generalized by making the Barbero-Immirzi (BI) parameter a scalar field, whose value could be dynamically determined. The modified theory leads to a nonzero torsion tensor that corrects the field equations through quadratic first derivatives of the BI field. Such a correction is equivalent to general relativity in the presence of a scalar field with nontrivial kinetic energy. This stress energy of this field is automatically covariantly conserved by its own dynamical equations of motion, thus satisfying the strong equivalence principle. Every general relativistic solution remains a solution to the modified theory for any constant value of the BI field. For arbitrary time-varying BI fields, a study of cosmological solutions reduces the scalar-field stress energy to that of a pressureless perfect fluid in a comoving reference frame, forcing the scale-factor dynamics to be equivalent to those of a stiff equation of state. Upon ultraviolet completion, this model could provide a natural mechanism for k inflation, where the role of the inflaton is played by the BI field and inflation is driven by its nontrivial kinetic energy instead of a potential.
Unified dark energy and dark matter from a scalar field different from quintessence
Gao Changjun; Kunz, Martin; Liddle, Andrew R.; Parkinson, David
2010-02-15
We explore unification of dark matter and dark energy in a theory containing a scalar field of non-Lagrangian type, obtained by direct insertion of a kinetic term into the energy-momentum tensor. This scalar is different from quintessence, having an equation of state between -1 and 0 and a zero sound speed in its rest frame. We solve the equations of motion for an exponential potential via a rewriting as an autonomous system, and demonstrate the observational viability of the scenario, for sufficiently small exponential potential parameter {lambda}, by comparison to a compilation of kinematical cosmological data.
Noncommutative Skyrmions in Quantum Hall Systems
NASA Astrophysics Data System (ADS)
Ezawa, Z. F.; Tsitsishvili, G.
Charged excitations in quantum Hall (QH) systems are noncommutative skyrmions. QH systems represent an ideal system equipped with noncommutative geometry. When an electron is confined within the lowest Landau level, its position is described solely by the guiding center, whose X and Y coordinates do not commute with one another. Topological excitations in such a noncommutative plane are noncommutative skyrmions flipping several spins coherently. We construct a microscopic skyrmion state by applying a certain unitary transformation to an electron or hole state. A remarkable property is that a noncommutative skyrmion carries necessarily the electron number proportional to the topological charge. More remarkable is the bilayer QH system with the layer degree of freedom acting as the pseudospin, where the quasiparticle is a topological soliton to be identified with the pseudospin skyrmion. Such a skyrmion is deformed into a bimeron (a pair of merons) by the parallel magnetic field penetrated between the two layers. Each meron carries the electric charge ±e/2.
Sensitivity of Atom Interferometry to Ultralight Scalar Field Dark Matter.
Geraci, Andrew A; Derevianko, Andrei
2016-12-23
We discuss the use of atom interferometry as a tool to search for dark matter (DM) composed of virialized ultralight fields (VULFs). Previous work on VULF DM detection using accelerometers has considered the possibility of equivalence-principle-violating effects whereby gradients in the dark matter field can directly produce relative accelerations between media of differing composition. In atom interferometers, we find that time-varying phase signals induced by coherent oscillations of DM fields can also arise due to changes in the atom rest mass that can occur between light pulses throughout the interferometer sequence as well as changes in Earth's gravitational field. We estimate that several orders of magnitude of unexplored phase space for VULF DM couplings can be probed due to these new effects.
Anomalous scaling of a scalar field advected by turbulence
Kraichnan, R.H.
1995-12-31
Recent work leading to deduction of anomalous scaling exponents for the inertial range of an advected passive field from the equations of motion is reviewed. Implications for other turbulence problems are discussed.
Sensitivity of Atom Interferometry to Ultralight Scalar Field Dark Matter
NASA Astrophysics Data System (ADS)
Geraci, Andrew A.; Derevianko, Andrei
2016-12-01
We discuss the use of atom interferometry as a tool to search for dark matter (DM) composed of virialized ultralight fields (VULFs). Previous work on VULF DM detection using accelerometers has considered the possibility of equivalence-principle-violating effects whereby gradients in the dark matter field can directly produce relative accelerations between media of differing composition. In atom interferometers, we find that time-varying phase signals induced by coherent oscillations of DM fields can also arise due to changes in the atom rest mass that can occur between light pulses throughout the interferometer sequence as well as changes in Earth's gravitational field. We estimate that several orders of magnitude of unexplored phase space for VULF DM couplings can be probed due to these new effects.
Scalar field probes of power-law space-time singularities
NASA Astrophysics Data System (ADS)
Blau, Matthias; Frank, Denis; Weiss, Sebastian
2006-08-01
We analyse the effective potential of the scalar wave equation near generic space-time singularities of power-law type (Szekeres-Iyer metrics) and show that the effective potential exhibits a universal and scale invariant leading inverse square behaviour ~ x-2 in the ``tortoise coordinate'' x provided that the metrics satisfy the strict Dominant Energy Condition (DEC). This result parallels that obtained in [1] for probes consisting of families of massless particles (null geodesic deviation, a.k.a. the Penrose Limit). The detailed properties of the scalar wave operator depend sensitively on the numerical coefficient of the x-2-term, and as one application we show that timelike singularities satisfying the DEC are quantum mechanically singular in the sense of the Horowitz-Marolf (essential self-adjointness) criterion. We also comment on some related issues like the near-singularity behaviour of the scalar fields permitted by the Friedrichs extension.
PDF approach for turbulent scalar field: Some recent developments
NASA Technical Reports Server (NTRS)
Gao, Feng
1993-01-01
The probability density function (PDF) method has been proven a very useful approach in turbulence research. It has been particularly effective in simulating turbulent reacting flows and in studying some detailed statistical properties generated by a turbulent field There are, however, some important questions that have yet to be answered in PDF studies. Our efforts in the past year have been focused on two areas. First, a simple mixing model suitable for Monte Carlo simulations has been developed based on the mapping closure. Secondly, the mechanism of turbulent transport has been analyzed in order to understand the recently observed abnormal PDF's of turbulent temperature fields generated by linear heat sources.
NASA Astrophysics Data System (ADS)
Suroso, Agus; Zen, Freddy P.; Hikmawan, Getbogi
2015-09-01
The energy conditions is a set of linear equations of energy density ρ and pressure p which ensure the the field(s) that we used in our model is physically "reasonable". We study the energy conditions for four dimensional nonminimal derivative coupling of scalar field and curvature tensor. Considering the scalar field as a perfect fluid, we find some constraint for the coupling constant ξ in order the energy conditions is satisfied or violated. We find that strong energy conditions (SEC) is violated if -1/9H2 ≤ ξ < 1/18H2. For de Sitter solution a ∝ eH0t for some constant H0, we find that while null, weak, and dominant energy conditions violated when ξ <-[12 H02(2 +9 H02) ] -1 . The accelerating universe is exist for the power law solution (a ∝ tp for constant p) if ξ < 0.
Quantized scalar field as DM: the axion's case
Barranco, J.; Bernal, A.
2008-12-04
We derive a rough estimation of the radius and the mass of a self-gravitating system made of axions. The system is a stationary solution of the Einstein-Klein-Gordon equations with a source term given by the vacuum expectation value of the energy-momentum operator constructed from the axion field. We found that such system would have masses of the order of asteroids ({approx}10{sup -10} M{sub {center_dot}}) and radius of the order of few centimeters. Some implications of such type of objects are discussed.
VOFI - A library to initialize the volume fraction scalar field
NASA Astrophysics Data System (ADS)
Bnà, S.; Manservisi, S.; Scardovelli, R.; Yecko, P.; Zaleski, S.
2016-03-01
The VOFI library has been developed to accurately calculate the volume fraction field demarcated by implicitly-defined fluid interfaces in Cartesian grids with cubic cells. The method enlists a number of algorithms to compute the integration limits and the local height function, that is the integrand of a double Gauss-Legendre integration with a variable number of nodes. Tests in two and three dimensions are presented to demonstrate the accuracy of the method and are provided in the software distribution with C/C++ and FORTRAN interfaces.
Scalings of scalar structure functions in a velocity field with coherent vortical structures
NASA Astrophysics Data System (ADS)
Khan, M. A.; Vassilicos, J. C.
2002-01-01
In planar turbulence modeled as an isotropic and homogeneous collection of two-dimensional noninteracting compact vortices, the structure functions Sp(r) of a statistically stationary passive scalar field have the following scaling behavior in the limit where the Péclet number Pe-->∞: Sp(r)~const+ln(r/L Pe-1/3) for L Pe-1/3<
Vacuum energy density and pressure of a massive scalar field
NASA Astrophysics Data System (ADS)
Mera, Fernando Daniel; Fulling, S. A.
2015-06-01
With a view toward application of the Pauli-Villars regularization method to the Casimir energy of boundaries, we calculate the expectation values of the components of the stress tensor of a confined massive field in 1+1 space-time dimensions. Previous papers by Hays and Fulling are bridged and generalized. The Green function for the time-independent Schrödinger equation is constructed from the Green function for the whole line by the method of images; equivalently, the one-dimensional system is solved exactly in terms of closed classical paths and periodic orbits. Terms in the energy density and in the eigenvalue density attributable to the two boundaries individually and those attributable to the confinement of the field to a finite interval are distinguished so that their physical origins are clear. Then the pressure is found similarly from the cylinder kernel, the Green function associated most directly with an exponential frequency cutoff of the Fourier mode expansion. Finally, we discuss how the theory could be rendered finite by the Pauli-Villars method.
Does there exist a sensible quantum theory of an ``algebra-valued'' scalar field\\?
NASA Astrophysics Data System (ADS)
Anco, Stephen C.; Wald, Robert M.
1989-04-01
Consider a scalar field φ in Minkowski spacetime, but let φ be valued in an associative, commutative algebra openA rather than openR. One may view the resulting theory as describing a collection of coupled real scalar fields. At the classical level, theories of this type are completely well behaved and have a global symmetry group which is a nontrivial enlargement of the Poincaré group. (They are analogs of the new class of gauge theories for massless spin-2 fields found recently by one of us, whose gauge group is a nontrivial enlargement of the usual diffeomorphism group.) We investigate the quantization of such scalar field theories here by studying the case of a λφ4 field, with φ valued in the two-dimensional algebra generated by an identity element e and a nilpotent element v satisfying v2=0. The Coleman-Mandula theorem, which states that the symmetry group of a nontrivial quantum field theory cannot be a nontrivial enlargement of the Poincaré group, is evaded here because the finite ``extra'' symmetries of the classical theory fail to be implemented in the quantum theory by unitary operators and the infinitesimal symmetries (which can be represented in the quantum theory by quadratic forms) connect the one-particle Hilbert space to multiparticle states. Nevertheless, we find that the conventional Feynman rules for this theory lead to vacuum decay at the tree level and fail to yield a well-defined S matrix. Some alternative approaches are investigated, but these also appear to fail. Thus, although the classical theory is perfectly well behaved, it seems that there does not exist a sensible quantum theory of an algebra-valued scalar field.
Mapping a Massless Scalar Field Theory on a Yang-Mills Theory:. Classical Case
NASA Astrophysics Data System (ADS)
Frasca, Marco
We analyze a recent proposal to map a massless scalar field theory onto a Yang-Mills theory at classical level. It is seen that this mapping exists at a perturbative level when the expansion is a gradient expansion. In this limit the theories share the spectrum, at the leading order, that is the one of a harmonic oscillator. Gradient expansion is exploited maintaining Lorentz covariance by introducing a fifth coordinate and turning the theory to Euclidean space. These expansions give common solutions to scalar and Yang-Mills field equations that are so proved to exist by construction, confirming that the selected components of the Yang-Mills field are indeed an extremum of the corresponding action functional.
Higgs couplings in noncommutative Standard Model
NASA Astrophysics Data System (ADS)
Batebi, S.; Haghighat, M.; Tizchang, S.; Akafzade, H.
2015-06-01
We consider the Higgs and Yukawa parts of the Noncommutative Standard Model (NCSM). We explore the NC-action to give all Feynman rules for couplings of the Higgs boson to electroweak gauge fields and fermions.
Localization and mass spectra of various matter fields on scalar-tensor brane
Xie, Qun-Ying; Zhao, Zhen-Hua; Zhong, Yi; Yang, Jie; Zhou, Xiang-Nan
2015-03-10
Recently, a new scalar-tensor braneworld model was presented in [http://dx.doi.org/10.1103/PhysRevD.86.127502]. It not only solves the gauge hierarchy problem but also reproduces a correct Friedmann-like equation on the brane. In this new model, there are two different brane solutions, for which the mass spectra of gravity on the brane are the same. In this paper, we investigate localization and mass spectra of various bulk matter fields (i.e., scalar, vector, Kalb-Ramond, and fermion fields) on the brane. It is shown that the zero modes of all the matter fields can be localized on the positive tension brane under some conditions, and the mass spectra of each kind of bulk matter field for the two brane solutions are different except for some special cases, which implies that the two brane solutions are not physically equivalent. When the coupling constants between the dilaton and bulk matter fields take special values, the mass spectra for both solutions are the same, and the scalar and vector zero modes are localized on the negative tension brane, while the KR zero mode is still localized on the positive tension brane.
NASA Astrophysics Data System (ADS)
Morales, Manuel D.; Sarbach, Olivier
2017-02-01
Motivated by the goal for high accuracy modeling of gravitational radiation emitted by isolated systems, recently, there has been renewed interest in the numerical solution of the hyperboloidal initial value problem for Einstein's field equations in which the outer boundary of the numerical grid is placed at null infinity. In this article, we numerically implement the tetrad-based approach presented by Bardeen, Sarbach, and Buchman [Phys. Rev. D 83, 104045 (2011), 10.1103/PhysRevD.83.104045] for a spherically symmetric, minimally coupled, self-gravitating scalar field. When this field is massless, the evolution system reduces to a regular, first-order symmetric hyperbolic system of equations for the conformally rescaled scalar field which is coupled to a set of singular elliptic constraints for the metric coefficients. We show how to solve this system based on a numerical finite-difference approximation, obtaining stable numerical evolutions for initial black hole configurations which are surrounded by a spherical shell of scalar field, part of which disperses to infinity and part of which is accreted by the black hole. As a nontrivial test, we study the tail decay of the scalar field along different curves, including one along the marginally trapped tube, one describing the world line of a timelike observer at a finite radius outside the horizon, and one corresponding to a generator of null infinity. Our results are in perfect agreement with the usual power-law decay discussed in previous work. This article also contains a detailed analysis for the asymptotic behavior and regularity of the lapse, conformal factor, extrinsic curvature and the Misner-Sharp mass function along constant mean curvature slices.
Scalar field self-force effects on a particle orbiting a Reissner-Nordström black hole
NASA Astrophysics Data System (ADS)
Bini, Donato; Carvalho, Gabriel G.; Geralico, Andrea
2016-12-01
Scalar field self-force effects on a scalar charge orbiting a Reissner-Nordström black hole are investigated. The scalar wave equation is solved analytically in a post-Newtonian framework, and the solution is used to compute the self-field (up to 7.5 post-Newtonian order) as well as the components of the self-force at the particle's location. The energy fluxes radiated to infinity and down the hole are also evaluated. Comparison with previous numerical results in the Schwarzschild case shows a reasonable agreement in both strong field and weak field regimes.
The most general second-order field equations of bi-scalar-tensor theory in four dimensions
NASA Astrophysics Data System (ADS)
Ohashi, Seiju; Tanahashi, Norihiro; Kobayashi, Tsutomu; Yamaguchi, Masahide
2015-07-01
The Horndeski theory is known as the most general scalar-tensor theory with second-order field equations. In this paper, we explore the bi-scalar extension of the Horndeski theory. Following Horndeski's approach, we determine all the possible terms appearing in the second-order field equations of the bi-scalar-tensor theory. We compare the field equations with those of the generalized multi-Galileons, and confirm that our theory contains new terms that are not included in the latter theory. We also discuss the construction of the Lagrangian leading to our most general field equations.
Evolution of a self-interacting scalar field in the spacetime of a higher dimensional black hole
Moderski, Rafal; Rogatko, Marek
2005-08-15
In the spacetime of n-dimensional static charged black hole we examine the mechanism by which the self-interacting scalar hair decay. It is turned out that the intermediate asymptotic behavior of the self-interacting scalar field is determined by an oscillatory inverse power law. We confirm our results by numerical calculations.
Scalar field measurements of a laminar starting plume cap using digital processing of interferograms
NASA Astrophysics Data System (ADS)
Chay, Avraham; Shlien, D. J.
1986-08-01
The scalar field (heat or species concentration) of a small-source laminar starting plume was measured at a single dimensionless buoyancy injection rate for two values of the ratio of momentum diffusivity to scalar diffusivity, Pr=7 and 300. Digital image processing was used to extract concentration contours from the interferograms, which considerably reduced the data reduction time and permitted an improved resolution. The effect of Pr was clearly visible in the scalar contours, especially in terms of the entrained fluid that is found to be undiluted far inside the cap of the higher Pr. The scalar contours were not self-similar when a single length scale was used, but the data collapsed well using a two-length scale normalization. The convective velocity of the cap was also measured for the two cases, suggesting a possible logarithmic effect of Pr. An analysis confirms the speculation. It was also found that about 37% of the total injection rate into the starting plume is convected into the cap. This work is the first experimental investigation demonstrating the effect of change in Pr on the motion of small buoyancy-source laminar gravitational convection phenomena.
Efficient visualization of unsteady and huge scalar and vector fields
NASA Astrophysics Data System (ADS)
Vetter, Michael; Olbrich, Stephan
2016-04-01
and methods, we are developing a stand-alone post-processor, adding further data structures and mapping algorithms, and cooperating with the ICON developers and users. With the implementation of a DSVR-based post-processor, a milestone was achieved. By using the DSVR post-processor the mentioned 3 processes are completely separated: the data set is processed in a batch mode - e.g. on the same supercomputer, which the data is generated on - and the interactive 3D rendering is done afterwards on the scientist's local system. At the actual status of implementation the DSVR post-processor supports the generation of isosurfaces and colored slicers on volume data set time series based on rectilinear grids as well as the visualization of pathlines on time varying flow fields based on either rectilinear grids or prism grids. The software implementation and evaluation is done on the supercomputers at DKRZ, including scalability tests using ICON output files in NetCDF format. The next milestones will be (a) the in-situ integration of the DSVR library in the ICON model and (b) the implementation of an isosurface algorithm for prism grids.
NASA Astrophysics Data System (ADS)
Mackrory, Jonathan B.; Bhattacharya, Tanmoy; Steck, Daniel A.
2016-10-01
We present a worldline method for the calculation of Casimir energies for scalar fields coupled to magnetodielectric media. The scalar model we consider may be applied in arbitrary geometries, and it corresponds exactly to one polarization of the electromagnetic field in planar layered media. Starting from the field theory for electromagnetism, we work with the two decoupled polarizations in planar media and develop worldline path integrals, which represent the two polarizations separately, for computing both Casimir and Casimir-Polder potentials. We then show analytically that the path integrals for the transverse-electric polarization coupled to a dielectric medium converge to the proper solutions in certain special cases, including the Casimir-Polder potential of an atom near a planar interface, and the Casimir energy due to two planar interfaces. We also evaluate the path integrals numerically via Monte Carlo path-averaging for these cases, studying the convergence and performance of the resulting computational techniques. While these scalar methods are only exact in particular geometries, they may serve as an approximation for Casimir energies for the vector electromagnetic field in other geometries.
Metric-affine formalism of higher derivative scalar fields in cosmology
Li, Mingzhe; Wang, Xiulian E-mail: wangxiulian2000@yahoo.com.cn
2012-07-01
Higher derivative scalar field theories have received considerable attention for the potentially explanations of the initial state of the universe or the current cosmic acceleration which they might offer. They have also attracted many interests in the phenomenological studies of infrared modifications of gravity. These theories are mostly studied by the metric variational approach in which only the metric is the fundamental field to account for the gravitation. In this paper we study the higher derivative scalar fields with the metric-affine formalism where the affine connection is treated arbitrarily at the beginning. Because the higher derivative scalar fields couple to the connection directly in a covariant theory these two formalisms will lead to different results. These differences are suppressed by the powers of the Planck mass and are usually expected to have small effects. But in some cases they may cause non-negligible deviations. We show by a higher derivative dark energy model that the two formalisms lead to significantly different pictures of the future universe.
k-Inflation in noncommutative space-time
NASA Astrophysics Data System (ADS)
Feng, Chao-Jun; Li, Xin-Zhou; Liu, Dao-Jun
2015-02-01
The power spectra of the scalar and tensor perturbations in the noncommutative k-inflation model are calculated in this paper. In this model, all the modes created when the stringy space-time uncertainty relation is satisfied, and they are generated inside the sound/Hubble horizon during inflation for the scalar/tensor perturbations. It turns out that a linear term describing the noncommutative space-time effect contributes to the power spectra of the scalar and tensor perturbations. Confronting the general noncommutative k-inflation model with latest results from Planck and BICEP2, and taking and as free parameters, we find that it is well consistent with observations. However, for the two specific models, i.e. the tachyon and DBI inflation models, it is found that the DBI model is not favored, while the tachyon model lies inside the contour, when the e-folding number is assumed to be around.
Accreting Scalar-Field Models of Dark Energy Onto Morris-Thorne Wormhole
NASA Astrophysics Data System (ADS)
Chattopadhyay, Surajit; Pasqua, Antonio; Radinschi, Irina
2016-10-01
The present paper reports a study on accreting tachyon, Dirac-Born-Infeld essence and h-essence scalar field models of dark energy onto Morris-Thorne wormhole. Using three different parameterisation schemes and taking H = {H_0} + {{{H_1}} over t}, we have derived the mass of the wormhole for all of the three parameterisation schemes that are able to get hold of both quintessence and phantom behaviour. With suitable choice of parameters, we observed that accreting scalar field dark energy models are increasing the mass of the wormhole in the phantom phase and the mass is decreasing in the quintessence phase. Finally, we have considered accretion with power law form of scale factor and without any parameterisation scheme for the equation of state parameter and observed the fact that phantom-type dark energy supports the existence of wormholes.
Stability of black holes in Einstein-charged scalar field theory in a cavity
NASA Astrophysics Data System (ADS)
Dolan, Sam R.; Ponglertsakul, Supakchai; Winstanley, Elizabeth
2015-12-01
Can a black hole that suffers a superradiant instability evolve towards a "hairy" configuration which is stable? We address this question in the context of Einstein-charged scalar field theory. First, we describe a family of static black hole solutions which possess charged scalar-field hair confined within a mirror-like boundary. Next, we derive a set of equations which govern the linear, spherically symmetric perturbations of these hairy solutions. We present numerical evidence which suggests that, unlike the vacuum solutions, the (single-node) hairy solutions are stable under linear perturbations. Thus, it is plausible that stable hairy black holes represent the end point of the superradiant instability of electrically charged Reissner-Nordström black holes in a cavity; we outline ways to explore this hypothesis.
Static black hole solutions with a self-interacting conformally coupled scalar field
Dotti, Gustavo; Gleiser, Reinaldo J.; Martinez, Cristian
2008-05-15
We study static, spherically symmetric black hole solutions of the Einstein equations with a positive cosmological constant and a conformally coupled self-interacting scalar field. Exact solutions for this model found by Martinez, Troncoso, and Zanelli were subsequently shown to be unstable under linear gravitational perturbations, with modes that diverge arbitrarily fast. We find that the moduli space of static, spherically symmetric solutions that have a regular horizon--and satisfy the weak and dominant energy conditions outside the horizon--is a singular subset of a two-dimensional space parametrized by the horizon radius and the value of the scalar field at the horizon. The singularity of this space of solutions provides an explanation for the instability of the Martinez, Troncoso, and Zanelli spacetimes and leads to the conclusion that, if we include stability as a criterion, there are no physically acceptable black hole solutions for this system that contain a cosmological horizon in the exterior of its event horizon.
Future evolution in a backreaction model and the analogous scalar field cosmology
NASA Astrophysics Data System (ADS)
Ali, Amna; Majumdar, A. S.
2017-01-01
We investigate the future evolution of the universe using the Buchert framework for averaged backreaction in the context of a two-domain partition of the universe. We show that this approach allows for the possibility of the global acceleration vanishing at a finite future time, provided that none of the subdomains accelerate individually. The model at large scales is analogously described in terms of a homogeneous scalar field emerging with a potential that is fixed and free from phenomenological parametrization. The dynamics of this scalar field is explored in the analogous FLRW cosmology. We use observational data from Type Ia Supernovae, Baryon Acoustic Oscillations, and Cosmic Microwave Background to constrain the parameters of the model for a viable cosmology, providing the corresponding likelihood contours.
A scalar field condensation instability of rotating Anti-de Sitter black holes
NASA Astrophysics Data System (ADS)
Dias, Óscar J. C.; Monteiro, Ricardo; Reall, Harvey S.; Santos, Jorge E.
2010-11-01
Near-extreme Reissner-Nordström-anti-de Sitter black holes are unstable against the condensation of an uncharged scalar field with mass close to the Breitenlöhner-Freedman bound. It is shown that a similar instability afflicts near-extreme large rotating AdS black holes, and near-extreme hyperbolic Schwarzschild-AdS black holes. The resulting nonlinear hairy black hole solutions are determined numerically. Some stability results for (possibly charged) scalar fields in black hole backgrounds are proved. For most of the extreme black holes we consider, these demonstrate stability if the “effective mass” respects the near-horizon BF bound. Small spherical Reissner-Nordström-AdS black holes are an interesting exception to this result.
Generalized second law of thermodynamics for non-canonical scalar field model with corrected-entropy
NASA Astrophysics Data System (ADS)
Das, Sudipta; Debnath, Ujjal; Mamon, Abdulla Al
2015-10-01
In this work, we have considered a non-canonical scalar field dark energy model in the framework of flat FRW background. It has also been assumed that the dark matter sector interacts with the non-canonical dark energy sector through some interaction term. Using the solutions for this interacting non-canonical scalar field dark energy model, we have investigated the validity of generalized second law (GSL) of thermodynamics in various scenarios using first law and area law of thermodynamics. For this purpose, we have assumed two types of horizons viz apparent horizon and event horizon for the universe and using first law of thermodynamics, we have examined the validity of GSL on both apparent and event horizons. Next, we have considered two types of entropy-corrections on apparent and event horizons. Using the modified area law, we have examined the validity of GSL of thermodynamics on apparent and event horizons under some restrictions of model parameters.
Scalar field as a Bose-Einstein condensate in a Schwarzschild-de Sitter spacetime
NASA Astrophysics Data System (ADS)
Castellanos, Elías; Escamilla-Rivera, Celia; Lämmerzahl, Claus; Macías, Alfredo
In this paper, we analyze some properties of a scalar field configuration, where it is considered as a trapped Bose-Einstein condensate in a Schwarzschild-de Sitter background spacetime. In a natural way, the geometry of the curved spacetime provides an effective trapping potential for the scalar field configuration. This allows us to explore some thermodynamical properties of the system. Additionally, the curved geometry of the spacetime also induces a position-dependent self-interaction parameter, which can be interpreted as a kind of gravitational Feshbach resonance, that could affect the stability of the cloud and could be used to obtain information about the interactions among the components of the system.
Self-interacting scalar field cosmologies: unified exact solutions and symmetries
Charters, T.
2010-08-01
We investigate a mechanism that generates exact solutions of scalar field cosmologies in a unified way. The procedure investigated here permits to recover almost all known solutions, and allows one to derive new solutions as well. In particular, we derive and discuss one novel solution defined in terms of the Lambert function. The solutions are organised in a classification which depends on the choice of a generating function which we have denoted by x(φ) that reflects the underlying thermodynamics of the model. We also analyse and discuss the existence of form-invariance dualities between solutions. A general way of defining the latter in an appropriate fashion for scalar fields is put forward.
Search for Chameleon Scalar Fields with the Axion Dark Matter Experiment
Rybka, G.; Hotz, M.; Rosenberg, L. J; Asztalos, S. J.; Carosi, G.; Hagmann, C.; Kinion, D.; van Bibber, K.; Hoskins, J.; Martin, C.; Sikivie, P.; Tanner, D. B.; Bradley, R.; Clarke, J.
2010-07-30
Scalar fields with a 'chameleon' property, in which the effective particle mass is a function of its local environment, are common to many theories beyond the standard model and could be responsible for dark energy. If these fields couple weakly to the photon, they could be detectable through the afterglow effect of photon-chameleon-photon transitions. The ADMX experiment was used in the first chameleon search with a microwave cavity to set a new limit on scalar chameleon-photon coupling {beta}{sub {gamma}}excluding values between 2x10{sup 9} and 5x10{sup 14} for effective chameleon masses between 1.9510 and 1.9525 {mu}eV.
Evolution of a massless test scalar field on boson star space-times
Lora-Clavijo, F. D.; Cruz-Osorio, A.; Guzman, F. S.
2010-07-15
We numerically solve the massless test scalar field equation on the space-time background of boson stars and black holes. In order to do so, we use a numerical domain that contains future null infinity. We achieve this construction using a scri-fixing conformal compactification technique based on hyperboloidal constant mean curvature foliations of the space-time and solve the conformally invariant wave equation. We present two results: the scalar field shows oscillations of the quasinormal mode type found for black holes only for boson star configurations that are compact; and no signs of tail decay are found in the parameter space we explored. Even though our results do not correspond to the master equation of perturbations of boson star solutions, they indicate that the parameter space of boson stars as black hole mimickers is restricted to compact configurations.
Initial data for gravity coupled to scalar, electromagnetic, and Yang-Mills fields
NASA Astrophysics Data System (ADS)
Husain, Viqar
1999-02-01
We give Ansätze for solving classically the initial value constraints of general relativity minimally coupled to a scalar field, electromagnetism, or Yang-Mills theory. The results include both time-symmetric and asymmetric data. The time-asymmetric examples are used to test Penrose's cosmic censorship inequality. We find that the inequality can be violated if only the weak energy condition holds.
Complex q-ANALYSIS and Scalar Field Theory on a q-LATTICE
NASA Astrophysics Data System (ADS)
Ubriaco, Marcelo R.
We develop the basic formalism of complex q-analysis to study the solutions of second order q-difference equations which reduce, in the q → 1 limit, to the ordinary Laplace equation in Euclidean and Minkowski space. After defining an inner product on the function space we construct and study the properties of the solutions, and then apply this formalism to the Schrödinger equation and two-dimensional scalar field theory.
False vacuum bubble nucleation due to a nonminimally coupled scalar field
Lee, Wonwoo; Park, Chanyong; Lee, Bum-Hoon; Lee, Chul H.
2006-12-15
We study the possibility of forming the false vacuum bubble nucleated within the true vacuum background via the true-to-false vacuum phase transition in curved spacetime. We consider a semiclassical Euclidean bubble in the Einstein theory of gravity with a nonminimally coupled scalar field. In this paper we present the numerical computations as well as the approximate analytical computations. We mention the evolution of the false vacuum bubble after nucleation.
Comment on “A study of phantom scalar field cosmology using Lie and Noether symmetries”
NASA Astrophysics Data System (ADS)
Paliathanasis, Andronikos; Basilakos, Spyros; Tsamparlis, Michael
We show that the recent results of [S. Dutta and S. Chakraborty, Int. J. Mod. Phys. D 25 (2016) 1650051] on the application of Lie/Noether symmetries in scalar field cosmology are well-known in the literature while the problem could have been solved easily under a coordinate transformation. That follows from the property, that the admitted group of invariant transformations of dynamical system is independent on the coordinate system.
Graceful exit from inflation for minimally coupled Bianchi A scalar field models
NASA Astrophysics Data System (ADS)
Beyer, F.; Escobar, L.
2013-10-01
We consider the dynamics of Bianchi A scalar field models which undergo inflation. The main question is under which conditions does inflation come to an end and is succeeded by a decelerated epoch. This so-called ‘graceful exit’ from inflation is an important ingredient in the standard model of cosmology, but is, at this stage, only understood for restricted classes of solutions. We present new results obtained by a combination of analytical and numerical techniques.
Real Scalar Field Scattering Around the Extreme Reissner-Nordström Black Hole in de Sitter Spacetime
NASA Astrophysics Data System (ADS)
Guo, Guanghai; Yan, Pengfei; Wang, Suojie
2015-02-01
The real scalar field scattering of the extreme Reissner-Nordström black hole in de Sitter spacetime is investigated numerically via the polynomial approximation. It is found that the scalar field behaves like harmonic waves under the tortoise coordinate, while piles up near the outer event horizon and the cosmological horizon. The abnormity in previous work is eliminated by appropriate application of the boundary conditions in numerical calculations. Substituting the continuous effective potential with a stair potential of n steps, we evaluate the transmission and reflection coefficients of the scalar field in high and low energy regimes, where an asymptotical formula is derived.
NASA Astrophysics Data System (ADS)
Saha, Pameli; Debnath, Ujjal
2016-11-01
In this work, we study a new kind of dark energy (DE), which is named as “Yang—Mills condensate” (YMC). We study the stability and wde — w'de analysis of YMC DE model. Then we correspond it with quintessence, k-essence, tachyon, phantom, dilaton, DBI-essence and hessence scalar field models of DE in FRW spacetime to reconstruct potentials as well as the dynamics for these scalar fields for describing the acceleration of the universe. We also analyze the models in graphically to interpret the nature of the scalar fields and corresponding potentials.
Static, spherically symmetric solutions with a scalar field in Rastall gravity
NASA Astrophysics Data System (ADS)
Bronnikov, K. A.; Fabris, J. C.; Piattella, O. F.; Santos, E. C.
2016-12-01
Rastall's theory belongs to the class of non-conservative theories of gravity. In vacuum, the only non-trivial static, spherically symmetric solution is the Schwarzschild one, except for a very special case. When a canonical scalar field is coupled to the gravity sector in this theory, new exact solutions appear for some values of the Rastall parameter a. Some of these solutions describe the same space-time geometry as the recently found solutions in the k-essence theory with a power function for the kinetic term of the scalar field. There is a large class of solutions (in particular, those describing wormholes and regular black holes) whose geometry coincides with that of solutions of GR coupled to scalar fields with nontrivial self-interaction potentials; the form of these potentials, however, depends on the Rastall parameter a. We also note that all solutions of GR with a zero trace of the energy-momentum tensor, including black-hole and wormhole ones, may be re-interpreted as solutions of Rastall's theory.
Detailed balance condition and ultraviolet stability of scalar field in Horava-Lifshitz gravity
NASA Astrophysics Data System (ADS)
Borzou, Ahmad; Lin, Kai; Wang, Anzhong
2011-05-01
Detailed balance and projectability conditions are two main assumptions when Horava recently formulated his theory of quantum gravity - the Horava-Lifshitz (HL) theory. While the latter represents an important ingredient, the former often believed needs to be abandoned, in order to obtain an ultraviolet stable scalar field, among other things. In this paper, because of several attractive features of this condition, we revisit it, and show that the scalar field can be stabilized, if the detailed balance condition is allowed to be softly broken. Although this is done explicitly in the non-relativistic general covariant setup of Horava-Melby-Thompson with an arbitrary coupling constant λ, generalized lately by da Silva, it is also true in other versions of the HL theory. With the detailed balance condition softly breaking, the number of independent coupling constants can be still significantly reduced. It is remarkable to note that, unlike other setups, in this da Silva generalization, there exists a master equation for the linear perturbations of the scalar field in the flat Friedmann-Robertson-Walker background.
Computationally efficient scalar nonparaxial modeling of optical wave propagation in the far-field.
Nguyen, Giang-Nam; Heggarty, Kevin; Gérard, Philippe; Serio, Bruno; Meyrueis, Patrick
2014-04-01
We present a scalar model to overcome the computation time and sampling interval limitations of the traditional Rayleigh-Sommerfeld (RS) formula and angular spectrum method in computing wide-angle diffraction in the far-field. Numerical and experimental results show that our proposed method based on an accurate nonparaxial diffraction step onto a hemisphere and a projection onto a plane accurately predicts the observed nonparaxial far-field diffraction pattern, while its calculation time is much lower than the more rigorous RS integral. The results enable a fast and efficient way to compute far-field nonparaxial diffraction when the conventional Fraunhofer pattern fails to predict correctly.
Gravity-Driven Acceleration and Kinetic Inflation in Noncommutative Brans-Dicke Setting
NASA Astrophysics Data System (ADS)
Rasouli, S. M. M.; Vargas Moniz, Paulo
By assuming the spatially flat FLRW line-element and employing the Hamiltonian formalism, a noncommutative (NC) setting of the Brans-Dicke (BD) theory is introduced. We investigate gravity-driven acceleration and kinetic inflation in this NC BD cosmology. Despite to the commutative case, in which both the scale factor and BD scalar field are obtained in power-law forms (in terms of the cosmic time), in our herein NC model, we see that the power-law scalar factor is multiplied by a dynamical exponential warp factor. This warp factor depends on not only the noncommutative parameter but also the momentum conjugate associated to the BD scalar field. For very small values of this parameter, we obtain an appropriate inflationary solution, which can overcome problems within standard BD cosmology in a more efficient manner. Moreover, we see that a graceful exit from an early acceleration epoch towards a decelerating radiation epoch is provided. For late times, due to the presence of the NC parameter, we obtain a zero acceleration epoch, which can be interpreted as the coarse-grained explanation.
Mota, David F.; Shaw, Douglas J.
2007-03-15
We show that, as a result of nonlinear self-interactions, it is feasible, at least in light of the bounds coming from terrestrial tests of gravity, measurements of the Casimir force and those constraints imposed by the physics of compact objects, big-bang nucleosynthesis and measurements of the cosmic microwave background, for there to exist, in our Universe, one or more scalar fields that couple to matter much more strongly than gravity does. These scalar fields behave like chameleons: changing their properties to fit their surroundings. As a result these scalar fields can be not only very strongly coupled to matter, but also remain relatively light over solar-system scales. These fields could also be detected by a number of future experiments provided they are properly designed to do so. These results open up an altogether new window, which might lead to a completely different view of the role played by light scalar fields in particle physics and cosmology.
Strong gravitational lensing in a noncommutative black-hole spacetime
Ding Chikun; Kang Shuai; Chen Changyong; Chen Songbai; Jing Jiliang
2011-04-15
Noncommutative geometry may be a starting point to a quantum gravity. We study the influence of the spacetime noncommutative parameter on the strong field gravitational lensing in the noncommutative Schwarzschild black-hole spacetime and obtain the angular position and magnification of the relativistic images. Supposing that the gravitational field of the supermassive central object of the galaxy can be described by this metric, we estimate the numerical values of the coefficients and observables for strong gravitational lensing. In comparison to the Reissner-Norstroem black hole, we find that the influences of the spacetime noncommutative parameter is similar to those of the charge, but these influences are much smaller. This may offer a way to distinguish a noncommutative black hole from a Reissner-Norstroem black hole, and may permit us to probe the spacetime noncommutative constant {theta} by the astronomical instruments in the future.
Classical electrodynamics in a space with spin noncommutativity of coordinates
NASA Astrophysics Data System (ADS)
Vasyuta, V. M.; Tkachuk, V. M.
2016-10-01
We propose a relativistic Lorentz-invariant spin-noncommutative algebra. Using the Weyl ordering of noncommutative position operators, we find a mapping from a space of commutative functions into space of noncommutative functions. The Lagrange function of an electromagnetic field in the space with spin noncommutativity is constructed. In such a space electromagnetic field becomes non-abelian. A gauge transformation law of this field is also obtained. Exact nonlinear field equations of noncommutative electromagnetic field are derived from the least action principle. Within the perturbative approach we consider field of a point charge in a constant magnetic field and interaction of two plane waves. An exact solution of a plane wave propagation in a constant magnetic and electric fields is found.
Statistical analysis of the velocity and scalar fields in reacting turbulent wall-jets
NASA Astrophysics Data System (ADS)
Pouransari, Z.; Biferale, L.; Johansson, A. V.
2015-02-01
The concept of local isotropy in a chemically reacting turbulent wall-jet flow is addressed using direct numerical simulation (DNS) data. Different DNS databases with isothermal and exothermic reactions are examined. The chemical reaction and heat release effects on the turbulent velocity, passive scalar, and reactive species fields are studied using their probability density functions (PDFs) and higher order moments for velocities and scalar fields, as well as their gradients. With the aid of the anisotropy invariant maps for the Reynolds stress tensor, the heat release effects on the anisotropy level at different wall-normal locations are evaluated and found to be most accentuated in the near-wall region. It is observed that the small-scale anisotropies are persistent both in the near-wall region and inside the jet flame. Two exothermic cases with different Damköhler numbers are examined and the comparison revealed that the Damköhler number effects are most dominant in the near-wall region, where the wall cooling effects are influential. In addition, with the aid of PDFs conditioned on the mixture fraction, the significance of the reactive scalar characteristics in the reaction zone is illustrated. We argue that the combined effects of strong intermittency and strong persistency of anisotropy at the small scales in the entire domain can affect mixing and ultimately the combustion characteristics of the reacting flow.
Backreaction for Einstein-Rosen waves coupled to a massless scalar field
NASA Astrophysics Data System (ADS)
Szybka, Sebastian J.; Wyrebowski, Michał J.
2016-07-01
We present a one-parameter family of exact solutions to Einstein's equations that may be used to study the nature of the Green-Wald backreaction framework. Our explicit example is a family of Einstein-Rosen waves coupled to a massless scalar field. This solution may be reinterpreted as a generalized three-torus polarized Gowdy cosmology with scalar and gravitational waves. We use it to illustrate essential properties of the Green-Wald approach. Among other things we show that within our model the Green-Wald framework uniquely determines backreaction for finite-size inhomogeneities on a predefined background. The results agree with those calculated in the Charach-Malin approach. In the vacuum limit, the Green-Wald, the Charach-Malin and the Isaacson methods imply identical backreaction, as expected.
Noncommutative Gauge Theory with Covariant Star Product
Zet, G.
2010-08-04
We present a noncommutative gauge theory with covariant star product on a space-time with torsion. In order to obtain the covariant star product one imposes some restrictions on the connection of the space-time. Then, a noncommutative gauge theory is developed applying this product to the case of differential forms. Some comments on the advantages of using a space-time with torsion to describe the gravitational field are also given.
Does there exist a sensible quantum theory of an ''algebra-valued'' scalar field
Anco, S.C.; Wald, R.M.
1989-04-15
Consider a scalar field phi in Minkowski spacetime, but let phi be valued in an associative, commutative algebra openA rather than openR. One may view the resulting theory as describing a collection of coupled real scalar fields. At the classical level, theories of this type are completely well behaved and have a global symmetry group which is a nontrivial enlargement of the Poincare group. (They are analogs of the new class of gauge theories for massless spin-2 fields found recently by one of us, whose gauge group is a nontrivial enlargement of the usual diffeomorphism group.) We investigate the quantization of such scalar field theories here by studying the case of a lambdaphi/sup 4/ field, with phi valued in the two-dimensional algebra generated by an identity element e and a nilpotent element v satisfying v/sup 2/ = 0. The Coleman-Mandula theorem, which states that the symmetry group of a nontrivial quantum field theory cannot be a nontrivial enlargement of the Poincare group, is evaded here because the finite ''extra'' symmetries of the classical theory fail to be implemented in the quantum theory by unitary operators and the infinitesimal symmetries (which can be represented in the quantum theory by quadratic forms) connect the one-particle Hilbert space to multiparticle states. Nevertheless, we find that the conventional Feynman rules for this theory lead to vacuum decay at the tree level and fail to yield a well-defined S matrix. Some alternative approaches are investigated, but these also appear to fail.
The Model for Final Stage of Gravitational Collapse Massless Scalar Field
NASA Astrophysics Data System (ADS)
Gladush, V. D.; Mironin, D. V.
It is known that in General relativity, for some spherically symmetric initial conditions, the massless scalar field (SF) experience the gravitational collapse (Choptuik, 1989), and arise a black hole (BH). According Bekenstein, a BH has no "hair scalar", so the SF is completely under the horizon. Thus, the study of the final stage for the gravitational collapse of a SF is reduced to the construction of a solution of Einstein's equations describing the evolution of a SF inside the BH. In this work, we build the Lagrangian for scalar and gravitationalfields in the spherically symmetric case, when the metric coefficients and SF depends only on the time. In this case, it is convenient to use the methods of classical mechanics. Since the metric allows an arbitrary transformation of time, then the corresponding field variable (g00) is included in the Lagrangian without time derivative. It is a non-dynamic variable, and is included in the Lagrangian as a Lagrange multiplier. A variation of the action on this variable gives the constraint. It turns out that Hamiltonian is proportional to the constraint, and so it is zero. The corresponding Hamilton-Jacobi equation easily integrated. Hence, we find the relation between the SF and the metric. To restore of time dependence we using an equation dL / dq' = dS / dq After using a gauge condition, it allows us to find solution. Thus, we find the evolution of the SF inside the BH, which describes the final stage of the gravitational collapse of a SF. It turns out that the mass BH associated with a scalar charge G of the corresponding SF inside the BH ratio M = G/(2√ κ).
Uniqueness of the Fock quantization of scalar fields in spatially flat cosmological spacetimes
Gomar, Laura Castelló; Cortez, Jerónimo; Blas, Daniel Martín-de; Marugán, Guillermo A. Mena; Velhinho, José M. E-mail: jacq@ciencias.unam.mx E-mail: jvelhi@ubi.pt
2012-11-01
We study the Fock quantization of scalar fields in (generically) time dependent scenarios, focusing on the case in which the field propagation occurs in –either a background or effective– spacetime with spatial sections of flat compact topology. The discussion finds important applications in cosmology, like e.g. in the description of test Klein-Gordon fields and scalar perturbations in Friedmann-Robertson-Walker spacetime in the observationally favored flat case. Two types of ambiguities in the quantization are analyzed. First, the infinite ambiguity existing in the choice of a Fock representation for the canonical commutation relations, understandable as the freedom in the choice of inequivalent vacua for a given field. Besides, in cosmological situations, it is customary to scale the fields by time dependent functions, which absorb part of the evolution arising from the spacetime, which is treated classically. This leads to an additional ambiguity, this time in the choice of a canonical pair of field variables. We show that both types of ambiguities are removed by the requirements of (a) invariance of the vacuum under the symmetries of the three-torus, and (b) unitary implementation of the dynamics in the quantum theory. In this way, one arrives at a unique class of unitarily equivalent Fock quantizations for the system. This result provides considerable robustness to the quantum predictions and renders meaningful the confrontation with observation.
Development of Techniques for Visualization of Scalar and Vector Fields in the Immersive Environment
NASA Technical Reports Server (NTRS)
Bidasaria, Hari B.; Wilson, John W.; Nealy, John E.
2005-01-01
Visualization of scalar and vector fields in the immersive environment (CAVE - Cave Automated Virtual Environment) is important for its application to radiation shielding research at NASA Langley Research Center. A complete methodology and the underlying software for this purpose have been developed. The developed software has been put to use for the visualization of the earth s magnetic field, and in particular for the study of the South Atlantic Anomaly. The methodology has also been put to use for the visualization of geomagnetically trapped protons and electrons within Earth's magnetosphere.
Classical and quantum Big Brake cosmology for scalar field and tachyonic models
NASA Astrophysics Data System (ADS)
Kamenshchik, A. Yu.; Manti, S.
2013-02-01
We study a relation between the cosmological singularities in classical and quantum theory, comparing the classical and quantum dynamics in some models possessing the Big Brake singularity - the model based on a scalar field and two models based on a tachyon-pseudo-tachyon field . It is shown that the effect of quantum avoidance is absent for the soft singularities of the Big Brake type while it is present for the Big Bang and Big Crunch singularities. Thus, there is some kind of a classical - quantum correspondence, because soft singularities are traversable in classical cosmology, while the strong Big Bang and Big Crunch singularities are not traversable.
Classical and quantum big brake cosmology for scalar field and tachyonic models
NASA Astrophysics Data System (ADS)
Kamenshchik, Alexander Y.; Manti, Serena
2012-06-01
We study a relation between the cosmological singularities in classical and quantum theory, comparing the classical and quantum dynamics in some models possessing the big brake singularity—the model based on a scalar field and two models based on a tachyon-pseudo-tachyon field. It is shown that the effect of quantum avoidance is absent for the soft singularities of the big brake type while it is present for the big bang and big crunch singularities. Thus, there is some kind of a classical-quantum correspondence, because soft singularities are traversable in classical cosmology, while the strong big bang and big crunch singularities are not traversable.
Classical and Quantum Big Brake Cosmology for Scalar Field and Tachyonic Models
NASA Astrophysics Data System (ADS)
Kamenshchik, Alexander; Manti, Serena
2015-01-01
We study a relation between the cosmological singularities in classical and quantum theory, comparing the classical and quantum dynamics in some models possessing the Big Brake singularity - the model based on a scalar field and two models based on a tachyon-pseudo-tachyon field. It is shown that the effect of quantum avoidance is absent for the soft singularities of the Big Brake type while it is present for the Big Bang and Big Crunch singularities. Thus, there is some kind of a classical - quantum correspondence, because soft singularities are traversable in classical cosmology, while the strong Big Bang and Big Crunch singularities are not traversable.
Addendum to "Absorption of a massive scalar field by a charged black hole"
NASA Astrophysics Data System (ADS)
Benone, Carolina L.; de Oliveira, Ednilton S.; Dolan, Sam R.; Crispino, Luís C. B.
2017-02-01
In [1] we studied the absorption cross section of a scalar field of mass m impinging on a static black hole of mass M and charge Q . We presented numerical results using the partial-wave method, and analytical results in the high- and low-frequency limit. Our low-frequency approximation was only valid if the (dimensionless) field velocity v exceeds vc=2 π M m . In this addendum we give the complementary result for v ≲vc, and we consider the possible physical relevance of this regime.
Dimensional reduction of the Standard Model coupled to a new singlet scalar field
NASA Astrophysics Data System (ADS)
Brauner, Tomáš; Tenkanen, Tuomas V. I.; Tranberg, Anders; Vuorinen, Aleksi; Weir, David J.
2017-03-01
We derive an effective dimensionally reduced theory for the Standard Model augmented by a real singlet scalar. We treat the singlet as a superheavy field and integrate it out, leaving an effective theory involving only the Higgs and SU(2) L × U(1) Y gauge fields, identical to the one studied previously for the Standard Model. This opens up the possibility of efficiently computing the order and strength of the electroweak phase transition, numerically and nonperturbatively, in this extension of the Standard Model. Understanding the phase diagram is crucial for models of electroweak baryogenesis and for studying the production of gravitational waves at thermal phase transitions.
Classical and quantum Big Brake cosmology for scalar field and tachyonic models
Kamenshchik, A. Yu.; Manti, S.
2013-02-21
We study a relation between the cosmological singularities in classical and quantum theory, comparing the classical and quantum dynamics in some models possessing the Big Brake singularity - the model based on a scalar field and two models based on a tachyon-pseudo-tachyon field . It is shown that the effect of quantum avoidance is absent for the soft singularities of the Big Brake type while it is present for the Big Bang and Big Crunch singularities. Thus, there is some kind of a classical - quantum correspondence, because soft singularities are traversable in classical cosmology, while the strong Big Bang and Big Crunch singularities are not traversable.
Casimir force for a scalar field in a single brane world
Linares, R.; Morales-Tecotl, H. A.; Pedraza, O.
2010-02-10
Vacuum force is an interesting low energy test for brane worlds due to its dependence on field's modes and its role in submillimeter gravity experiments. In this contribution we obtain the scalar field vacuum force between two parallel plates lying in the brane of a Randall-Sundrum scenario extended by p compact dimensions (RSII-{sub p}). We obtain the force using the Green's function technique and we compare our results with the ones obtained by using the zeta function regularization method. As a result we obtain agreement in the expression for the force independently of the method used, thus we solve a previous discrepancy between the two approaches.
Boson stars in a theory of complex scalar fields coupled to the U(1) gauge field and gravity
NASA Astrophysics Data System (ADS)
Kumar, Sanjeev; Kulshreshtha, Usha; Shankar Kulshreshtha, Daya
2014-08-01
We study boson shells and boson stars in a theory of a complex scalar field coupled to the U(1) gauge field {{A}_{\\mu }} and Einstein gravity with the potential V(|\\Phi |)\\;:=\\frac{1}{2}{{m}^{2}}{{\\left( |\\Phi |+a \\right)}^{2}}. This could be considered either as a theory of a massive complex scalar field coupled to an electromagnetic field and gravity in a conical potential, or as a theory in the presence of a potential that is an overlap of a parabolic and conical potential. Our theory has a positive cosmological constant (\\Lambda :=4\\pi G{{m}^{2}}{{a}^{2}}). Boson stars are found to come in two types, having either ball-like or shell-like charge density. We studied the properties of these solutions and also determined their domains of existence for some specific values of the parameters of the theory. Similar solutions have also been obtained by Kleihaus, Kunz, Laemmerzahl and List, in a V-shaped scalar potential.
NASA Astrophysics Data System (ADS)
Beckwith, Andrew
2005-04-01
We have shown that a scalar field can be used, employing Scherrer's k essence cosmological sound calculation, to model how we evolve from a dark matter-dark energy mix to a cosmological constant. Here, we are exploring what initiates the decay of the near perfect thin wall approximation on that scalar field to circumstances permitting a k essence speed-of-sound argument in favor of traditional models of Einstein's cosmological constant as a driving force for inflationary expansion.
NASA Astrophysics Data System (ADS)
Zhdanov, V.; Stashko, O.
2016-12-01
We study exact special solutions of the joint system of Einstein equations and scalar field equations with a non-zero self-interaction potential, which describe spherically symmetric static configurations. The space-time is asymptotically flat with a naked singularity at the center. The testbody motion is analyzed; we found conditions for existence of non-connected regions of stable circular orbits. We show the existence of static trajectories of particles that hang above the configuration.
Relativistic Two and Three-Particle Bound States in Scalar Quantum Field Theory.
NASA Astrophysics Data System (ADS)
di Leo, Leo
This thesis is concerned with the application of the variational method, within the Hamiltonian formalism of quantum field theory (QFT), to describe relativistic two and three particle states in scalar field theories. Two models are considered: scalar particles interacting through the exchange of scalar quanta, and the Higgs sector of the Minimal Standard Model. We derive relativistic particle-antiparticle wave equations for scalar particles, phi and |phi, interacting via a massive or massless scalar field, chi (the Wick-Cutkosky model), using simple Fock space ansatze. The variational method, within the Hamiltonian formalism of QFT, is used to derive equations with and without coupling of this quasi-bound phi|phi system to the chichi decay channel. The equations are then approximately decoupled to yield a relativistic momentum-space (Schrodinger-like) wave equation from which we determine bound-state energies numerically, perturbatively or variationally for various strengths of the coupling. Bound-state energies in the massless case are compared to the known ladder Bethe-Salpeter and light-cone solutions of this model. In the case of coupling to the decay channel, which is easily accomplished in the present formalism by expanding our Fock-space ansatz, the quasi-bound phi|phi states are seen to arise as resonances in the chichi scattering cross section. Numerical results are presented for the massive and massless chi case for various coupling strengths. The same variational method can be easily extended to derive relativistic three-particle wave equations for scalar particles phi,phi and |phi, interacting via a massive or massless scalar field, chi. In this case, the equations are obtained using a simple |phiphi|phi > +| phiphi|{phi}chi > ansatz. Approximate variational solutions (using product-type hydrogenic wave functions) of these equations are presented for various strengths of the coupling. The magnitude of the relativistic effects in the three
Fold-change detection and scalar symmetry of sensory input fields
Goentoro, Lea; Hart, Yuval; Mayo, Avi; Sontag, Eduardo; Alon, Uri
2010-01-01
Recent studies suggest that certain cellular sensory systems display fold-change detection (FCD): a response whose entire shape, including amplitude and duration, depends only on fold changes in input and not on absolute levels. Thus, a step change in input from, for example, level 1 to 2 gives precisely the same dynamical output as a step from level 2 to 4, because the steps have the same fold change. We ask what the benefit of FCD is and show that FCD is necessary and sufficient for sensory search to be independent of multiplying the input field by a scalar. Thus, the FCD search pattern depends only on the spatial profile of the input and not on its amplitude. Such scalar symmetry occurs in a wide range of sensory inputs, such as source strength multiplying diffusing/convecting chemical fields sensed in chemotaxis, ambient light multiplying the contrast field in vision, and protein concentrations multiplying the output in cellular signaling systems. Furthermore, we show that FCD entails two features found across sensory systems, exact adaptation and Weber's law, but that these two features are not sufficient for FCD. Finally, we present a wide class of mechanisms that have FCD, including certain nonlinear feedback and feed-forward loops. We find that bacterial chemotaxis displays feedback within the present class and hence, is expected to show FCD. This can explain experiments in which chemotaxis searches are insensitive to attractant source levels. This study, thus, suggests a connection between properties of biological sensory systems and scalar symmetry stemming from physical properties of their input fields. PMID:20729472
Stability of Gauss-Bonnet black holes in anti-de Sitter space-time against scalar field condensation
Brihaye, Yves; Hartmann, Betti
2011-10-15
We study the stability of static, hyperbolic Gauss-Bonnet black holes in (4+1)-dimensional anti-de Sitter (AdS) space-time against the formation of scalar hair. Close to extremality the black holes possess a near-horizon topology of AdS{sub 2}xH{sup 3} such that within a certain range of the scalar field mass one would expect that they become unstable to the condensation of an uncharged scalar field. We confirm this numerically and observe that there exists a family of hairy black hole solutions labeled by the number of nodes of the scalar field function. We construct explicit examples of solutions with a scalar field that possesses zero nodes, one node, and two nodes, respectively, and show that the solutions with nodes persist in the limit of Einstein gravity, i.e. for vanishing Gauss-Bonnet coupling. We observe that the interval of the mass for which scalar field condensation appears decreases with increasing Gauss-Bonnet coupling and/or with increasing node number.
Quantum mechanics with coordinate dependent noncommutativity
NASA Astrophysics Data System (ADS)
Kupriyanov, V. G.
2013-11-01
Noncommutative quantum mechanics can be considered as a first step in the construction of quantum field theory on noncommutative spaces of generic form, when the commutator between coordinates is a function of these coordinates. In this paper we discuss the mathematical framework of such a theory. The noncommutativity is treated as an external antisymmetric field satisfying the Jacobi identity. First, we propose a symplectic realization of a given Poisson manifold and construct the Darboux coordinates on the obtained symplectic manifold. Then we define the star product on a Poisson manifold and obtain the expression for the trace functional. The above ingredients are used to formulate a nonrelativistic quantum mechanics on noncommutative spaces of general form. All considered constructions are obtained as a formal series in the parameter of noncommutativity. In particular, the complete algebra of commutation relations between coordinates and conjugated momenta is a deformation of the standard Heisenberg algebra. As examples we consider a free particle and an isotropic harmonic oscillator on the rotational invariant noncommutative space.
Uniqueness of the Fock quantization of scalar fields in a Bianchi I cosmology with unitary dynamics
NASA Astrophysics Data System (ADS)
Cortez, Jerónimo; Navascués, Beatriz Elizaga; Martín-Benito, Mercedes; Mena Marugán, Guillermo A.; Olmedo, Javier; Velhinho, José M.
2016-11-01
The Fock quantization of free scalar fields is subject to an infinite ambiguity when it comes to choosing a set of annihilation and creation operators, a choice that is equivalent to the determination of a vacuum state. In highly symmetric situations, this ambiguity can be removed by asking vacuum invariance under the symmetries of the system. Similarly, in stationary backgrounds, one can demand time-translation invariance plus positivity of the energy. However, in more general situations, additional criteria are needed. For the case of free (test) fields minimally coupled to a homogeneous and isotropic cosmology, it has been proven that the ambiguity is resolved by introducing the criterion of unitary implementability of the quantum dynamics, as an endomorphism in Fock space. This condition determines a specific separation of the time dependence of the field, so that this splits into a very precise background dependence and a genuine quantum evolution. Furthermore, together with the condition of vacuum invariance under the spatial Killing symmetries, unitarity of the dynamics selects a unique Fock representation for the canonical commutation relations, up to unitary equivalence. In this work, we generalize these results to anisotropic spacetimes with shear, which are therefore not conformally symmetric, by considering the case of a free scalar field in a Bianchi I cosmology.
Noncommutative Valuation of Options
NASA Astrophysics Data System (ADS)
Herscovich, Estanislao
2016-12-01
The aim of this note is to show that the classical results in finance theory for pricing of derivatives, given by making use of the replication principle, can be extended to the noncommutative world. We believe that this could be of interest in quantum probability. The main result called the First fundamental theorem of asset pricing, states that a noncommutative stock market admits no-arbitrage if and only if it admits a noncommutative equivalent martingale probability.
Noncommutative geometry of Zitterbewegung
NASA Astrophysics Data System (ADS)
Eckstein, Michał; Franco, Nicolas; Miller, Tomasz
2017-03-01
Drawing from the advanced mathematics of noncommutative geometry, we model a "classical" Dirac fermion propagating in a curved spacetime. We demonstrate that the inherent causal structure of the model encodes the possibility of Zitterbewegung—the "trembling motion" of the fermion. We recover the well-known frequency of Zitterbewegung as the highest possible speed of change in the fermion's "internal space." Furthermore, we show that the bound does not change in the presence of an external electromagnetic field and derive its explicit analogue when the mass parameter is promoted to a Yukawa field. We explain the universal character of the model and discuss a table-top experiment in the domain of quantum simulation to test its predictions.
Strong Planck constraints on braneworld and non-commutative inflation
Calcagni, Gianluca; Kuroyanagi, Sachiko; Ohashi, Junko; Tsujikawa, Shinji E-mail: skuro@rs.tus.ac.jp E-mail: shinji@rs.kagu.tus.ac.jp
2014-03-01
We place observational likelihood constraints on braneworld and non-commutative inflation for a number of inflaton potentials, using Planck, WMAP polarization and BAO data. Both braneworld and non-commutative scenarios of the kind considered here are limited by the most recent data even more severely than standard general-relativity models. At more than 95 % confidence level, the monomial potential V(φ)∝φ{sup p} is ruled out for p ≥ 2 in the Randall-Sundrum (RS) braneworld cosmology and, for p > 0, also in the high-curvature limit of the Gauss-Bonnet (GB) braneworld and in the infrared limit of non-commutative inflation, due to a large scalar spectral index. Some parameter values for natural inflation, small-varying inflaton models and Starobinsky inflation are allowed in all scenarios, although some tuning is required for natural inflation in a non-commutative spacetime.
On the topology of the level sets of a scalar field
Pascucci, V
2000-12-12
This paper introduces a new simple algorithm for the construction of the Contour Tree of a 3D scalar field augmented with the Betti numbers of each contour component. The algorithm has {Omicron}(n log n) time complexity and {Omicron}(n) auxiliary storage. where n is the number of vertices in the domain of the field. The algorithm can be applied to fields of any dimension in which case it computes the Contour Tree augmented, with the Euler characteristic of each contour. The complexity in any dimension remains {Omicron}(n logn). This is the same complexity as in [4] but with correct computation of the tree for fields with bounded domains.
Garcia Aspeitia, Miguel A.; Matos, Tonatiuh; Rodriguez, Pablo A.; Magana, Juan Aldebaran
2010-07-12
In this work we explore the primordial perturbations by the slow-roll inflation produced by the simplest chaotic inflation model driven by a scalar field with potential V{sub {Phi}}= (1/2)m{sub {Phi}}{sup 2{Phi}2} in a hidden brane and it is analyzed through a dynamical system to explore the consecuences in the evolution of the visible brane (our Universe). We use the most accepted constraints of the five dimensional Planck mass endorsed by the current experimental data in our universe (visible brane) to fit the initial conditions of {Phi} and {Phi} of the inflation in the hidden brane.
Real scalar field scattering in the nearly extremal Schwarzschild—de Sitter space
NASA Astrophysics Data System (ADS)
Guo, Guang-Hai
2010-11-01
Reasonable approximations are introduced to investigate the real scalar field scattering in the nearly extremal Schwarzschild—de Sitter (SdS) space. The approximations naturally lead to the invertible x(r) and the global replacement of the true potential by a Pöshl—Teller one. Meanwhile, the Schrödinger-like wave equation is transformed into a solvable form. Our numerical solutions to the wave equation show that the wave is characteristically similar to the harmonic under the tortoise coordinate x, while the wave piles up near the two horizons and the wavelength tends to its maximum as the potential approaches to the peak under the radial coordinate r.
Confinement Driven by Scalar Field in 4d Non Abelian Gauge Theories
Chabab, Mohamed
2007-01-12
We review some of the most recent work on confinement in 4d gauge theories with a massive scalar field (dilaton). Emphasis is put on the derivation of confining analytical solutions to the Coulomb problem versus dilaton effective couplings to gauge terms. It is shown that these effective theories can be relevant to model quark confinement and may shed some light on confinement mechanism. Moreover, the study of interquark potential, derived from Dick Model, in the heavy meson sector proves that phenomenological investigation of tmechanism is more than justified and deserves more efforts.
Bramble, J.H.; Pasciak, J.E.
1981-01-01
The linearized scalar potential formulation of the magnetostatic field problem is considered. The approach involves a reformulation of the continuous problem as a parametric boundary problem. By the introduction of a spherical interface and the use of spherical harmonics, the infinite boundary condition can also be satisfied in the parametric framework. The reformulated problem is discretized by finite element techniques and a discrete parametric problem is solved by conjugate gradient iteration. This approach decouples the problem in that only standard Neumann type elliptic finite element systems on separate bounded domains need be solved. The boundary conditions at infinity and the interface conditions are satisfied during the boundary parametric iteration.
Ultrahard fluid and scalar field in the Kerr-Newman metric
Babichev, E.; Chernov, S.; Dokuchaev, V.; Eroshenko, Yu.
2008-11-15
An analytic solution for the accretion of ultrahard perfect fluid onto a moving Kerr-Newman black hole is found. This solution is a generalization of the previously known solution by Petrich, Shapiro, and Teukolsky for a Kerr black hole. We show that the found solution is applicable for the case of a nonextreme black hole, however it cannot describe the accretion onto an extreme black hole due to violation of the test fluid approximation. We also present a stationary solution for a massless scalar field in the metric of a Kerr-Newman naked singularity.
Monte carlo simulation of a nucleon interacting with a neutral scalar boson field
NASA Astrophysics Data System (ADS)
Szybisz, L.; Zabolitzky, J. G.
1985-04-01
A recently proposed Monte Carlo algorithm to solve a Schrödinger equation expressed in Fock-space representation, suitable for the case of hamiltonians describing problems in one-dimensional discrete momentum space, is now extended to the one-, two- and three-dimensional continuous k-spaces. This extension is tested by employing it for an analytically solvable hamiltonian. For this purpose the 'static source' limit of the hamiltonian corresponding to the interaction between a nucleon and a neutral, scalar boson field is simulated. The results of the Monte Carlo procedure reproduce very well the exact solution.
Hees, A; Guéna, J; Abgrall, M; Bize, S; Wolf, P
2016-08-05
We use 6 yrs of accurate hyperfine frequency comparison data of the dual rubidium and caesium cold atom fountain FO2 at LNE-SYRTE to search for a massive scalar dark matter candidate. Such a scalar field can induce harmonic variations of the fine structure constant, of the mass of fermions, and of the quantum chromodynamic mass scale, which will directly impact the rubidium/caesium hyperfine transition frequency ratio. We find no signal consistent with a scalar dark matter candidate but provide improved constraints on the coupling of the putative scalar field to standard matter. Our limits are complementary to previous results that were only sensitive to the fine structure constant and improve them by more than an order of magnitude when only a coupling to electromagnetism is assumed.
NASA Astrophysics Data System (ADS)
Hees, A.; Guéna, J.; Abgrall, M.; Bize, S.; Wolf, P.
2016-08-01
We use 6 yrs of accurate hyperfine frequency comparison data of the dual rubidium and caesium cold atom fountain FO2 at LNE-SYRTE to search for a massive scalar dark matter candidate. Such a scalar field can induce harmonic variations of the fine structure constant, of the mass of fermions, and of the quantum chromodynamic mass scale, which will directly impact the rubidium/caesium hyperfine transition frequency ratio. We find no signal consistent with a scalar dark matter candidate but provide improved constraints on the coupling of the putative scalar field to standard matter. Our limits are complementary to previous results that were only sensitive to the fine structure constant and improve them by more than an order of magnitude when only a coupling to electromagnetism is assumed.
Second quantized scalar QED in homogeneous time-dependent electromagnetic fields
Kim, Sang Pyo
2014-12-15
We formulate the second quantization of a charged scalar field in homogeneous, time-dependent electromagnetic fields, in which the Hamiltonian is an infinite system of decoupled, time-dependent oscillators for electric fields, but it is another infinite system of coupled, time-dependent oscillators for magnetic fields. We then employ the quantum invariant method to find various quantum states for the charged field. For time-dependent electric fields, a pair of quantum invariant operators for each oscillator with the given momentum plays the role of the time-dependent annihilation and the creation operators, constructs the exact quantum states, and gives the vacuum persistence amplitude as well as the pair-production rate. We also find the quantum invariants for the coupled oscillators for the charged field in time-dependent magnetic fields and advance a perturbation method when the magnetic fields change adiabatically. Finally, the quantum state and the pair production are discussed when a time-dependent electric field is present in parallel to the magnetic field.
A preferred ground state for the scalar field in de Sitter space
NASA Astrophysics Data System (ADS)
Aslanbeigi, S.; Buck, M.
2013-08-01
We investigate a recent proposal for a distinguished vacuum state of a free scalar quantum field in an arbitrarily curved spacetime, known as the Sorkin-Johnston (SJ) vacuum, by applying it to de Sitter space. We derive the associated two-point functions on both the global and Poincaré (cosmological) patches in general d + 1 dimensions. In all cases where it is defined, the SJ vacuum belongs to the family of de Sitter invariant α-vacua. We obtain different states depending on the spacetime dimension, mass of the scalar field, and whether the state is evaluated on the global or Poincaré patch. We find that the SJ vacuum agrees with the Euclidean/Bunch-Davies state for heavy ("principal series") fields on the global patch in even spacetime dimensions. We also compute the SJ vacuum on a causal set corresponding to a causal diamond in 1 + 1 dimensional de Sitter space. Our simulations show that the mean of the SJ two-point function on the causal set agrees well with its expected continuum counterpart.
Fold-change detection and scalar symmetry of sensory input fields
NASA Astrophysics Data System (ADS)
Shoval, Oren; Goentoro, Lea; Hart, Yuval; Mayo, Avi; Sontag, Eduardo; Alon, Uri
2012-02-01
Recent studies suggest that certain cellular sensory systems display fold-change detection (FCD): a response whose entire shape, including amplitude and duration, depends only on fold-changes in input, and not on absolute changes. We show that FCD is necessary and sufficient for sensory search to depend only on the spatial profile of the input, and not on its amplitude. Such amplitude scalar symmetry occurs in a wide range of sensory inputs, such as source strength multiplying diffusing chemical fields sensed in chemotaxis, ambient light multiplying the contrast field in vision, and protein concentrations multiplying the output in cellular signaling systems. We present a wide class of mechanisms that have FCD, including certain nonlinear feedback and feedforward loops. In addition, we find that bacterial chemotaxis displays feedback within the present class, and has indeed recently been shown to exhibit FCD. This can explain experiments in which chemotaxis searches are insensitive to attractant source levels. This study thus suggests a connection between properties of biological sensory systems and scalar symmetry stemming from physical properties of their input fields.
A kinetic theory of diffusion in general relativity with cosmological scalar field
Calogero, Simone
2011-11-01
A new model to describe the dynamics of particles undergoing diffusion in general relativity is proposed. The evolution of the particle system is described by a Fokker-Planck equation without friction on the tangent bundle of spacetime. It is shown that the energy-momentum tensor for this matter model is not divergence-free, which makes it inconsistent to couple the Fokker-Planck equation to the Einstein equations. This problem can be solved by postulating the existence of additional matter fields in spacetime or by modifying the Einstein equations. The case of a cosmological scalar field term added to the left hand side of the Einstein equations is studied in some details. For the simplest cosmological model, namely the flat Robertson-Walker spacetime, it is shown that, depending on the initial value of the cosmological scalar field, which can be identified with the present observed value of the cosmological constant, either unlimited expansion or the formation of a singularity in finite time will occur in the future. Future collapse into a singularity also takes place for a suitable small but positive present value of the cosmological constant, in contrast to the standard diffusion-free scenario.
Scalar field localization on 3-branes placed at a warped resolved conifold
Silva, J. E. G.; Almeida, C. A. S.
2011-10-15
We have studied the localization of a scalar field on a 3-brane embedded in a six-dimensional warped bulk of the form M{sub 4}xC{sub 2}, where M{sub 4} is a 3-brane and C{sub 2} is a 2-cycle of a six-dimensional resolved conifold C{sub 6} over a T{sup 1,1} space. Since the resolved conifold is singularity-free in r=0 depending on a resolution parameter a, we have analyzed the behavior of the localization of a scalar field when we vary the resolution parameter. On one hand, this enables us to study the effects that a singularity has on the field. On the other hand we can use the resolution parameter as a fine-tuning between the bulk Planck mass and 3-brane Planck mass and so it opens a new perspective to extend the hierarchy problem. Using a linear and a nonlinear warp factor, we have found that the massive and massless modes are trapped to the brane even in the singular cone (a{ne}0). We have also compared the results obtained in this geometry and those obtained in other six-dimensional models, such as stringlike geometry and cigarlike universe geometry.
NASA Astrophysics Data System (ADS)
Goncharov, Yu. P.
This survey is devoted to possible manifestations of remarkable topological duality between real scalar and spinor fields (TDSS) existing on a great number of manifolds important in physical applications. The given manifestations are demonstrated to occur within the framework of miscellaneous branches in ordinary and supersymmetric quantum field theories, supergravity, Kaluza-Klein type theories, cosmology, strings, membranes and p-branes. All this allows one to draw the condusion that the above duality will seem to be an essential ingredient in many questions of present and future investigations.
Reheating signature in the gravitational wave spectrum from self-ordering scalar fields
Kuroyanagi, Sachiko; Hiramatsu, Takashi; Yokoyama, Jun'ichi E-mail: hiramatz@yukawa.kyoto-u.ac.jp
2016-02-01
We investigate the imprint of reheating on the gravitational wave spectrum produced by self-ordering of multi-component scalar fields after a global phase transition. The equation of state of the Universe during reheating, which usually has different behaviour from that of a radiation-dominated Universe, affects the evolution of gravitational waves through the Hubble expansion term in the equations of motion. This gives rise to a different power-law behavior of frequency in the gravitational wave spectrum. The reheating history is therefore imprinted in the shape of the spectrum. We perform 512{sup 3} lattice simulations to investigate how the ordering scalar field reacts to the change of the Hubble expansion and how the reheating effect arises in the spectrum. We also compare the result with inflation-produced gravitational waves, which has a similar spectral shape, and discuss whether it is possible to distinguish the origin between inflation and global phase transition by detecting the shape with future direct detection gravitational wave experiments such as DECIGO.
Massless scalar fields at null and spatial infinity in the Schwarzschild space-time
Habisohn, C.X.
1989-05-01
It is known that massless scalar, Maxwell, and linearized metric fields (in an appropriate gauge) having data of compact support will evolve to be asymptotically flat on any asymptotically flat background space-time. However, little is known about the evolution of data that is reasonably well behaved but has nontrivial falloff at spatial infinity. Is the set of such data that evolves to be asymptotically flat at null infinity in a curved asymptotically flat space-time of the same size as, and does it consist of elements with falloff rates similar to the set of such data in Minkowski space-time. Stewart and Schmidt analyzed massless scalar fields on both the Minkowski and Schwarzschild space-times. Their calculations indicated that the set of Schwarzschild data in question was much smaller than the Minkowski set. In this paper, this problem is reexamined and it is determined, contrary to the indications of Stewart and Schmidt, that the Schwarzschild set is of the same size, and its elements have falloff rates similar to the corresponding Minkowski set. This result supports the ability of the definition of asymptotic flatness to admit a large class of space-times.
New agegraphic dark energy model in Brans-Dicke theory with logarithmic form of scalar field
NASA Astrophysics Data System (ADS)
Kumar, Pankaj; Singh, C. P.
2017-03-01
In this paper, the cosmological evolution of new agegraphic dark energy (NADE) model is analyzed in Brans-Dicke theory within the framework of Friedmann-Robertson-Walker Universe. The power-law assumption on Brans-Dicke scalar field is reconsidered by assuming the logarithmic form. We derive the equation of state parameter wD and deceleration parameter q of NADE model. It is observed that wD→ -1 when a→ ∞, i.e., the NADE mimics cosmological constant in the late time evolution. Indeed, due to the assumption of logarithmic form of Brans-Dicke scalar field the NADE in Brans-Dicke theory behaves like NADE in general relativity in the late time evolution. The NADE model shows a phase transition from matter dominated phase in early time to accelerated phase in late time. We further extend NADE model by including the interaction between dark matter and NADE. In this case, wD definitely crosses the phantom divide line (wD=-1) in the late time evolution. The phase transition from matter dominated to NADE dominated phase may be achieved at early stage in interacting model. Further, we show that the interacting NADE model resolves the cosmic coincidence problem as the energy density ratio may evolve sufficiently slow at present.
Effect of a chameleon scalar field on the cosmic microwave background
Davis, Anne-Christine; Schelpe, Camilla A. O.; Shaw, Douglas J.
2009-09-15
We show that a direct coupling between a chameleonlike scalar field and photons can give rise to a modified Sunyaev-Zel'dovich (SZ) effect in the cosmic microwave background (CMB). The coupling induces a mixing between chameleon particles and the CMB photons when they pass through the magnetic field of a galaxy cluster. Both the intensity and the polarization of the radiation are modified. The degree of modification depends strongly on the properties of the galaxy cluster such as magnetic field strength and electron number density. Existing SZ measurements of the Coma cluster enable us to place constraints on the photon-chameleon coupling. The constrained conversion probability in the cluster is P{sub Coma}(204 GHz)<6.2x10{sup -5} at 95% confidence, corresponding to an upper bound on the coupling strength of g{sub eff}{sup (cell)}<2.2x10{sup -8} GeV{sup -1} or g{sub eff}{sup (Kolmo)}<(7.2-32.5)x10{sup -10} GeV{sup -1}, depending on the model that is assumed for the cluster magnetic field structure. We predict the radial profile of the chameleonic CMB intensity decrement. We find that the chameleon effect extends farther toward the edges of the cluster than the thermal SZ effect. Thus we might see a discrepancy between the x-ray emission data and the observed SZ intensity decrement. We further predict the expected change to the CMB polarization arising from the existence of a chameleonlike scalar field. These predictions could be verified or constrained by future CMB experiments.
NASA Astrophysics Data System (ADS)
Bernardini, Alex Eduardo; Bertolami, Orfeu
An equivalence between Born-Infeld and effective real scalar field theories for brane structures is built in some specific warped space-time scenarios. Once the equations of motion for tachyon fields related to the Born-Infeld action are written as first-order equations, a simple analytical connection with a particular class of real scalar field superpotentials can be found. This equivalence leads to the conclusion that, for a certain class of superpotentials, both systems can support identical thick brane solutions as well as brane structures described through localized energy densities, T_{00}(y), in the 5(th) dimension, y. Our results indicate that thick brane solutions realized by the Born-Infeld cosmology can be connected to real scalar field brane scenarios which can be used to effectively map the tachyon condensation mechanism, which is relevant in several dark sector scenarios.
NASA Astrophysics Data System (ADS)
Bernardini, A. E.; Bertolami, O.
2013-10-01
An equivalence between Born-Infeld and effective real scalar field theories for brane structures is built in some specific warped space-time scenarios. Once the equations of motion for tachyon fields related to the Born-Infeld action are written as first-order equations, a simple analytical connection with a particular class of real scalar field superpotentials can be found. This equivalence leads to the conclusion that, for a certain class of superpotentials, both systems can support identical thick brane solutions as well as brane structures described through localized energy densities, T00(y), in the 5th dimension, y. Our results indicate that thick brane solutions realized by the Born-Infeld cosmology can be connected to real scalar field brane scenarios which can be used to effectively map the tachyon condensation mechanism.
Aguilar, José Edgar Madriz; Bellini, Mauricio E-mail: mbellini@mdp.edu.ar
2010-11-01
We study scalar field fluctuations of the inflaton field in an early inflationary universe on an effective 4D Schwarzschild-de Sitter (SdS) metric, which is obtained after make a planar coordinate transformation on a 5D Ricci-flat Schwarzschild-de Sitter (SdS) static metric. We obtain the important result that the spectrum of fluctuations at zeroth order is independent of the scalar field mass M on Schwarzschild scales, while on cosmological scales it exhibits a mass dependence. However, in the first-order expansion, the spectrum depends of the inflaton mass and the amplitude is linear with the Black-Hole (BH) mass m.
Real scalar field scattering with polynomial approximation around Schwarzschild—de Sitter black-hole
NASA Astrophysics Data System (ADS)
Liu, Mo-Lin; Liu, Hong-Ya; Zhang, Jing-Fei; Yu, Fei
2008-05-01
As one of the fitting methods, the polynomial approximation is effective to process sophisticated problem. In this paper, we employ this approach to handle the scattering of scalar field around the Schwarzschild—de Sitter black-hole. The complicated relationship between tortoise coordinate and radial coordinate is replaced by the approximate polynomial. The Schrödinger-like equation, the real boundary conditions and the polynomial approximation construct a full Sturm-Liouville type problem. Then this boundary value problem can be solved numerically for two limiting cases: the first one is the Nariai black-hole whose horizons are close to each other, the second one is the black-hole with the horizons widely separated. Compared with previous results (Brevik and Tian), the field near the event horizon and cosmological horizon can have a better description.
The stability of de Sitter space with a scalar quantum field (II). The linear analysis
NASA Astrophysics Data System (ADS)
Rogers, Barrett; Isaacson, Jeffrey A.
1992-01-01
Using the semiclassical Einstein equations, we study the spatially homogeneous perturbations of a spatially flat de Sitter metric arising from fluctuations of a scalar quantum field about the Bunch-Davies vacuum state. The exact solution for the metric perturbation in the linear approzimation is obtained in terms of its Laplace transform, and analyzed for late times and arbitrary initial conditions. The results indicate the existence of only two undamped modes: (i) a "neutrally stable" mode, which derives from a spatial coordinate re-scaling symmetry in flat, Robertson-Walker space-times, and (ii) an unstable but unphysical "ghost" mode with a typical time scale m P-1 = G, which is related to the Landau ghost of the underlying quantum field theory. We show how to remove the latter mode by a restriction on the initial data. The existence of any physical instability in this spatially homogeneous system has been ruled out.
Noncommutative integrable systems and quasideterminants
Hamanaka, Masashi
2010-03-08
We discuss extension of soliton theories and integrable systems into noncommutative spaces. In the framework of noncommutative integrable hierarchy, we give infinite conserved quantities and exact soliton solutions for many noncommutative integrable equations, which are represented in terms of Strachan's products and quasi-determinants, respectively. We also present a relation to an noncommutative anti-self-dual Yang-Mills equation, and make comments on how 'integrability' should be considered in noncommutative spaces.
Noncommutativity Parameter and Composite Fermions
NASA Astrophysics Data System (ADS)
Jellal, Ahmed
We determine some particular values of the noncommutativity parameter θ and show that the Murthy Shankar approach is in fact a particular case of a more general one. Indeed, using the fractional quantum Hall effect (FQHE) experimental data, we give a measurement of θ. This measurement can be obtained by considering some values of the filling factor ν and other ingredients, magnetic field B and electron density ρ. Moreover, it is found that θ can be quantized either fractionally or integrally in terms of the magnetic length l0 and the quantization is exactly what Murthy and Shankar formulated recently for the FQHE. On the other hand, we show that the mapping of the FQHE in terms of the composite fermion basis has a noncommutative geometry nature and therefore there is a more general way than the Murthy Shankar method to do this mapping.
Gravitational forces in the Randall-Sundrum model with a scalar stabilizing field
NASA Astrophysics Data System (ADS)
Arnowitt, R.; Dent, J.
2007-03-01
We consider the problem of gravitational forces between point particles on the branes in a five-dimensional (5D) Randall-Sundrum model with two branes (at y1 and y2) and S1/Z2 symmetry of the fifth dimension. The matter on the branes is viewed as a perturbation on the vacuum metric and treated to linear order. In a previous work [R. Arnowitt and J. Dent, Phys. Rev. D 71, 124024 (2005).PRVDAQ0556-282110.1103/PhysRevD.71.124024] it was seen that the trace of the transverse part of the 4D metric on the TeV brane, fT(y2), contributed a Newtonian potential enhanced by e2βy2≅1032 and thus produced gross disagreement with the experiment. In this work we include a scalar stabilizing field ϕ and solve the coupled Einstein and scalar equations to leading order for the case where ϕ02/M53 is small and the vacuum field ϕ0(y) is a decreasing function of y. fT then grows a mass factor e-μr where, however, μ is suppressed from its natural value, O(MPl), by an exponential factor e-(1+λb)βy2, λb>0. Thus agreement with the experiment depends on the interplay between the enhancing and decaying exponentials. Current data eliminates a significant part of the parameter space, and the Randall-Sundrum model will be sensitive to any improvements on the tests of the Newtonian force law at smaller distances. An example of coupling of the ϕ field to the Higgs field is examined and found to generally produce very small effects.
NASA Astrophysics Data System (ADS)
Guo, X.; Yang, K.; Yang, W.; Li, S.; Long, Z.
2011-12-01
We present a field investigation over a melting valley glacier on the Tibetan Plateau. One particular aspect lies in that three melt phases are distinguished during the glacier's ablation season, which enables us to compare results over snow, bare-ice, and hummocky surfaces [with aerodynamic roughness lengths (z0M) varying on the order of 10-4-10-2 m]. We address two issues of common concern in the study of glacio-meteorology and micrometeorology. First, we study turbulent energy flux estimation through a critical evaluation of three parameterizations of the scalar roughness lengths (z0T for temperature and z0q for humidity), viz. key factors for the accurate estimation of sensible heat and latent heat fluxes using the bulk aerodynamic method. The first approach (Andreas 1987, Boundary-Layer Meteorol 38:159-184) is based on surface-renewal models and has been very widely applied in glaciated areas; the second (Yang et al. 2002, Q J Roy Meteorol Soc 128:2073-2087) has never received application over an ice/snow surface, despite its validity in arid regions; the third approach (Smeets and van den Broeke 2008, Boundary-Layer Meteorol 128:339-355) is proposed for use specifically over rough ice defined as z0M > 10-3 m or so. This empirical z0M threshold value is deemed of general relevance to glaciated areas (e.g. ice sheet/cap and valley/outlet glaciers), above which the first approach gives underestimated z0T and z0q. The first and the third approaches tend to underestimate and overestimate turbulent heat/moisture exchange, respectively (relative errors often > 30%). Overall, the second approach produces fairly low errors in energy flux estimates; it thus emerges as a practically useful choice to parameterize z0T and z0q over an ice/snow surface. Our evaluation of z0T and z0q parameterizations hopefully serves as a useful source of reference for physically based modeling of land-ice surface energy budget and mass balance. Second, we explore how scalar turbulence
Brane SUSY breaking and inflation: Implications for scalar fields and CMB distortion
NASA Astrophysics Data System (ADS)
Sagnotti, Augusto
2014-12-01
I elaborate on a link between the string-scale breaking of supersymmetry that occurs in a class of superstring models and the onset of inflation. The link rests on spatially flat cosmologies supported by a scalar field driven by an exponential potential. If, as in String Theory, this potential is steep enough, under some assumptions that are spelled out in the text the scalar can only climb up as it emerges from an initial singularity. In the presence of another mild exponential, slow-roll inflation is thus injected during the ensuing descent and definite imprints are left in the CMB power spectrum: the quadrupole is systematically reduced and, depending on the choice of two parameters, an oscillatory behavior can also emerge for low multipoles l < 50, in qualitative agreement with WMAP9 and PLANCK data. The experimentally favored value of the spectral index, n s ≈ 0.96, points to a potentially important role for the NS fivebrane, which is unstable in this class of models, in the Early Universe.
Conformally-invariant scalar field with trace-free energy-momentum tensor in Robertson-Walker models
NASA Astrophysics Data System (ADS)
Singh, N. I.; Singh, N. B.
1992-02-01
Exact solutions of Einstein's field equations for a conformally-invariant scalar field with trace-free energy-momentum tensor is presented for the Robertson-Walker models with K = + 1, - 1. The physical properties of the solution are also studied
Holographic entanglement entropy for noncommutative anti-de Sitter space
NASA Astrophysics Data System (ADS)
Momeni, Davood; Raza, Muhammad; Myrzakulov, Ratbay
2016-04-01
A metric is proposed to explore the noncommutative form of the anti-de Sitter (AdS) space due to quantum effects. It has been proved that the noncommutativity in AdS space induces a single component gravitoelectric field. The holographic Ryu-Takayanagi (RT) algorithm is then applied to compute the entanglement entropy (EE) in dual CFT2. This calculation can be exploited to compute ultraviolet-infrared (UV-IR) cutoff dependent central charge of the certain noncommutative CFT2. This noncommutative computation of the EE can be interpreted in the form of the surface/state correspondence. We have shown that noncommutativity increases the dimension of the effective Hilbert space of the dual conformal field theory (CFT).
Combined cosmological tests of a bivalent tachyonic dark energy scalar field model
Keresztes, Zoltán; Gergely, László Á. E-mail: gergely@physx.u-szeged.hu
2014-11-01
A recently investigated tachyonic scalar field dark energy dominated universe exhibits a bivalent future: depending on initial parameters can run either into a de Sitter exponential expansion or into a traversable future soft singularity followed by a contraction phase. We also include in the model (i) a tiny amount of radiation, (ii) baryonic matter (Ω{sub b}h{sup 2} = 0.022161, where the Hubble constant is fixed as h = 0.706) and (iii) cold dark matter (CDM). Out of a variety of six types of evolutions arising in a more subtle classification, we identify two in which in the past the scalar field effectively degenerates into a dust (its pressure drops to an insignificantly low negative value). These are the evolutions of type IIb converging to de Sitter and type III hitting the future soft singularity. We confront these background evolutions with various cosmological tests, including the supernova type Ia Union 2.1 data, baryon acoustic oscillation distance ratios, Hubble parameter-redshift relation and the cosmic microwave background (CMB) acoustic scale. We determine a subset of the evolutions of both types which at 1σ confidence level are consistent with all of these cosmological tests. At perturbative level we derive the CMB temperature power spectrum to find the best agreement with the Planck data for Ω{sub CDM} = 0.22. The fit is as good as for the ΛCDM model at high multipoles, but the power remains slightly overestimated at low multipoles, for both types of evolutions. The rest of the CDM is effectively generated by the tachyonic field, which in this sense acts as a combined dark energy and dark matter model.
Phillips, Carolyn L.; Guo, Hanqi; Peterka, Tom; ...
2016-02-19
In type-II superconductors, the dynamics of magnetic flux vortices determine their transport properties. In the Ginzburg-Landau theory, vortices correspond to topological defects in the complex order parameter field. Earlier, we introduced a method for extracting vortices from the discretized complex order parameter field generated by a large-scale simulation of vortex matter. With this method, at a fixed time step, each vortex [simplistically, a one-dimensional (1D) curve in 3D space] can be represented as a connected graph extracted from the discretized field. Here we extend this method as a function of time as well. A vortex now corresponds to a 2Dmore » space-time sheet embedded in 4D space time that can be represented as a connected graph extracted from the discretized field over both space and time. Vortices that interact by merging or splitting correspond to disappearance and appearance of holes in the connected graph in the time direction. This method of tracking vortices, which makes no assumptions about the scale or behavior of the vortices, can track the vortices with a resolution as good as the discretization of the temporally evolving complex scalar field. In addition, even details of the trajectory between time steps can be reconstructed from the connected graph. With this form of vortex tracking, the details of vortex dynamics in a model of a superconducting materials can be understood in greater detail than previously possible.« less
NASA Astrophysics Data System (ADS)
Antonov, N. V.; Gulitskiy, N. M.; Kostenko, M. M.; Lučivjanský, T.
2017-03-01
The field theoretic renormalization group (RG) and the operator product expansion (OPE) are applied to the model of a density field advected by a random turbulent velocity field. The latter is governed by the stochastic Navier-Stokes equation for a compressible fluid. The model is considered near the special space dimension d = 4. It is shown that various correlation functions of the scalar field exhibit anomalous scaling behaviour in the inertial-convective range. The scaling properties in the RG+OPE approach are related to fixed points of the renormalization group equations. In comparison with physically interesting case d = 3, at d = 4 additional Green function has divergences which affect the existence and stability of fixed points. From calculations it follows that a new regime arises there and then by continuity moves into d = 3. The corresponding anomalous exponents are identified with scaling dimensions of certain composite fields and can be systematically calculated as series in y (the exponent, connected with random force) and ɛ = 4 - d. All calculations are performed in the leading one-loop approximation.
Phillips, Carolyn L.; Guo, Hanqi; Peterka, Tom; Karpeyev, Dmitry; Glatz, Andreas
2016-02-19
In type-II superconductors, the dynamics of magnetic flux vortices determine their transport properties. In the Ginzburg-Landau theory, vortices correspond to topological defects in the complex order parameter field. Earlier, we introduced a method for extracting vortices from the discretized complex order parameter field generated by a large-scale simulation of vortex matter. With this method, at a fixed time step, each vortex [simplistically, a one-dimensional (1D) curve in 3D space] can be represented as a connected graph extracted from the discretized field. Here we extend this method as a function of time as well. A vortex now corresponds to a 2D space-time sheet embedded in 4D space time that can be represented as a connected graph extracted from the discretized field over both space and time. Vortices that interact by merging or splitting correspond to disappearance and appearance of holes in the connected graph in the time direction. This method of tracking vortices, which makes no assumptions about the scale or behavior of the vortices, can track the vortices with a resolution as good as the discretization of the temporally evolving complex scalar field. In addition, even details of the trajectory between time steps can be reconstructed from the connected graph. With this form of vortex tracking, the details of vortex dynamics in a model of a superconducting materials can be understood in greater detail than previously possible.
Randall-Sundrum cosmological model with nonminimal derivative coupling of scalar field
Widiyani, Agustina Suroso, Agus Zen, Freddy P.
2015-04-16
Nonminimal derivative coupling (NMDC) of scalar field in time-dependent Randall-Sundrum model is investigated. Firstly, we take a simple relation between the scale factor on the brane, a(t), and the scale factor of the extradimension, b(t), as b = a{sup γ} where γ is a constant. Then, we derive the Einstein equation and find its cosmological solution for a special case of static extra dimension, γ = 0. As the result, we find that de Sitter solution is a typical solution of our model. We also find that the brane tension which is related to cosmological constant on the brane is related to the coupling constant of the model.
C-metric solution for conformal gravity with a conformally coupled scalar field
NASA Astrophysics Data System (ADS)
Meng, Kun; Zhao, Liu
2017-02-01
The C-metric solution of conformal gravity with a conformally coupled scalar field is presented. The solution belongs to the class of Petrov type D spacetimes and is conformal to the standard AdS C-metric appeared in vacuum Einstein gravity. For all parameter ranges, we identify some of the physically interesting static regions and the corresponding coordinate ranges. The solution may contain a black hole event horizon, an acceleration horizon, either of which may be cut by the conformal infinity or be hidden behind the conformal infinity. Since the model is conformally invariant, we also discussed the possible effects of the conformal gauge choices on the structure of the spacetime.
Can self-ordering scalar fields explain the BICEP2 B-mode signal?
Durrer, Ruth; Figueroa, Daniel G.; Kunz, Martin E-mail: daniel.figueroa@unige.ch
2014-08-01
We show that self-ordering scalar fields (SOSF), i.e. non-topological cosmic defects arising after a global phase transition, cannot explain the B-mode signal recently announced by BICEP2. We compute the full C{sub ℓ}{sup B} angular power spectrum of B-modes due to vector and tensor perturbations of SOSF, modeled in the large N limit of a spontaneously broken global O(N) symmetry. We conclude that the low ℓ multipoles detected by BICEP2 cannot be due mainly to SOSF, since they have the wrong spectrum at low multipoles. As a byproduct we derive the first cosmological constraints on this model, showing that the BICEP2 B-mode polarization data admits at most a 2-3% contribution from SOSF in the temperature anisotropies, similar to (but somewhat tighter than) the recently studied case of cosmic strings.
Inflation from non-minimally coupled scalar field in loop quantum cosmology
Artymowski, Michał; Dapor, Andrea; Pawłowski, Tomasz E-mail: adapor@fuw.edu.pl
2013-06-01
The FRW model with non-minimally coupled massive scalar field has been investigated in LQC framework. Considered form of the potential and coupling allows applications to Higgs driven inflation. Out of two frames used in the literature to describe such systems: Jordan and Einstein frame, the latter one is applied. Specifically, we explore the idea of the Einstein frame being the natural 'environment' for quantization and the Jordan picture having an emergent nature. The resulting dynamics qualitatively modifies the standard bounce paradigm in LQC in two ways: (i) the bounce point is no longer marked by critical matter energy density, (ii) the Planck scale physics features the ''mexican hat'' trajectory with two consecutive bounces and rapid expansion and recollapse between them. Furthermore, for physically viable coupling strength and initial data the subsequent inflation exceeds 60 e-foldings.
Scalar field-perfect fluid correspondence and non-linear perturbation equations
Mainini, Roberto
2008-07-15
The properties of dynamical dark energy (DE) and, in particular, the possibility that it can form or contribute to stable inhomogeneities have been widely debated in recent literature, and also in association with a possible coupling between DE and dark matter (DM). In order to clarify this issue, in this paper we present a general framework for the study of the non-linear phases of structure formation, showing the equivalence of two possible descriptions of DE: a scalar field {phi} self-interacting through a potential V ({phi}) and a perfect fluid with an assigned negative equation of state w(a). This enables us to show that, in the presence of coupling, the mass of DE quanta may increase where large DM condensations are present, with the result that also DE may be involved in the clustering process.
The effective two-dimensional phase space of cosmological scalar fields
NASA Astrophysics Data System (ADS)
Edwards, David C.
2016-08-01
It has been shown by Remmen and Carroll [1] that, for a model universe which contains only a kinetically canonical scalar field minimally coupled to gravity it is possible to choose `special coordinates' to describe a two-dimensional effective phase space. The special, non-canonical, coordinates are phi,dot phi and the ability to describe an effective phase space with these coordinates empowers the common usage of phi-dot phi as the space to define inflationary initial conditions. This paper extends the result to the full Horndeski action. The existence of a two-dimensional effective phase space is shown for the general case. Subsets of the Horndeski action, relevant to cosmology are considered as particular examples to highlight important aspects of the procedure.
A relation between massive scalar field in AdSd+1 and diffusion in channels
NASA Astrophysics Data System (ADS)
Romero, Juan M.; Gaona, Alejandro
2014-05-01
It is shown that, when the diffusion coefficient is a constant and is taken a particular family of channels, the Fick-Jacobs equation is invariant under conformal symmetry. In addition, using the diffusion coefficient and the geometric parameters of the channels, a representation for the conformal algebra is obtained. Furthermore, it is found that for these systems the Fick-Jacobs equation is equivalent to the Schrödinger equation for the 1-dimensional conformal quantum mechanics. Moreover, using this equivalence, it is found a relation between a massive scalar field equation in AdSd+i background and Fick-Jacobs equation, where the geometric parameter of the channels and the geometric parameters of AdSd+1 are identified.
Monte Carlo simulation of finite mass nucleons interacting via a neutral, scalar boson field
NASA Astrophysics Data System (ADS)
Szybisz, L.; Zabolitzky, J. G.
1987-03-01
A recently proposed Monte Carlo method to solve the Schrödinger equation when expressed in Fock space is applied to the hamiltonian which describes the interaction of nucleons via a neutral, scalar boson field. The fact that a nucleon has finite mass is taken into account and a gaussian cut-off for the nucleon form factor is adopted. The problem is solved for systems with A = 1 and 2 sources (nucleons) in the three-dimensional continuous space. From the results for A = 1 a bare nucleon mass, mB c2 = 962.58 ± 0.06 MeV, is obtained. This value is used to determine the binding energy for an A = 2 system by means of this new algorithm. The result, B(2) = 2.14 ± 0.50 MeV, is consistent with the value corresponding to the static potential approximation.
Renormalization group flow for noncommutative Fermi liquids
Estrada-Jimenez, Sendic; Garcia-Compean, Hugo; Wu Yongshi
2011-06-15
Some recent studies of the AdS/CFT correspondence for condensed matter systems involve the Fermi liquid theory as a boundary field theory. Adding B-flux to the boundary D-branes leads in a certain limit to the noncommutative Fermi liquid, which calls for a field theory description of its critical behavior. As a preliminary step to more general consideration, the modification of the Landau's Fermi liquid theory due to noncommutativity of spatial coordinates is studied in this paper. We carry out the renormalization of interactions at tree level and one loop in a weakly coupled fermion system in two spatial dimensions. Channels ZS, ZS' and BCS are discussed in detail. It is shown that while the Gaussian fixed-point remains unchanged, the BCS instability is modified due to the space noncommutativity.
NASA Astrophysics Data System (ADS)
Guilleux, Maxime; Serreau, Julien
2017-02-01
Nonperturbative renormalization group techniques have recently proven a powerful tool to tackle the nontrivial infrared dynamics of light scalar fields in de Sitter space. In the present article, we develop the formalism beyond the local potential approximation employed in earlier works. In particular, we consider the derivative expansion, a systematic expansion in powers of field derivatives, appropriate for long wavelength modes, that we generalize to the relevant case of a curved metric with Lorentzian signature. The method is illustrated with a detailed discussion of the so-called local potential approximation prime which, on top of the full effective potential, includes a running (but field-independent) field renormalization. We explicitly compute the associated anomalous dimension for O (N ) theories. We find that it can take large values along the flow, leading to sizable differences as compared to the local potential approximation. However, it does not prevent the phenomenon of gravitationally induced dimensional reduction pointed out in previous studies. We show that, as a consequence, the effective potential at the end of the flow is unchanged as compared to the local potential approximation, the main effect of the running anomalous dimension being merely to slow down the flow. We discuss some consequences of these findings.
Magnetic Pressure as a Scalar Representation of Field Effects in Magnetic Suspensions.
Zborowski, Maciej; Moore, Lee R; Williams, P Stephen; Chalmers, Jeffrey J
2010-01-01
Magnetic microsphere suspensions undergo complex motion when exposed to finite sources of the magnetic field, such as small permanent magnets. The computational complexity is compounded by a difficulty in choosing a suitable choice of visualization tools because this often requires using the magnetic force vector field in three dimensions. Here we present a potentially simpler approach by using the magnetic pressure. It is a scalar quantity, pm = B(2)/2μ0, and its usefulness has been already demonstrated in applications to magnetohydrodynamics and ferrohydrodynamics (where B is the applied field and μ0 = 4π×10(-7) T.m/A). The equilibrium distribution of the magnetic bead plug in aqueous suspension is calculated as an isosurface of the magnitude of the magnetic pressure pm = const, in the field of two permanent magnet blocks calculated from closed formulas. The geometry was adapted from a publication on the magnetic bead suspensions in microsystems and the predicted bead plug distribution is shown to agree remarkably well with the experiment.
Magnetic Pressure as a Scalar Representation of Field Effects in Magnetic Suspensions
Zborowski, Maciej; Moore, Lee R.; Williams, P. Stephen; Chalmers, Jeffrey J.
2014-01-01
Magnetic microsphere suspensions undergo complex motion when exposed to finite sources of the magnetic field, such as small permanent magnets. The computational complexity is compounded by a difficulty in choosing a suitable choice of visualization tools because this often requires using the magnetic force vector field in three dimensions. Here we present a potentially simpler approach by using the magnetic pressure. It is a scalar quantity, pm = B2/2μ0, and its usefulness has been already demonstrated in applications to magnetohydrodynamics and ferrohydrodynamics (where B is the applied field and μ0 = 4π×10−7 T.m/A). The equilibrium distribution of the magnetic bead plug in aqueous suspension is calculated as an isosurface of the magnitude of the magnetic pressure pm = const, in the field of two permanent magnet blocks calculated from closed formulas. The geometry was adapted from a publication on the magnetic bead suspensions in microsystems and the predicted bead plug distribution is shown to agree remarkably well with the experiment. PMID:25382882
A note on nonlinear σ-models in noncommutative geometry
NASA Astrophysics Data System (ADS)
Lee, Hyun Ho
2016-03-01
We study nonlinear σ-models defined on a noncommutative torus as a two-dimensional string worldsheet. We consider (i) a two-point space, (ii) a circle, (iii) a noncommutative torus, (iv) a classical group SU(2, ℂ) as examples of space-time. Based on established results, the trivial harmonic unitaries of the noncommutative chiral model known as local minima are shown not to be global minima by comparing them to the symmetric unitaries derived from instanton solutions of the noncommutative Ising model corresponding to a two-point space. In addition, a ℤ2-action on field maps is introduced to a noncommutative torus, and its action on solutions of various Euler-Lagrange equations is described.
C, P, and T invariance of noncommutative gauge theories
Sheikh-Jabbari
2000-06-05
In this paper we study the invariance of the noncommutative gauge theories under C, P, and T transformations. For the noncommutative space (when only the spatial part of straight theta is nonzero) we show that noncommutative QED (NCQED) is parity invariant. In addition, we show that under charge conjugation the theory on noncommutative R(4)(straight theta) is transformed to the theory on R(4)(-straight theta), so NCQED is a CP violating theory. The theory remains invariant under time reversal if, together with proper changes in fields, we also change straight theta by -straight theta. Hence altogether NCQED is CPT invariant. Moreover, we show that the CPT invariance holds for general noncommutative space-time.
Exact solutions with noncommutative symmetries in Einstein and gauge gravity
NASA Astrophysics Data System (ADS)
Vacaru, Sergiu I.
2005-04-01
We present new classes of exact solutions with noncommutative symmetries constructed in vacuum Einstein gravity (in general, with nonzero cosmological constant), five-dimensional (5D) gravity and (anti) de Sitter gauge gravity. Such solutions are generated by anholonomic frame transforms and parametrized by generic off-diagonal metrics. For certain particular cases, the new classes of metrics have explicit limits with Killing symmetries but, in general, they may be characterized by certain anholonomic noncommutative matrix geometries. We argue that different classes of noncommutative symmetries can be induced by exact solutions of the field equations in commutative gravity modeled by a corresponding moving real and complex frame geometry. We analyze two classes of black ellipsoid solutions (in the vacuum case and with cosmological constant) in four-dimensional gravity and construct the analytic extensions of metrics for certain classes of associated frames with complex valued coefficients. The third class of solutions describes 5D wormholes which can be extended to complex metrics in complex gravity models defined by noncommutative geometric structures. The anholonomic noncommutative symmetries of such objects are analyzed. We also present a descriptive account how the Einstein gravity can be related to gauge models of gravity and their noncommutative extensions and discuss such constructions in relation to the Seiberg-Witten map for the gauge gravity. Finally, we consider a formalism of vielbeins deformations subjected to noncommutative symmetries in order to generate solutions for noncommutative gravity models with Moyal (star) product.
Curvature and geometric modules of noncommutative spheres and tori
Arnlind, Joakim
2014-04-15
When considered as submanifolds of Euclidean space, the Riemannian geometry of the round sphere and the Clifford torus may be formulated in terms of Poisson algebraic expressions involving the embedding coordinates, and a central object is the projection operator, projecting tangent vectors in the ambient space onto the tangent space of the submanifold. In this note, we point out that there exist noncommutative analogues of these projection operators, which implies a very natural definition of noncommutative tangent spaces as particular projective modules. These modules carry an induced connection from Euclidean space, and we compute its scalar curvature.
Noncommutative black hole thermodynamics
Banerjee, Rabin; Majhi, Bibhas Ranjan; Samanta, Saurav
2008-06-15
We give a general derivation, for any static spherically symmetric metric, of the relation T{sub h}=(K/2{pi}) connecting the black hole temperature (T{sub h}) with the surface gravity (K), following the tunneling interpretation of Hawking radiation. This derivation is valid even beyond the semi-classical regime, i.e. when quantum effects are not negligible. The formalism is then applied to a spherically symmetric, stationary noncommutative Schwarzschild space-time. The effects of backreaction are also included. For such a black hole the Hawking temperature is computed in a closed form. A graphical analysis reveals interesting features regarding the variation of the Hawking temperature (including corrections due to noncommutativity and backreaction) with the small radius of the black hole. The entropy and tunneling rate valid for the leading order in the noncommutative parameter are calculated. We also show that the noncommutative Bekenstein-Hawking area law has the same functional form as the usual one.
Thermodynamic potentials from shifted boundary conditions: the scalar-field theory case
NASA Astrophysics Data System (ADS)
Giusti, Leonardo; Meyer, Harvey B.
2011-11-01
In a thermal field theory, the cumulants of the momentum distribution can be extracted from the dependence of the Euclidean path integral on a shift in the fields built into the temporal boundary condition. When combined with the Ward identities associated with the invariance of the theory under the Poincaré group, thermodynamic potentials such as the entropy or the pressure can be directly inferred from the response of the system to the shift. Crucially the argument holds, up to harmless finite-size and discretization effects, even if translational and rotational invariance are broken to a discrete subgroup of finite shifts and rotations such as in a lattice box. The formulas are thus applicable at finite lattice spacing and volume provided the derivatives are replaced by their discrete counterpart, and no additive or multiplicative ultraviolet-divergent renormalizations are needed to take the continuum limit. In this paper we present a complete derivation of the relevant formulas in the scalar field theory, where several technical complications are avoided with respect to gauge theories. As a by-product we obtain a recursion relation among the cumulants of the momentum distribution, and formulæ for finite-volume corrections to several well-known thermodynamic identities.
Continuum dynamics and the electromagnetic field in the scalar ether theory of gravitation
NASA Astrophysics Data System (ADS)
Arminjon, Mayeul
2016-01-01
An alternative, scalar theory of gravitation has been proposed, based on a mechanism/interpretation of gravity as being a pressure force: Archimedes' thrust. In it, the gravitational field affects the physical standards of space and time, but motion is governed by an extension of the relativistic form of Newton's second law. This implies Einstein's geodesic motion for free particles only in a constant gravitational field. In this work, equations governing the dynamics of a continuous medium subjected to gravitational and non-gravitational forces are derived. Then, the case where the non-gravitational force is the Lorentz force is investigated. The gravitational modification of Maxwell's equations is obtained under the requirement that a charged continuous medium, subjected to the Lorentz force, obeys the equation derived for continuum dynamics under external forces. These Maxwell equations are shown to be consistent with the dynamics of a "free" photon, and thus with the geometrical optics of this theory. However, these equations do not imply local charge conservation, except for a constant gravitational field.
Boundary parametric approximation to the linearized scalar potential magnetostatic field problem
Bramble, J.H.; Pasciak, J.E.
1984-01-01
We consider the linearized scalar potential formulation of the magnetostatic field problem in this paper. Our approach involves a reformulation of the continuous problem as a parametric boundary problem. By the introduction of a spherical interface and the use of spherical harmonics, the infinite boundary conditions can also be satisfied in the parametric framework. That is, the field in the exterior of a sphere is expanded in a harmonic series of eigenfunctions for the exterior harmonic problem. The approach is essentially a finite element method coupled with a spectral method via a boundary parametric procedure. The reformulated problem is discretized by finite element techniques which lead to a discrete parametric problem which can be solved by well conditioned iteration involving only the solution of decoupled Neumann type elliptic finite element systems and L/sup 2/ projection onto subspaces of spherical harmonics. Error and stability estimates given show exponential convergence in the degree of the spherical harmonics and optimal order convergence with respect to the finite element approximation for the resulting fields in L/sup 2/. 24 references.
Inertial-diffusive range for a passive scalar advected by a white-in-time velocity field
NASA Astrophysics Data System (ADS)
Frisch, U.; Wirth, A.
1996-09-01
It is shown analytically and by Monte Carlo simulations that a passive scalar with finite diffusivity, advected by a white-in-time velocity field with a power law spectrum propto k-1-ξ (0 < ξ < 2), has an inertial-diffusive range with a spectrum propto k-3-ξ. This is the analog of the Batchelor-Howells-Townsend (J. Fluid Mech., 5 (1959) 134) phenomenological derivation of the k-17/3 law for low-Schmidt-number passive-scalar dynamics in ordinary turbulence.
Cosmological constraints on Bose-Einstein-condensed scalar field dark matter
NASA Astrophysics Data System (ADS)
Li, Bohua; Rindler-Daller, Tanja; Shapiro, Paul R.
2014-04-01
Despite the great successes of the cold dark matter (CDM) model in explaining a wide range of observations of the global evolution and the formation of galaxies and large-scale structure in the Universe, the origin and microscopic nature of dark matter is still unknown. The most common form of CDM considered to date is that of weakly interacting massive particles (WIMPs), but, so far, attempts to detect WIMPs directly or indirectly have not yet succeeded, and the allowed range of particle parameters has been significantly restricted. Some of the cosmological predictions for this kind of CDM are even in apparent conflict with observations (e.g., cuspy-cored halos and an overabundance of satellite dwarf galaxies). For these reasons, it is important to consider the consequences of different forms of CDM. We focus here on the hypothesis that the dark matter is comprised, instead, of ultralight bosons that form a Bose-Einstein condensate, described by a complex scalar field, for which particle number per unit comoving volume is conserved. We start from the Klein-Gordon and Einstein field equations to describe the evolution of the Friedmann-Robertson-Walker universe in the presence of this kind of dark matter. We find that, in addition to the radiation-, matter-, and Λ-dominated phases familiar from the standard CDM model, there is an earlier phase of scalar-field domination, which is special to this model. In addition, while WIMP CDM is nonrelativistic at all times after it decouples, the equation of state of Bose-Einstein condensed scalar field dark matter (SFDM) is found to be relativistic at early times, evolving from stiff (p ¯=ρ ¯) to radiationlike (p ¯=ρ ¯/3), before it becomes nonrelativistic and CDM-like at late times (p ¯=0). The timing of the transitions between these phases and regimes is shown to yield fundamental constraints on the SFDM model parameters, particle mass m, and self-interaction coupling strength λ. We show that SFDM is compatible with
Maeda, Kengo; Fujii, Shunsuke; Koga, Jun-ichirou
2010-06-15
We investigate instability of four-dimensional Reissner-Nordstroem-anti-de Sitter (RN-AdS{sub 4}) black holes with various topologies by charged scalar field perturbations. We numerically find that the RN-AdS{sub 4} black holes become unstable against the linear perturbations below a critical temperature. It is analytically shown that charge extraction from the black holes occurs during the unstable evolution. To explore the end state of the instability, we perturbatively construct static black hole solutions with the scalar hair near the critical temperature. It is numerically found that the entropy of the hairy black hole is always larger than the one of the unstable RN-AdS{sub 4} black hole in the microcanonical ensemble. Our results support the speculation that the black hole with charged scalar hair always appears as the final fate of the instability of the RN-AdS{sub 4} black hole.
Deconstructing Noncommutativity with a Giant Fuzzy Moose
Adams, Allan W.
2001-12-05
We argue that the world volume theories of D-branes probing orbifolds with discrete torsion develop, in the large quiver limit, new non-commutative directions. This provides an explicit ''deconstruction'' of a wide class of noncommutative theories. This also provides insight into the physical meaning of discrete torsion and its relation to the T-dual B field. We demonstrate that the strict large quiver limit reproduces the matrix theory construction of higher-dimensional D-branes, and argue that finite ''fuzzy moose'' theories provide novel regularizations of non-commutative theories and explicit string theory realizations of gauge theories on fuzzy tori. We also comment briefly on the relation to NCOS, (2,0) and little string theories.
Noncommutative QFT and renormalization
NASA Astrophysics Data System (ADS)
Grosse, H.; Wulkenhaar, R.
2006-03-01
It was a great pleasure for me (Harald Grosse) to be invited to talk at the meeting celebrating the 70th birthday of Prof. Julius Wess. I remember various interactions with Julius during the last years: At the time of my studies at Vienna with Walter Thirring, Julius left already Vienna, I learned from his work on effective chiral Lagrangians. Next we met at various conferences and places like CERN (were I worked with Andre Martin, an old friend of Julius), and we all learned from Julius' and Bruno's creation of supersymmetry, next we realized our common interests in noncommutative quantum field theory and did have an intensive exchange. Julius influenced our perturbative approach to gauge field theories were we used the Seiberg-Witten map after his advice. And finally I lively remember the sad days when during my invitation to Vienna Julius did have the serious heart attack. So we are very happy, that you recovered so well, and we wish you all the best for the forthcoming years. Many happy recurrences.
Noncommutative potential theory: A survey
NASA Astrophysics Data System (ADS)
Cipriani, Fabio
2016-07-01
The aim of these notes is to provide an introduction to Noncommutative Potential Theory as given at I.N.D.A.M.-C.N.R.S. ;Noncommutative Geometry and Applications; Lectures, Villa Mondragone-Frascati June 2014.
Generation of families of spectra in PT-symmetric quantum mechanics and scalar bosonic field theory.
Schmidt, Steffen; Klevansky, S P
2013-04-28
This paper explains the systematics of the generation of families of spectra for the -symmetric quantum-mechanical Hamiltonians H=p(2)+x(2)(ix)(ε), H=p(2)+(x(2))(δ) and H=p(2)-(x(2))(μ). In addition, it contrasts the results obtained with those found for a bosonic scalar field theory, in particular in one dimension, highlighting the similarities to and differences from the quantum-mechanical case. It is shown that the number of families of spectra can be deduced from the number of non-contiguous pairs of Stokes wedges that display PT symmetry. To do so, simple arguments that use the Wentzel-Kramers-Brillouin approximation are used, and these imply that the eigenvalues are real. However, definitive results are in most cases presently only obtainable numerically, and not all eigenvalues in each family may be real. Within the approximations used, it is illustrated that the difference between the quantum-mechanical and the field-theoretical cases lies in the number of accessible regions in which the eigenfunctions decay exponentially. This paper reviews and implements well-known techniques in complex analysis and PT-symmetric quantum theory.
Vacuum for a massless quantum scalar field outside a collapsing shell in anti-de Sitter space-time
NASA Astrophysics Data System (ADS)
Abel, Paul G.; Winstanley, Elizabeth
2016-08-01
We consider a massless quantum scalar field on a two-dimensional space-time describing a thin shell of matter collapsing to form a Schwarzschild-anti-de Sitter black hole. At early times, before the shell starts to collapse, the quantum field is in the vacuum state, corresponding to the Boulware vacuum on an eternal black hole space-time. The scalar field satisfies reflecting boundary conditions on the anti-de Sitter boundary. Using the Davies-Fulling-Unruh prescription for computing the renormalized expectation value of the stress-energy tensor, we find that at late times the black hole is in thermal equilibrium with a heat bath at the Hawking temperature, so the quantum field is in a state analogous to the Hartle-Hawking vacuum on an eternal black hole space-time.
Dimension dependence of the critical phenomena in gravitational collapse of massless scalar field
NASA Astrophysics Data System (ADS)
Bland, Jason Bryan
2007-12-01
A study of the critical behaviour which is observed in numerical calculations of spherically symmetric scalar field collapse has been performed. The gravitational collapse calculations are carried out using the field equations of Einstein's general theory of relativity in the context of a two dimensional dilaton gravity theory. The problem is formulated by considering a spherically symmetric matter distribution in an arbitrary number of space-time dimensions greater than three. A spherical distribution will only depend on two space-time coordinates, therefore, the action of the model can be reduced to a specific case of a 1 + 1 dilaton gravity theory. The evolution equations of the problem are simplified by carrying out a conformal transformation of the metric field. The number of space-time dimensions then appears as an input parameter of the field equations. Initial data is defined on a discrete space-time grid and numerical simulations of gravitational collapse are carried out. The computer code is optimized to increase numerical stability near the critical solutions. Discrete self-similarity and mass scaling in the near critical solutions are observed for each of the dimensions studied. The critical phenomena are described with a high level of confidence by smooth functions of space-time dimension. It is hypothesized that the critical solution of the theory at the limit of large dimension is discretely self-similar with a period of 5/2 and contains critical scaling with a constant of 1/2. Evidence will also be presented which suggests the critical solution in three dimensions with zero cosmological constant is not discretely self-similar but contains a critical scaling constant of approximately 0.11.
Noncommutative spaces from matrix models
NASA Astrophysics Data System (ADS)
Lu, Lei
Noncommutative (NC) spaces commonly arise as solutions to matrix model equations of motion. They are natural generalizations of the ordinary commutative spacetime. Such spaces may provide insights into physics close to the Planck scale, where quantum gravity becomes relevant. Although there has been much research in the literature, aspects of these NC spaces need further investigation. In this dissertation, we focus on properties of NC spaces in several different contexts. In particular, we study exact NC spaces which result from solutions to matrix model equations of motion. These spaces are associated with finite-dimensional Lie-algebras. More specifically, they are two-dimensional fuzzy spaces that arise from a three-dimensional Yang-Mills type matrix model, four-dimensional tensor-product fuzzy spaces from a tensorial matrix model, and Snyder algebra from a five-dimensional tensorial matrix model. In the first part of this dissertation, we study two-dimensional NC solutions to matrix equations of motion of extended IKKT-type matrix models in three-space-time dimensions. Perturbations around the NC solutions lead to NC field theories living on a two-dimensional space-time. The commutative limit of the solutions are smooth manifolds which can be associated with closed, open and static two-dimensional cosmologies. One particular solution is a Lorentzian fuzzy sphere, which leads to essentially a fuzzy sphere in the Minkowski space-time. In the commutative limit, this solution leads to an induced metric that does not have a fixed signature, and have a non-constant negative scalar curvature, along with singularities at two fixed latitudes. The singularities are absent in the matrix solution which provides a toy model for resolving the singularities of General relativity. We also discussed the two-dimensional fuzzy de Sitter space-time, which has irreducible representations of su(1,1) Lie-algebra in terms of principal, complementary and discrete series. Field
Quantum bound on the specific entropy in strongly coupled scalar field theory
Aparicio Alcalde, M.; Menezes, G.; Svaiter, N. F.
2008-06-15
We discuss the (g{sub 0}{phi}{sup p}){sub d} self-interacting scalar field theory, in the strong-coupling regime. We assume the presence of macroscopic boundaries confining the field in a hypercube of side L. We also consider that the system is in thermal equilibrium at temperature {beta}{sup -1}. For spatially bounded free fields, the Bekenstein bound states that the specific entropy satisfies the inequality (S/E)<2{pi}R, where R stands for the radius of the smallest sphere that circumscribes the system. Employing the strong-coupling perturbative expansion, we obtain the renormalized mean energy E and entropy S for the system up to the order (g{sub 0}){sup -(2/p)}, presenting an analytical proof that the specific entropy also satisfies in some situations a quantum bound. Defining {epsilon}{sub d}{sup (r)} as the renormalized zero-point energy for the free theory per unit length, the dimensionless quantity {xi}=({beta}/L) and h{sub 1}(d) and h{sub 2}(d) as positive analytic functions of d, for the case of high temperature, we get that the specific entropy satisfies (S/E)<2{pi}R(h{sub 1}(d)/h{sub 2}(d)){xi}. When considering the low-temperature behavior of the specific entropy, we have (S/E)<2{pi}R(h{sub 1}(d)/{epsilon}{sub d}{sup (r)}){xi}{sup 1-d}. Therefore the sign of the renormalized zero-point energy can invalidate this quantum bound. If the renormalized zero-point energy is a positive quantity, at intermediate temperatures and in the low-temperature limit, there is a quantum bound.
Cosmological dynamics with non-minimally coupled scalar field and a constant potential function
Hrycyna, Orest; Szydłowski, Marek E-mail: marek.szydlowski@uj.edu.pl
2015-11-01
Dynamical systems methods are used to investigate global behaviour of the spatially flat Friedmann-Robertson-Walker cosmological model in gravitational theory with a non-minimally coupled scalar field and a constant potential function. We show that the system can be reduced to an autonomous three-dimensional dynamical system and additionally is equipped with an invariant manifold corresponding to an accelerated expansion of the universe. Using this invariant manifold we find an exact solution of the reduced dynamics. We investigate all solutions for all admissible initial conditions using theory of dynamical systems to obtain a classification of all evolutional paths. The right-hand sides of the dynamical system depend crucially on the value of the non-minimal coupling constant therefore we study bifurcation values of this parameter under which the structure of the phase space changes qualitatively. We found a special bifurcation value of the non-minimal coupling constant which is distinguished by dynamics of the model and may suggest some additional symmetry in matter sector of the theory.
NASA Astrophysics Data System (ADS)
Zampeli, Adamantia; Pailas, Theodoros; Terzis, Petros A.; Christodoulakis, T.
2016-05-01
In this paper, the classical and quantum solutions of some axisymmetric cosmologies coupled to a massless scalar field are studied in the context of minisuperspace approximation. In these models, the singular nature of the Lagrangians entails a search for possible conditional symmetries. These have been proven to be the simultaneous conformal symmetries of the supermetric and the superpotential. The quantization is performed by adopting the Dirac proposal for constrained systems, i.e. promoting the first-class constraints to operators annihilating the wave function. To further enrich the approach, we follow [1] and impose the operators related to the classical conditional symmetries on the wave function. These additional equations select particular solutions of the Wheeler-DeWitt equation. In order to gain some physical insight from the quantization of these cosmological systems, we perform a semiclassical analysis following the Bohmian approach to quantum theory. The generic result is that, in all but one model, one can find appropriate ranges of the parameters, so that the emerging semiclassical geometries are non-singular. An attempt for physical interpretation involves the study of the effective energy-momentum tensor which corresponds to an imperfect fluid.
CMB-galaxy correlation in Unified Dark Matter scalar field cosmologies
Bertacca, Daniele; Bartolo, Nicola; Matarrese, Sabino; Raccanelli, Alvise; Piattella, Oliver F.; Pietrobon, Davide; Giannantonio, Tommaso E-mail: alvise.raccanelli@port.ac.uk E-mail: davide.pietrobon@jpl.nasa.gov E-mail: sabino.matarrese@pd.infn.it
2011-03-01
We present an analysis of the cross-correlation between the CMB and the large-scale structure (LSS) of the Universe in Unified Dark Matter (UDM) scalar field cosmologies. We work out the predicted cross-correlation function in UDM models, which depends on the speed of sound of the unified component, and compare it with observations from six galaxy catalogues (NVSS, HEAO, 2MASS, and SDSS main galaxies, luminous red galaxies, and quasars). We sample the value of the speed of sound and perform a likelihood analysis, finding that the UDM model is as likely as the ΛCDM, and is compatible with observations for a range of values of c{sub ∞} (the value of the sound speed at late times) on which structure formation depends. In particular, we obtain an upper bound of c{sub ∞}{sup 2} ≤ 0.009 at 95% confidence level, meaning that the ΛCDM model, for which c{sub ∞}{sup 2} = 0, is a good fit to the data, while the posterior probability distribution peaks at the value c{sub ∞}{sup 2} = 10{sup −4} . Finally, we study the time dependence of the deviation from ΛCDM via a tomographic analysis using a mock redshift distribution and we find that the largest deviation is for low-redshift sources, suggesting that future low-z surveys will be best suited to constrain UDM models.
Pair production of Dirac particles in a -dimensional noncommutative space-time
NASA Astrophysics Data System (ADS)
Ousmane Samary, Dine; N'Dolo, Emanonfi Elias; Hounkonnou, Mahouton Norbert
2014-11-01
This work addresses the computation of the probability of fermionic particle pair production in -dimensional noncommutative Moyal space. Using Seiberg-Witten maps, which establish relations between noncommutative and commutative field variables, up to the first order in the noncommutative parameter , we derive the probability density of vacuum-vacuum pair production of Dirac particles. The cases of constant electromagnetic, alternating time-dependent, and space-dependent electric fields are considered and discussed.
Martins, R. A.
2007-08-15
The recent extension of the standard model to include massive neutrinos in the framework of noncommutative geometry and the spectral action principle involves new scalar fields and their interactions with the usual complex scalar doublet. After ensuring that they bring no unphysical consequences, we address the question of how these fields affect the physics predicted in the Weinberg-Salam theory, particularly in the context of the electroweak phase transition. Applying the Dolan-Jackiw procedure, we calculate the finite temperature corrections, and find that the phase transition is first order. The new scalar interactions significantly improve the stability of the electroweak Z string, through the 'bag' phenomenon described by Vachaspati and Watkins ['Bound states can stabilize electroweak strings', Phys. Lett. B 318, 163-168 (1993)]. (Recently, cosmic strings have climbed back into interest due to a new evidence.) Sourced by static embedded strings, an internal space analogy of Cartan's torsion is drawn, and a possible Higgs-force-like 'gravitational' effect of this nonpropagating torsion on the fermion masses is described. We also check that the field generating the Majorana mass for the {nu}{sub R} is nonzero in the physical vacuum.
Noncommuting spherical coordinates
Bander, Myron
2004-10-15
Restricting the states of a charged particle to the lowest Landau level introduces a noncommutativity between Cartesian coordinate operators. This idea is extended to the motion of a charged particle on a sphere in the presence of a magnetic monopole. Restricting the dynamics to the lowest energy level results in noncommutativity for angular variables and to a definition of a noncommuting spherical product. The values of the commutators of various angular variables are not arbitrary but are restricted by the discrete magnitude of the magnetic monopole charge. An algebra, isomorphic to angular momentum, appears. This algebra is used to define a spherical star product. Solutions are obtained for dynamics in the presence of additional angular dependent potentials.
Melnikov, Kirill
2002-08-08
We develop a Hamiltonian formalism which can be used to discuss the physics of a massless scalar field in a gravitational background of a Schwarzschild black hole. Using this formalism we show that the time evolution of the system is unitary and yet all known results such as the existence of Hawking radiation can be readily understood. We then point out that the Hamiltonian formalism leads to interesting observations about black hole entropy and the information paradox.
Results from a strong-coupling expansion for a lattice Yukawa model with a real scalar field
Abada, A.; Shrock, R.E. )
1991-01-15
Results are presented from a strong bare Yukawa coupling expansion for a lattice Yukawa theory with a real scalar field. It is found that the effective action involves competing interactions, consistent with the existence of a ferrimagnetic phase at intermediate Yukawa coupling {ital y}. We also give evidence that the (bosonic) continuum theory defined at the ferromagnetic-paramagnetic phase boundary at large {ital y} is free.
NASA Astrophysics Data System (ADS)
Kinney, William H.
1996-01-01
Inflationary cosmology is an elegant and straightforward solution to two of the largest puzzles presented by the standard "Big Bang" cosmology: why is the universe so flat, and why is the cosmic microwave background in such excellent thermal equilibrium? However, models of inflation in particle physics typically suffer from the shortcoming that the fundamental energy scale for inflation is driven to nearly the Planck scale by observational constraints. In addition, models of inflation often require the "fine-tuning" of parameters to very small values in order to remain consistent with observation. This thesis investigates inflationary potentials in a general context, and shows that the difficulty of fundamental scales being forced to the Planck scale is in fact characteristic only of scalar field potentials V(phi) dominated near their maxima by terms of order phi^2. It is found that potentials dominated by terms of order phim with m > 2 can satisfy observational constraints at an essentially arbitrary symmetry breaking scale. Potentials characterized by m = 2 and m = 4 are illustrated in the context of several "natural inflation" models, with particular emphasis on questions of fine-tuning and fundamental scale. Natural inflation theories are a class of models in which inflation is driven by a pseudo Nambu-Goldstone boson, which acquires a mass as a result of radiative corrections. Two models characterized by m = 2 are evaluated, in which the potential for inflation is generated by loop effects from a fermion sector which explicitly breaks a global U(1) symmetry. The m = 4 case is implemented in a model with a broken SO(3) symmetry, in which the potential is generated by gauge boson loops. Constraints from the Cosmic Background Explorer (COBE) Differential Microwave Radiometer (DMR) measurement of the temperature anisotropy of the cosmic background radiation are used to limit the parameters of the models.
Light scalar field constraints from gravitational-wave observations of compact binaries
NASA Astrophysics Data System (ADS)
Berti, Emanuele; Gualtieri, Leonardo; Horbatsch, Michael; Alsing, Justin
2012-06-01
Scalar-tensor theories are among the simplest extensions of general relativity. In theories with light scalars, deviations from Einstein’s theory of gravity are determined by the scalar mass ms and by a Brans-Dicke-like coupling parameter ωBD. We show that gravitational-wave observations of nonspinning neutron star-black hole binary inspirals can be used to set lower bounds on ωBD and upper bounds on the combination ms/ωBD. We estimate via a Fisher matrix analysis that individual observations with signal-to-noise ratio ρ would yield (ms/ωBD)(ρ/10)≲10-15, 10-16, and 10-19eV for Advanced LIGO, ET, and eLISA, respectively. A statistical combination of multiple observations may further improve these bounds.
Fractional Zero-Point Angular Momenta in Noncommutative Quantum Mechanics
NASA Astrophysics Data System (ADS)
Liu, Si-Jia; Zhang, Yu-Fei; Long, Zheng-Wen; Jing, Jian
2016-09-01
The charged particle confined by a harmonic potential in a noncommutative planar phase space interacting with a homogeneous dynamical magnetic field and Aharonov-Bohm potentials is studied. We find that the canonical orbital angular momenta of the reduced models, which are obtained by setting the mass and a dimensionless parameter to zero, take fractional values. These fractional angular momenta are not only determined by the flux inside the thin long solenoid but also affected by the noncommutativities of phase space.
Background independent noncommutative gravity from Fedosov quantization of endomorphism bundle
NASA Astrophysics Data System (ADS)
Dobrski, Michał
2017-04-01
A model of noncommutative gravity is constructed by means of Fedosov deformation quantization of an endomorphism bundle. The fields describing noncommutativity—symplectic form and symplectic connection—are dynamical, and the resulting theory is coordinate covariant and background independent. Its interpretation in terms of a Seiberg–Witten map is provided. Also, a new action for ordinary (commutative) general relativity is given, which in the present context appears as a commutative limit of noncommutative theory.
Cosmology and the noncommutative approach to the standard model
Nelson, William; Sakellariadou, Mairi
2010-04-15
We study cosmological consequences of the noncommutative approach to the standard model of particle physics. Neglecting the nonminimal coupling of the Higgs field to the curvature, noncommutative corrections to Einstein's equations are present only for inhomogeneous and anisotropic space-times. Considering the nonminimal coupling however, corrections are obtained even for background cosmologies. Links with dilatonic gravity as well as chameleon cosmology are briefly discussed, and potential experimental consequences are mentioned.
Lectures on Matrix Field Theory
NASA Astrophysics Data System (ADS)
Ydri, Badis
The subject of matrix field theory involves matrix models, noncommutative geometry, fuzzy physics and noncommutative field theory and their interplay. In these lectures, a lot of emphasis is placed on the matrix formulation of noncommutative and fuzzy spaces, and on the non-perturbative treatment of the corresponding field theories. In particular, the phase structure of noncommutative $\\phi^4$ theory is treated in great detail, and an introduction to noncommutative gauge theory is given.
NASA Astrophysics Data System (ADS)
Haro, Jaume; Amoros, Jaume
2011-08-01
There are two nonequivalent ways to check if quantum effects in the context of semiclassical gravity can moderate or even cancel the final singularity appearing in a universe filled with dark energy: The method followed in [J. D. Bates and P. R. Anderson, Phys. Rev. DPRVDAQ1550-7998 82, 024018 (2010).10.1103/PhysRevD.82.024018] is to introduce the classical Friedmann solution in the energy density of the quantum field, and to compare the result with the density of dark energy determined by the Friedmann equation. The method followed in this comment is to solve directly the semiclassical equations. The results obtained by either method are very different, leading to opposed conclusions. The authors of [J. D. Bates and P. R. Anderson, Phys. Rev. DPRVDAQ1550-7998 82, 024018 (2010)10.1103/PhysRevD.82.024018] find that for a perfect fluid with state equation p=ωρ and ω<-1 (phantom fluid), considering realistic values of ω leads to a quantum field energy density that remains small compared to the dark energy density until the curvature reaches the Planck scale or higher, at which point the semiclassical approach stops being valid. The conclusion is that quantum effects do not affect significantly the expansion of the universe until the scalar curvature reaches the Planck scale. In this comment we will show by numerical integration of the semiclassical equations that quantum effects modify drastically the expansion of the universe from an early point. We also present an analytic argument explaining why the method of [J. D. Bates and P. R. Anderson, Phys. Rev. DPRVDAQ1550-7998 82, 024018 (2010)10.1103/PhysRevD.82.024018] fails to detect this. The units employed are the same as in [J. D. Bates and P. R. Anderson, Phys. Rev. DPRVDAQ1550-7998 82, 024018 (2010)10.1103/PhysRevD.82.024018] (c=ℏ=G=1).
Noncommutative geometry and fluid dynamics
NASA Astrophysics Data System (ADS)
Das, Praloy; Ghosh, Subir
2016-11-01
In the present paper we have developed a Non-Commutative (NC) generalization of perfect fluid model from first principles, in a Hamiltonian framework. The noncommutativity is introduced at the Lagrangian (particle) coordinate space brackets and the induced NC fluid bracket algebra for the Eulerian (fluid) field variables is derived. Together with a Hamiltonian this NC algebra generates the generalized fluid dynamics that satisfies exact local conservation laws for mass and energy, thereby maintaining mass and energy conservation. However, nontrivial NC correction terms appear in the charge and energy fluxes. Other non-relativistic spacetime symmetries of the NC fluid are also discussed in detail. This constitutes the study of kinematics and dynamics of NC fluid. In the second part we construct an extension of the Friedmann-Robertson-Walker (FRW) cosmological model based on the NC fluid dynamics presented here. We outline the way in which NC effects generate cosmological perturbations bringing about anisotropy and inhomogeneity in the model. We also derive a NC extended Friedmann equation.
NASA Astrophysics Data System (ADS)
Kanemura, Shinya; Kikuchi, Mariko; Yagyu, Kei
2016-06-01
We calculate renormalized Higgs boson couplings with gauge bosons and fermions at the one-loop level in the model with an additional isospin singlet real scalar field. These coupling constants can deviate from the predictions in the standard model due to tree-level mixing effects and one-loop contributions of the extra neutral scalar boson. We investigate how they can be significant under the theoretical constraints from perturbative unitarity and vacuum stability and also the condition of avoiding the wrong vacuum. Furthermore, comparing with the predictions in the Type I two Higgs doublet model, we numerically demonstrate how the singlet extension model can be distinguished and identified by using precision measurements of the Higgs boson couplings at future collider experiments.
Canonical single field slow-roll inflation with a non-monotonic tensor-to-scalar ratio
NASA Astrophysics Data System (ADS)
Germán, Gabriel; Herrera-Aguilar, Alfredo; Hidalgo, Juan Carlos; Sussman, Roberto A.
2016-05-01
We take a pragmatic, model independent approach to single field slow-roll canonical inflation by imposing conditions, not on the potential, but on the slow-roll parameter epsilon(phi) and its derivatives epsilon'(phi) and epsilon''(phi), thereby extracting general conditions on the tensor-to-scalar ratio r and the running nsk at phiH where the perturbations are produced, some 50-60 e-folds before the end of inflation. We find quite generally that for models where epsilon(phi) develops a maximum, a relatively large r is most likely accompanied by a positive running while a negligible tensor-to-scalar ratio implies negative running. The definitive answer, however, is given in terms of the slow-roll parameter ξ2(phi). To accommodate a large tensor-to-scalar ratio that meets the limiting values allowed by the Planck data, we study a non-monotonic epsilon(phi) decreasing during most part of inflation. Since at phiH the slow-roll parameter epsilon(phi) is increasing, we thus require that epsilon(phi) develops a maximum for phi > phiH after which epsilon(phi) decrease to small values where most e-folds are produced. The end of inflation might occur trough a hybrid mechanism and a small field excursion Δphie ≡ |phiH-phie| is obtained with a sufficiently thin profile for epsilon(phi) which, however, should not conflict with the second slow-roll parameter η(phi). As a consequence of this analysis we find bounds for Δphie, rH and for the scalar spectral index nsH. Finally we provide examples where these considerations are explicitly realised.
Searching for chameleon-like scalar fields with the ammonia method
NASA Astrophysics Data System (ADS)
Levshakov, S. A.; Molaro, P.; Lapinov, A. V.; Reimers, D.; Henkel, C.; Sakai, T.
2010-03-01
Aims: We probe the dependence of the electron-to-proton mass ratio, μ = me/mp, on the ambient matter density by means of radio astronomical observations. Methods: The ammonia method, which has been proposed to explore the electron-to-proton mass ratio, is applied to nearby dark clouds in the Milky Way. This ratio, which is measured in different physical environments of high (terrestrial) and low (interstellar) densities of baryonic matter is supposed to vary in chameleon-like scalar field models, which predict strong dependences of both masses and coupling constant on the local matter density. High resolution spectral observations of molecular cores in lines of NH3 (J,K) = (1,1), HC_3N J = 2-1, and N_2H^+ J = 1-0 were performed at three radio telescopes to measure the radial velocity offsets, Δ V ≡ Vrot - Vinv, between the inversion transition of NH_3 (1,1) and the rotational transitions of other molecules with different sensitivities to the parameter Δμ/μ ≡ (μ_obs - μ_lab)/μ_lab. Results: The measured values of Δ V exhibit a statistically significant velocity offset of 23±4_stat ± 3_sys m s-1 . When interpreted in terms of the electron-to-proton mass ratio variation, this infers that Δμ/μ = (2.2±0.4_stat ± 0.3_sys) × 10-8. If only a conservative upper bound is considered, then the maximum offset between ammonia and the other molecules is |Δ V| ≤ 30 m s-1 . This provides the most accurate reference point at z = 0 for Δμ/μ of |Δ μ/μ| ≤ 3×10-8. Based on observations obtained with the Medicina 32-m telescope operated by INAF - Istituto di Radioastronomia, the 100-m telescope of the Max-Planck Institut für Radioastronomie at Effelsberg, and the Nobeyama Radio Observatory 45-m telescope of the National Astronomical Observatory of Japan.
Noncommutative topological theories of gravity
NASA Astrophysics Data System (ADS)
García-Compeán, H.; Obregón, O.; Ramírez, C.; Sabido, M.
2003-08-01
The possibility of noncommutative topological gravity arising in the same manner as Yang-Mills theory is explored. We use the Seiberg-Witten map to construct such a theory based on a SL(2,C) complex connection, from which the Euler characteristic and the signature invariant are obtained. Finally, we speculate on the description of noncommutative gravitational instantons, as well as noncommutative local gravitational anomalies.
Towards noncommutative quantum black holes
Lopez-Dominguez, J. C.; Obregon, O.; Sabido, M.; Ramirez, C.
2006-10-15
In this paper we study noncommutative black holes. We use a diffeomorphism between the Schwarzschild black hole and the Kantowski-Sachs cosmological model, which is generalized to noncommutative minisuperspace. Through the use of the Feynman-Hibbs procedure we are able to study the thermodynamics of the black hole, in particular, we calculate the Hawking's temperature and entropy for the noncommutative Schwarzschild black hole.
Branes as Stable Holomorphic Line Bundles On the Non-Commutative Torus
NASA Astrophysics Data System (ADS)
Grange, Pascal
2004-10-01
It was suggested by A. Kapustin that turning on a B-field, and allowing some discrepancy between the left and and right-moving complex structures, must induce an identification of B-branes with holomorphic line bundles on a non-commutative complex torus. The stability condition for the branes is written as a topological identity of non-commutative gauge theory. This identifies stable B-branes with previously proposed non-commutative instanton equations. Consistency of the non-commutative description with complex geometry is examined, using the non-linearities of the Seiberg-Witten map.
Late time acceleration in a non-commutative model of modified cosmology
NASA Astrophysics Data System (ADS)
Malekolkalami, B.; Atazadeh, K.; Vakili, B.
2014-12-01
We investigate the effects of non-commutativity between the position-position, position-momentum and momentum-momentum of a phase space corresponding to a modified cosmological model. We show that the existence of such non-commutativity results in a Moyal Poisson algebra between the phase space variables in which the product law between the functions is of the kind of an α-deformed product. We then transform the variables in such a way that the Poisson brackets between the dynamical variables take the form of a usual Poisson bracket but this time with a noncommutative structure. For a power law expression for the function of the Ricci scalar with which the action of the gravity model is modified, the exact solutions in the commutative and noncommutative cases are presented and compared. In terms of these solutions we address the issue of the late time acceleration in cosmic evolution.
Non-Gaussianity of a single scalar field in general covariant Hořava-Lifshitz gravity
NASA Astrophysics Data System (ADS)
Huang, Yongqing; Wang, Anzhong
2012-11-01
In this paper, we study non-Gaussianity generated by a single scalar field in slow-roll inflation in the framework of the nonrelativistic general covariant Hořava-Lifshitz theory of gravity with the projectability condition and an arbitrary coupling constant λ, where λ characterizes the deviation of the theory from general relativity (GR) in the infrared. We find that the leading effect of self-interaction, contrary to the case of the minimal scenario of GR, is in general of the order α^nɛ3/2, where ɛ is a slow-roll parameter, and α^n(n=3,5) are the dimensionless coupling coefficients of the sixth-order operators of the Lifshitz scalar and have no contributions to power spectra and indices of both scalar and tensor. The bispectrum, comparing with the standard one given in GR, is enhanced and gives rise to a large value of the nonlinearity parameter fNL. We study how the modified dispersion relation with high order moment terms affects the evaluation of the mode function and in turn the bispectrum, and we show explicitly that the mode function takes various asymptotic forms during different periods of its evolution. In particular, we find that it is in general of superpositions of oscillatory functions, instead of plane waves like in the minimal scenario of GR. This results in a large enhancement of the folded shape in the bispectrum.
Reconstructing the evolution of the Universe from loop quantum cosmology scalar fields
NASA Astrophysics Data System (ADS)
Oikonomou, V. K.
2016-08-01
We extend the scalar-tensor reconstruction techniques for classical cosmology frameworks, in the context of loop quantum cosmology. After presenting in some detail how the equations are generalized in the loop quantum cosmology case, we discuss which new features and limitations the quantum framework introduces, and we use various illustrative examples in order to demonstrate how the method works. As we show, the energy density has two different classes of solutions, and one of these yields the correct classical limit, while the second captures the quantum phenomena. We study in detail the scalar tensor reconstruction method for both of these solutions. We also discuss some scenarios for which the Hubble rate becomes unbounded at finite time, which corresponds for example to the case in which the big rip occurs. As we show, this issue is nontrivial and we discuss how this case should be treated in a consistent way. Finally, we investigate how the classical stability conditions for the scalar-tensor solutions are generalized in the loop quantum framework.
Three-dimensional scalar field theory model of center vortices and its relation to k-string tensions
Cornwall, John M.
2004-09-15
In d=3 SU(N) gauge theory, we study a scalar-field theory model of center vortices, and their monopolelike companions called nexuses, that furnishes an approach to the determination of so-called k-string tensions. This model is constructed from stringlike quantum solitons introduced previously, and exploits the well-known relation between string partition functions and scalar-field theories in d=3. A basic feature of the model is that center vortices corresponding to magnetic flux J (in units of 2{pi}/N) are composites of J elementary J=1 constituent vortices that come in N-1 types, with repulsion between like constituents and attraction between unlike constituents. The scalar-field theory is of a somewhat unusual type, involving N scalar fields {phi}{sub i} (one of which is eliminated) that can merge, dissociate, and recombine while conserving flux modN. The properties of these fields are deduced directly from the corresponding gauge-theory quantum solitons. Every vacuum Feynman graph of the theory corresponds to a real-space configuration of center vortices. We use qualitative features of this theory based on the vortex action to study the problem of k-string tensions (explicitly at large N, although large N is in no way a restriction on the model in general), whose solution is far from obvious in center-vortex language. We construct a simplified dynamical picture of constituent-vortex merging, dissociation, and recombination, which allows in principle for the determination of vortex areal densities and k-string tensions. This picture involves pointlike molecules made of constituent atoms in d=2 which combine and disassociate dynamically. These molecules and atoms are cross sections of vortices piercing a test plane; the vortices evolve in a Euclidean 'time' which is the location of the test plane along an axis perpendicular to the plane. A simple approximation to the molecular dynamics is compatible with k-string tensions that are linear in k for k<
Hamiltonian Approach To Dp-Brane Noncommutativity
NASA Astrophysics Data System (ADS)
Nikolic, B.; Sazdovic, B.
2010-07-01
In this article we investigate Dp-brane noncommutativity using Hamiltonian approach. We consider separately open bosonic string and type IIB superstring which endpoints are attached to the Dp-brane. From requirement that Hamiltonian, as the time translation generator, has well defined derivatives in the coordinates and momenta, we obtain boundary conditions directly in the canonical form. Boundary conditions are treated as canonical constraints. Solving them we obtain initial coordinates in terms of the effective ones as well as effective momenta. Presence of momenta implies noncommutativity of the initial coordinates. Effective theory, defined as initial one on the solution of boundary conditions, is its Ω even projection, where Ω is world-sheet parity transformation Ω:σ→-σ. The effective background fields are expressed in terms of Ω even and squares of the Ω odd initial background fields.
NASA Technical Reports Server (NTRS)
Ransom, Jonathan B.
2002-01-01
A multifunctional interface method with capabilities for variable-fidelity modeling and multiple method analysis is presented. The methodology provides an effective capability by which domains with diverse idealizations can be modeled independently to exploit the advantages of one approach over another. The multifunctional method is used to couple independently discretized subdomains, and it is used to couple the finite element and the finite difference methods. The method is based on a weighted residual variational method and is presented for two-dimensional scalar-field problems. A verification test problem and a benchmark application are presented, and the computational implications are discussed.
NASA Astrophysics Data System (ADS)
Khanwale, Makrand A.; Khadamkar, Hrushikesh P.; Mathpati, Channamallikarjun S.
2015-11-01
Physics of development of flow structures around the drop rising with solute transfer is highly influenced by the interfacial behaviour and is remarkably different than a particle rising under the same conditions. We report on the use of simultaneous particle image velocimetry-planar laser induced fluorescence technique to measure scalar and velocity fields around a drop rising in a quiescent liquid channel. The selected continuous phase is glycerol, and the drop consists of a mixture of toluene, acetone, and a dye rhodamine-6G, with acetone working as a interfacial tension depressant. The drop lies in the spherical region with Eötvös number, Eo = 1.95, Morton number, M = 78.20 and the particle Reynolds number being, Rep = 0.053. With Rep approaching that of creeping flow, we analyse the effect of interfacial instabilities solely, contrary to other investigations [M. Wegener et al., "Impact of Marangoni instabilities on the fluid dynamic behaviour of organic droplets," Int. J. Heat Mass Transfer 52, 2543-2551 (2009); S. Burghoff and E. Y. Kenig, "A CFD model for mass transfer and interfacial phenomena on single droplets," AIChE J. 52, 4071-4078 (2006); J. Wang et al., "Numerical simulation of the Marangoni effect on transient mass transfer from single moving deformable drops," AIChE J. 57, 2670-2683 (2011); R. F. Engberg, M. Wegener, and E. Y. Kenig, "The impact of Marangoni convection on fluid dynamics and mass transfer at deformable single rising droplets—A numerical study," Chem. Eng. Sci. 116, 208-222 (2014)] which account for turbulence as well as interfacial instabilities with Rep in the turbulent range. The velocity and concentration fields obtained are subjected to scale-wise energy decomposition using continuous wavelet transform. Scale-wise probability distribution functions of wavelet coefficients are calculated to check intermittent non-Gaussian behaviour for simultaneous velocity and scalar statistics. Multi-fractal singularity spectra for scalar
NASA Astrophysics Data System (ADS)
Breev, A. I.; Kozlov, A. V.
2016-01-01
Within the framework of the method of orbits, expressions have been obtained for the vacuum averages of the energy-momentum tensor of a scalar field with an arbitrary coupling constant in a spacetime with a nonstationary metric of Robertson-Walker type, where space is a homogeneous Riemannian manifold. It is shown that the vacuum averages of the energy-momentum tensor are determined by the complete set of solutions of the reduced equation with a smaller number of independent variables and with algebraic characteristics of homogeneous space.
NASA Astrophysics Data System (ADS)
Carvalho, Paulo R. S.
2016-12-01
We compute analytically the all-loop level critical exponents for a massless thermal Lorentz-violating (LV) O(N) self-interacting λϕ4 scalar field theory. For that, we evaluate, firstly explicitly up to next-to-leading loop order and later in a proof by induction up to any loop level, the respective β-function and anomalous dimensions in a theory renormalized in the massless BPHZ method, where a reduced set of Feynman diagrams to be calculated is needed. We investigate the effect of the Lorentz violation in the outcome for the critical exponents and present the corresponding mathematical explanation and physical interpretation.
NASA Astrophysics Data System (ADS)
Adler, Stephen L.
2016-08-01
We study SU(8) symmetry breaking induced by minimizing the Coleman-Weinberg effective potential for a third rank antisymmetric tensor scalar field in the 56 representation. Instead of breaking {SU}(8)\\supset {SU}(3)× {SU}(5), we find that the stable minimum of the potential breaks the original symmetry according to {SU}(8)\\supset {SU}(3)× {Sp}(4). Using both numerical and analytical methods, we present results for the potential minimum, the corresponding Goldstone boson structure and BEH mechanism, and the group-theoretic classification of the residual states after symmetry breaking.
Qualitative study of Bianchi type-I, III and Kantowski-Sachs cosmological models with scalar field
NASA Astrophysics Data System (ADS)
Chaubey, Raghavendra; Raushan, Rakesh
2016-08-01
A qualitative analysis of Bianchi type-I, III and Kantowski-Sachs (KS) cosmological models with a scalar field and matter fluid is performed. The analysis of the resulting equations is made by the dynamical system method. To analyze the evolution equations, we have introduced suitable transformation of variables. The evolution of the corresponding solutions is represented by curves in the phase-plane diagram. We analyze the evolution of the effective equation of state parameter for Bianchi type-I, III and KS cosmological models. The nature of critical points are analyzed and stable attractors are examined for each cosmological model.
On non-commutative geodesic motion
NASA Astrophysics Data System (ADS)
Ulhoa, S. C.; Amorim, R. G. G.; Santos, A. F.
2014-07-01
In this work we study the geodesic motion on a noncommutative space-time. As a result we find a non-commutative geodesic equation and then we derive corrections of the deviation angle per revolution in terms of the non-commutative parameter when we specify the problem of Mercury's perihelion. In this way, we estimate the noncommutative parameter based in experimental data.
The Gribov problem in noncommutative QED
NASA Astrophysics Data System (ADS)
Canfora, Fabrizio; Kurkov, Maxim A.; Rosa, Luigi; Vitale, Patrizia
2016-01-01
It is shown that in the noncommutative version of QED (NCQED) Gribov copies induced by the noncommutativity of space-time appear in the Landau gauge. This is a genuine effect of noncommutative geometry which disappears when the noncommutative parameter vanishes.
Vieira, H.S.; Bezerra, V.B.; Silva, G.V.
2015-11-15
Charged massive scalar fields are considered in the gravitational and electromagnetic field produced by a dyonic black hole with a cosmic string along its axis of symmetry. Exact solutions of both angular and radial parts of the covariant Klein–Gordon equation in this background are obtained, and are given in terms of the confluent Heun functions. The role of the presence of the cosmic string in these solutions is showed up. From the radial solution, we obtain the exact wave solutions near the exterior horizon of the black hole, and discuss the Hawking radiation spectrum and the energy flux. -- Highlights: •A cosmic string is introduced along the axis of symmetry of the dyonic black hole. •The covariant Klein–Gordon equation for a charged massive scalar field in this background is analyzed. •Both angular and radial parts are transformed to a confluent Heun equation. •The resulting Hawking radiation spectrum and the energy flux are obtained.
NASA Astrophysics Data System (ADS)
Fialko, O.; Opanchuk, B.; Sidorov, A. I.; Drummond, P. D.; Brand, J.
2017-01-01
The quantum decay of a relativistic scalar field from a metastable state (‘false vacuum decay’) is a fundamental idea in quantum field theory and cosmology. This occurs via local formation of bubbles of true vacuum with their subsequent rapid expansion. It can be considered as a relativistic analog of a first-order phase transition in condensed matter. Here we expand upon our recent proposal (Fialko O et al 2015 Europhys. Lett. 110 56001) for an experimental test of false vacuum decay using an ultra-cold spinor Bose gas. A false vacuum for the relative phase of two spin components, serving as the unstable scalar field, is generated by means of a modulated linear coupling of the spin components. We analyze the system theoretically using the functional integral approach and show that various microscopic degrees of freedom in the system, albeit leading to dissipation in the relative phase sector, will not hamper the observation of the false vacuum decay in the laboratory. This is well supported by numerical simulations demonstrating the spontaneous formation of true vacuum bubbles on millisecond time-scales in two-component 7Li or 41K bosonic condensates in one-dimensional traps of ∼ 100 μ {{m}} size.
On Invariants and Scalar Chiral Correlation Functions in { n} = 1 Superconformal Field Theories
NASA Astrophysics Data System (ADS)
Knuth, Holger
A general expression for the four-point function with vanishing total R-charge of antichiral and chiral superfields in { N} = 1 superconformal theories is given. It is obtained by applying the exponential of a simple universal nilpotent differential operator to an arbitrary function of two cross-ratios. To achieve this the nilpotent superconformal invariants according to Park are focused. Several dependencies between these invariants are presented, so that eight nilpotent invariants and 27 monomials of these invariants of degree d > 1 are left being linearly independent. It is analyzed, how terms within the four-point function of general scalar superfields cancel in order to fulfill the chiral restrictions.
Varshovi, Amir Abbass
2013-07-15
The theory of α*-cohomology is studied thoroughly and it is shown that in each cohomology class there exists a unique 2-cocycle, the harmonic form, which generates a particular Groenewold-Moyal star product. This leads to an algebraic classification of translation-invariant non-commutative structures and shows that any general translation-invariant non-commutative quantum field theory is physically equivalent to a Groenewold-Moyal non-commutative quantum field theory.
NASA Astrophysics Data System (ADS)
Persico, F.; Power, E. A.
1987-07-01
The time dependence of the dressing-undressing process, i.e., the acquiring or losing by a source of a boson field intensity and hence of a field energy density in its neighborhood, is considered by examining some simple soluble models. First, the loss of the virtual field is followed in time when a point source is suddenly decoupled from a neutral scalar meson field. Second, an initially bare point source acquires a virtual meson cloud as the coupling is switched on. The third example is that of an initially bare molecule interacting with the vacuum of the electromagnetic field to acquire a virtual photon cloud. In all three cases the dressing-undressing is shown to take place within an expanding sphere of radius r=ct centered at the source. At each point in space the energy density tends, for large times, to that of the ground state of the total system. Differences in the time dependence of the dressing between the massive scalar field and the massless electromagnetic field are discussed. The results are also briefly discussed in the light of Feinberg's ideas on the nature of half-dressed states in quantum field theory.
NASA Astrophysics Data System (ADS)
Kim, Sang Pyo; Page, Don N.
1992-05-01
The expansion of the wave function of a quantum Friedmann-Robertson-Walker cosmology minimally coupled to a scalar field with a power-law potential by its scalar-field part decouples the gravitational-field part into an infinite system of linear homogeneous differential equations (equivalent to a matrix equation). The solutions for the gravitational-field part are found in the product integral formulation. It is shown that there exists a spectrum of the wave functions exponentially damped for large three-geometries under the condition that the cosmological constant should vanish. These are interpeted as the Hawking-Page wormholes.
On a family of (1+1)-dimensional scalar field theory models: Kinks, stability, one-loop mass shifts
Alonso-Izquierdo, A.; Mateos Guilarte, J.
2012-09-15
In this paper we construct a one-parametric family of (1+1)-dimensional one-component scalar field theory models supporting kinks. Inspired by the sine-Gordon and {phi}{sup 4} models, we look at all possible extensions such that the kink second-order fluctuation operators are Schroedinger differential operators with Poeschl-Teller potential wells. In this situation, the associated spectral problem is solvable and therefore we shall succeed in analyzing the kink stability completely and in computing the one-loop quantum correction to the kink mass exactly. When the parameter is a natural number, the family becomes the hierarchy for which the potential wells are reflectionless, the two first levels of the hierarchy being the sine-Gordon and {phi}{sup 4} models. - Highlights: Black-Right-Pointing-Pointer We construct a family of scalar field theory models supporting kinks. Black-Right-Pointing-Pointer The second-order kink fluctuation operators involve Poeschl-Teller potential wells. Black-Right-Pointing-Pointer We compute the one-loop quantum correction to the kink mass with different methods.
NASA Astrophysics Data System (ADS)
Ghosh, Kaushik
2016-01-01
In this article, we will discuss a Lorentzian sector calculation of the entropy of a minimally coupled scalar field in the Schwarzschild black hole background using the brick wall model of 't Hooft. In the original article, the Wentzel-Kramers-Brillouin (WKB) approximation was used for the modes that are globally stationary. In a previous article, we found that the WKB quantization rule together with a proper counting of the states, leads to a new expression of the scalar field entropy which is not proportional to the area of the horizon. The expression of the entropy is logarithmically divergent in the brick wall cut-off parameter in contrast to an inverse power divergence obtained earlier. In this article, we will consider the entropy for a thin shell of matter field of a given thickness surrounding the black hole horizon. The thickness is chosen to be large compared with the Planck length and is of the order of the atomic scale. We will discuss the corresponding boundary conditions and the appropriateness of the WKB approximation using the Regge-Wheeler tortoise coordinates. When expressed in terms of a covariant cut-off parameter, the entropy of a thin shell of matter field of a given thickness and surrounding the horizon in the Schwarzschild black hole background is given by an expression proportional to the area of the black hole horizon. This leading order divergent term in the cut-off parameter remains to be logarithmically divergent. The logarithmic divergence is expected from the nature of the near-horizon geometry and is discussed in detail at the end of Sect. 2. We will find that these discussions are significant in the context of the continuation to the Euclidean sector and the corresponding regularization schemes used to evaluate the thermodynamical properties of matter fields in curved spaces. These are related with to geometric aspects of curved spaces.
The charged black-hole bomb: A lower bound on the charge-to-mass ratio of the explosive scalar field
NASA Astrophysics Data System (ADS)
Hod, Shahar
2016-04-01
The well-known superradiant amplification mechanism allows a charged scalar field of proper mass μ and electric charge q to extract the Coulomb energy of a charged Reissner-Nordström black hole. The rate of energy extraction can grow exponentially in time if the system is placed inside a reflecting cavity which prevents the charged scalar field from escaping to infinity. This composed black-hole-charged-scalar-field-mirror system is known as the charged black-hole bomb. Previous numerical studies of this composed physical system have shown that, in the linearized regime, the inequality q / μ > 1 provides a necessary condition for the development of the superradiant instability. In the present paper we use analytical techniques to study the instability properties of the charged black-hole bomb in the regime of linearized scalar fields. In particular, we prove that the lower bound q/μ>√{rm/r--1/rm /r+-1 } provides a necessary condition for the development of the superradiant instability in this composed physical system (here r± are the horizon radii of the charged Reissner-Nordström black hole and rm is the radius of the confining mirror). This analytically derived lower bound on the superradiant instability regime of the composed black-hole-charged-scalar-field-mirror system is shown to agree with direct numerical computations of the instability spectrum.
A Riemann-Roch theorem for the noncommutative two torus
NASA Astrophysics Data System (ADS)
Khalkhali, Masoud; Moatadelro, Ali
2014-12-01
We prove the analogue of the Riemann-Roch formula for the noncommutative two torus Aθ = C(Tθ2)equipped with an arbitrary translation invariant complex structure and a Weyl factor represented by a positive element k ∈C∞(Tθ2). We consider a topologically trivial line bundle equipped with a general holomorphic structure and the corresponding twisted Dolbeault Laplacians. We define a spectral triple (Aθ , H , D) that encodes the twisted Dolbeault complex of Aθ and whose index gives the left hand side of the Riemann-Roch formula. Using Connes' pseudodifferential calculus and heat equation techniques, we explicitly compute the b2 terms of the asymptotic expansion of Tr(e-tD2) . We find that the curvature term on the right hand side of the Riemann-Roch formula coincides with the scalar curvature of the noncommutative torus recently defined and computed in Connes and Moscovici (2014) and independently computed in Fathizadeh and Khalkhali (2014).
NASA Astrophysics Data System (ADS)
Goncharov, Yu. P.; Firsova, N. E.
1997-02-01
We study, both analytically and numerically, the contribution of the twisted topologically inequivalent configurations (TICs) of complex scalar fields on the Reissner-Nordström black holes to the Hawking radiation. Physically this contribution is conditioned by the natural presence of the Dirac monopoles on the black holes. When neglecting the own (external) electric field of black hole it is established that while increasing the black hole electric charge Q to the extremal value Q = M (M is the black hole mass), the given contribution to the total luminosity (summed up over all the TICs) of the black hole decreases (from the one of order 17% at Q = 0) up to 0. At this value the total luminosity itself tends to 0.
A New Fate of a Warped 5D FLRW Model with a U(1) Scalar Gauge Field
NASA Astrophysics Data System (ADS)
Slagter, Reinoud Jan; Pan, Supriya
2016-09-01
If we live on the weak brane with zero effective cosmological constant in a warped 5D bulk spacetime, gravitational waves and brane fluctuations can be generated by a part of the 5D Weyl tensor and carries information of the gravitational field outside the brane. We consider on a cylindrical symmetric warped FLRW background a U(1) self-gravitating scalar field coupled to a gauge field without bulk matter. It turns out that brane fluctuations can be formed dynamically, due to the modified energy-momentum tensor components of the scalar-gauge field ("cosmic string"). As a result, we find that the late-time behavior could significantly deviate from the standard evolution of the universe. The effect is triggered by the time-dependent warpfactor with two branches of the form ± 1/√{τ r}√{(c_1e^{√{2τ } t}+c_2e^{-√{2τ } t})(c_3e^{√{2τ } r}+c_4e^{-√{2τ } r})} ( with τ , c_i constants) and the modified brane equations comparable with a dark energy effect. This is a brane-world mechanism, not present in standard 4D FLRW, where the large disturbances are rapidly damped as the expansion proceed. Because gravity can propagate in the bulk, the cosmic string can build up a huge angle deficit (or mass per unit length) by the warpfactor and can induce massive KK-modes felt on the brane. Disturbances in the spatial components of the stress-energy tensor cause cylindrical symmetric waves, amplified due to the presence of the bulk space and warpfactor. They could survive the natural damping due to the expansion of the universe. It turns out that one of the metric components becomes singular at the moment the warp factor develops an extremum. This behavior could have influence on the possibility of a transition from acceleration to deceleration or vice versa.
NASA Astrophysics Data System (ADS)
Rindler-Daller, Tanja; Li, Bohua; Shapiro, Paul
2017-01-01
We consider an alternative dark matter candidate to WIMP-CDM, ultralight bosonic dark matter (m >=10-22 eV) described by a complex scalar field (SFDM). In a ΛSFDM universe, SFDM starts relativistic, evolving from a maximal stiff equation of state to radiation-like, before becoming nonrelativistic at late times. The SFDM particle parameters, mass and selfinteraction coupling strength, are therefore constrained by cosmological observables, esp. Neff, the effective number of neutrino species during BBN, and the redshift of matter-radiation equality. Furthermore, since the energy density contributed by the stochastic gravitational wave background (SGWB) from inflation is amplified during the stiff phase, this makes possible the detection of this SGWB at high frequencies by current experiments, e.g. aLIGO/Virgo and eLISA. We show that, for SFDM particle parameters that satisfy those cosmological constraints, the amplified SGWB is detectable by aLIGO, for values of tensor-to-scalar ratio r currently allowed by CMB polarization measurements, for a broad range of possible reheat temperatures. A nondetection by aLIGO O1 would provide a new kind of cosmological constraint on SFDM. Also, a wider range of parameters and reheat temperatures will be probed by aLIGO O5.
Notes on "Quantum Gravity" and Noncommutative Geometry
NASA Astrophysics Data System (ADS)
Gracia-Bondía, J. M.
I hesitated for a long time before giving shape to these notes, originally intended for preliminary reading by the attendees to the Summer School "New paths towards quantum gravity" (Holbaek Bay, Denmark, May 2008). At the end, I decide against just selling my mathematical wares, and for a survey, necessarily very selective, but taking a global phenomenological approach to its subject matter. After all, noncommutative geometry does not purport yet to solve the riddle of quantum gravity; it is more of an insurance policy against the probable failure of the other approaches. The plan is as follows: the introduction invites students to the fruitful doubts and conundrums besetting the application of even classical gravity. Next, the first experiments detecting quantum gravitational states inoculate us a healthy dose of scepticism on some of the current ideologies. In Sect. 1.3 we look at the action for general relativity as a consequence of gauge theory for quantum tensor fields. Section 1.4 briefly deals with the unimodular variants. Section 1.5 arrives at noncommutative geometry. I am convinced that, if this is to play a role in quantum gravity, commutative and noncommutative manifolds must be treated on the same footing, which justifies the place granted to the reconstruction theorem. Together with Sect. 1.3, this part constitutes the main body of the notes. Only very summarily at the end of this section do we point to some approaches to gravity within the noncommutative realm. The last section delivers a last dose of scepticism. My efforts will have been rewarded if someone from the young generation learns to mistrust current mindsets.
A remark on polar noncommutativity
NASA Astrophysics Data System (ADS)
Iskauskas, Andrew
2015-06-01
Noncommutative space has been found to be of use in a number of different contexts. In particular, one may use noncommutative spacetime to generate quantised gravity theories. Via an identification between the Moyal ⋆-product on function space and commutators on a Hilbert space, one may use the Seiberg-Witten map to generate corrections to such gravity theories. However, care must be taken with the derivation of commutation relations. We examine conditions for the validity of such an approach, and motivate the correct form for polar noncommutativity in R2. Such an approach lends itself readily to extension to more complicated spacetime parametrisations.
NASA Astrophysics Data System (ADS)
Felder, Gary
2008-10-01
We describe an MPI C++ program that we have written and made available for calculating the evolution of interacting scalar fields in an expanding universe on parallel clusters. The program is a parallel programming extension of the simulation program LATTICEEASY. The ability to run these simulations on parallel clusters, however, greatly extends the range of scales and times that can be simulated. The program is particularly useful for the study of reheating and thermalization after inflation. The program and its full documentation are available on the Web at http://www.science.smith.edu/departments/Physics/fstaff/gfelder/latticeeasy/. In this paper we provide a brief overview of what the program does and what it is useful for. Catalogue identifier: AEBJ_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEBJ_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 7469 No. of bytes in distributed program, including test data, etc.: 613 334 Distribution format: tar.gz Programming language: C++/MPI Computer: Cluster. Must have the library FFTW installed Operating system: Any RAM: Typically 4 MB to 1 GB per processor Classification: 1.9 External routines: A single-precision version of the FFTW library (http://www.fftw.org/) must be available on the target machine. Nature of problem: After inflation the universe consisted of interacting fields in a high energy, nonthermal state [1]. The evolution of these fields cannot be described with standard approximation techniques such as linearization, kinetic theory, or Hartree expansion, and must thus be simulated numerically. Fortunately, the fields rapidly acquire large occupation numbers over a range of frequencies, so their evolution can be accurately modeled with classical field theory [2]. The specific fields and
Farakos, K.; Kouretsis, A. P.; Pasipoularides, P.
2009-09-15
We construct asymptotically AdS black hole solutions, with a self-interacting bulk scalar field, in the context of 5D general relativity. As the observable universe is characterized by spatial flatness, we focus on solutions where the horizon of the black hole, and subsequently all 3D hypersurfaces for fixed radial coordinate, have zero spatial curvature. We examine two cases for the black hole scalar hair: (a) an exponential decaying scalar field profile and (b) an inverse power scalar field profile. The scalar black hole solutions we present in this paper are characterized by four functions f(r), a(r), {phi}(r), and V({phi}(r)). Only the functions {phi}(r) and a(r) are determined analytically, while the functions f(r) and V({phi}(r)) are expressed semianalytically by integral formulas in terms of a(r). We present our numerical results and study in detail the characteristic properties of our solutions. We also note that the potential we obtain has a nonconvex form in agreement with the corresponding 'no hair theorem' for AdS spacetimes.
NASA Astrophysics Data System (ADS)
Dowker, J. S.
2016-04-01
I compute the conformal weights of the twist operators of free scalar fields for charged Rényi entropy in both odd and even dimensions. Explicit expressions can be found, in odd dimensions as a function of the chemical potential in the absence of a conical singularity and thence by images for all integer coverings. This method, developed some time ago, is equivalent, in results, to the replica technique. A review is given. The same method applies for even dimensions but a general form is more immediately available. For no chemical potential, the closed form in the covering order is written in an alternative way related to old trigonometric sums. Some derivatives are obtained. An analytical proof is given of a conjecture made by Bueno, Myers and Witczak-Krempa regarding the relation between the conformal weights and a corner coefficient (a universal quantity) in the Rényi entropy.
Instantons, quivers and noncommutative Donaldson-Thomas theory
NASA Astrophysics Data System (ADS)
Cirafici, Michele; Sinkovics, Annamaria; Szabo, Richard J.
2011-12-01
We construct noncommutative Donaldson-Thomas invariants associated with abelian orbifold singularities by analyzing the instanton contributions to a six-dimensional topological gauge theory. The noncommutative deformation of this gauge theory localizes on noncommutative instantons which can be classified in terms of three-dimensional Young diagrams with a colouring of boxes according to the orbifold group. We construct a moduli space for these gauge field configurations which allows us to compute its virtual numbers via the counting of representations of a quiver with relations. The quiver encodes the instanton dynamics of the noncommutative gauge theory, and is associated to the geometry of the singularity via the generalized McKay correspondence. The index of BPS states which compute the noncommutative Donaldson-Thomas invariants is realized via topological quantum mechanics based on the quiver data. We illustrate these constructions with several explicit examples, involving also higher rank Coulomb branch invariants and geometries with compact divisors, and connect our approach with other ones in the literature.
Non-Commutative Martingale Inequalities
NASA Astrophysics Data System (ADS)
Pisier, Gilles; Xu, Quanhua
We prove the analogue of the classical Burkholder-Gundy inequalites for non-commutative martingales. As applications we give a characterization for an Ito-Clifford integral to be an Lp-martingale via its integrand, and then extend the Ito-Clifford integral theory in L2, developed by Barnett, Streater and Wilde, to Lp for all 1
non-commutative analogue of the classical Fefferman duality between $H1 and BMO.
Principal Fibrations from Noncommutative Spheres
NASA Astrophysics Data System (ADS)
Landi, Giovanni; Suijlekom, Walter Van
2005-11-01
We construct noncommutative principal fibrations Sθ7→Sθ4 which are deformations of the classical SU(2) Hopf fibration over the four sphere. We realize the noncommutative vector bundles associated to the irreducible representations of SU(2) as modules of coequivariant maps and construct corresponding projections. The index of Dirac operators with coefficients in the associated bundles is computed with the Connes-Moscovici local index formula. "The algebra inclusion is an example of a not-trivial quantum principal bundle."
Two roads to noncommutative causality
NASA Astrophysics Data System (ADS)
Besnard, Fabien
2015-08-01
We review the physical motivations and the mathematical results obtained so far in the isocone-based approach to noncommutative causality. We also give a briefer account of the alternative framework of Franco and Eckstein which is based on Lorentzian spectral triples. We compare the two theories on the simple example of the product geometry of the Minkowski plane by the finite noncommutative space with algebra M2(C).
Particle phenomenology on noncommutative spacetime
Joseph, Anosh
2009-05-01
We introduce particle phenomenology on the noncommutative spacetime called the Groenewold-Moyal plane. The length scale of spacetime noncommutativity is constrained from the CPT violation measurements in the K{sup 0}-K{sup 0} system and g-2 difference of {mu}{sup +}-{mu}{sup -}. The K{sup 0}-K{sup 0} system provides an upper bound on the length scale of spacetime noncommutativity of the order of 10{sup -32} m, corresponding to a lower energy bound E of the order of E > or approx. 10{sup 16} GeV. The g-2 difference of {mu}{sup +}-{mu}{sup -} constrains the noncommutativity length scale to be of the order of 10{sup -20} m, corresponding to a lower energy bound E of the order of E > or approx. 10{sup 3} GeV. We also present the phenomenology of the electromagnetic interaction of electrons and nucleons at the tree level on the noncommutative spacetime. We show that the distributions of charge and magnetization of nucleons are affected by spacetime noncommutativity. The analytic properties of electromagnetic form factors are also changed and it may give rise to interesting experimental signals.
Belinsky, Moisey I
2016-05-02
The rotation behavior of the vector chirality κ, scalar chirality χ, and magnetization M in the rotating magnetic field H1 is considered for the V3 and Cu3 nanomagnets, in which the Dzialoshinsky-Moriya coupling is active. The polar rotation of the field H1 of the given strength H1 results in the energy spectrum characterized by different vector and scalar chiralities in the ground and excited states. The magnetochiral correlations between the vector and scalar chiralities, energy, and magnetization in the rotating field were considered. Under the uniform polar rotation of the field H1, the ground-state chirality vector κI performs sawtooth oscillations and the magnetization vector MI performs the sawtooth oscillating rotation that is accompanied by the correlated transformation of the scalar chirality χI. This demonstrates the magnetochiral effect of the joint rotation behavior and simultaneous frustrations of the spin chiralities and magnetization in the rotating field, which are governed by the correlation between the chiralities and magnetization.
NASA Astrophysics Data System (ADS)
Raymond, C. A.; Kulikov, I. K.; Jewell, J. B.; Purucker, M. E.; Smith, E. J.
2004-05-01
A Scalar Helium Magnetometer (SHM) built at the Jet Propulsion Laboratory was included as part of the Danish Magnetic Mapping Payload on the Argentine/NASA Satellite Applicaciones Cientificas-C (SAC-C) which launched in November, 2000. The SHM on SAC-C comprises two orthogonal sensors (gas cells) mounted at the end of an 8-meter boom. The SHM data must be corrected for biases termed "light shifts" that are an inherent characteristic of optically-pumped devices. Properly calibrated, the SHM is expected to achieve accuracy on the order of 1 nanotesla. The real light shift is a constant that adds to the measured magnitude, whereas the virtual light shift has a cosine dependency on the angle between the field direction and the sensor optical axis. There are also small offsets in the X, Y, and Z axes that are intrinsic to the sensors and also have a cosine dependency on field direction. SHM data processed using the correction parameters obtained in a pre-flight calibration produce poor agreeement with field models and near-coincident passes of Orsted and CHAMP; however, the uncalibrated data generally agree well. We have analyzed a selected SAC-C quiet day data set ( Kp < 2) spanning 2001-2003 to determine the optimal values of the instrument biases. An inversion was performed to derive the optimal correction parameters and to solve for the off-nominal, and poorly determined boom orientation about the Z-axis. The inversion minimized the fit to the Comprehensive Magnetic Field Model - 3 (CM3) predicted field, coincident passes of Orsted and CHAMP when available, as well as internal crossovers of SHM tracks that were temporally proximal. The CM3 model was also used to provide the field direction relative to the SHM sensors for the corrections. The methods will be discussed, along with the resulting total field maps and their errors.
NASA Astrophysics Data System (ADS)
Dahm, Werner J. A.; Buch, Kenneth A.
Results from highly resolved three-dimensional spatio-temporal measurements of the conserved scalar field zeta(x,t) in a turbulent shear flow. Each of these experiments consists of 256 to the 3rd individual point measurements of the local instantaneous conserved scalar value in the flow. The spatial and temporal resolution of these measurements reach beyond the local Kolmogorov scale and resolve the local strain-limited molecular diffusion scale in the flow. The results clearly show molecular mixing occurring in thin strained laminar diffusion layers in a turbulent flow.
NASA Astrophysics Data System (ADS)
Kleidis, K.; Oikonomou, V. K.
2017-04-01
In this work we shall investigate how to realize a cosmological evolution which describes all the evolution eras of our Universe, by using scalar-tensor theories. Particularly, we shall use single scalar and two-scalar theories, and by employing several well known reconstruction schemes, we shall investigate which scalar-tensor theories can realize the unification cosmology. For both the single and two-scalar theories, we find the kinetic terms and the potential of the theory and we also address the issue of the stability of the solutions towards linear perturbations. As we show, in the two-scalar description no instabilities occur, but in the single scalar description, certain solutions are unstable. Also we demonstrate that in the single scalar case, the power spectrum corresponding to early times is nearly scale invariant and compatible with the latest observational data. Finally, we perform an analysis of the effective equation of state, and we show that the EoS describes in a unified way early and late-time acceleration, and in addition it also describes the radiation and matter domination era between the acceleration eras.
Fuzzy Physics: A Brief Overview of Noncommutative Geometry in Physics
NASA Astrophysics Data System (ADS)
Maceda, Marco
2011-10-01
Noncommutative geometry (NCG) is a mathematical tool which has been used in the search for a quantum theory of gravity. However, its application is not limited to this field. In this brief note we present different uses of NCG in Theoretical Physics.
Geometric scalar theory of gravity
Novello, M.; Bittencourt, E.; Goulart, E.; Salim, J.M.; Toniato, J.D.; Moschella, U. E-mail: eduhsb@cbpf.br E-mail: egoulart@cbpf.br E-mail: toniato@cbpf.br
2013-06-01
We present a geometric scalar theory of gravity. Our proposal will be described using the ''background field method'' introduced by Gupta, Feynman, Deser and others as a field theory formulation of general relativity. We analyze previous criticisms against scalar gravity and show how the present proposal avoids these difficulties. This concerns not only the theoretical complaints but also those related to observations. In particular, we show that the widespread belief of the conjecture that the source of scalar gravity must be the trace of the energy-momentum tensor — which is one of the main difficulties to couple gravity with electromagnetic phenomenon in previous models — does not apply to our geometric scalar theory. From the very beginning this is not a special relativistic scalar gravity. The adjective ''geometric'' pinpoints its similarity with general relativity: this is a metric theory of gravity. Some consequences of this new scalar theory are explored.
Pair creation in noncommutative space-time
NASA Astrophysics Data System (ADS)
Hamil, B.; Chetouani, L.
2016-09-01
By taking two interactions, the Volkov plane wave and a constant electromagnetic field, the probability related to the process of pair creation from the vacuum is exactly and analytically determined via the Schwinger method in noncommutative space-time. For the plane wave, it is shown that the probability is simply null and for the electromagnetic wave it is found that the expression of the probability has a similar form to that obtained by Schwinger in a commutative space-time. For a certain critical value of H, the probability is simply equal to 1.
NASA Astrophysics Data System (ADS)
Hashino, Katsuya; Kakizaki, Mitsuru; Kanemura, Shinya; Ko, Pyungwon; Matsui, Toshinori
2017-03-01
We calculate the spectrum of gravitational waves originated from strongly first order electroweak phase transition in the extended Higgs model with a real singlet scalar field. In order to calculate the bubble nucleation rate, we perform a two-field analysis and evaluate bounce solutions connecting the true and the false vacua using the one-loop effective potential at finite temperatures. Imposing the Sakharov condition of the departure from thermal equilibrium for baryogenesis, we survey allowed regions of parameters of the model. We then investigate the gravitational waves produced at electroweak bubble collisions in the early Universe, such as the sound wave, the bubble wall collision and the plasma turbulence. We find that the strength at the peak frequency can be large enough to be detected at future space-based gravitational interferometers such as eLISA, DECIGO and BBO. Predicted deviations in the various Higgs boson couplings are also evaluated at the zero temperature, and are shown to be large enough too. Therefore, in this model strongly first order electroweak phase transition can be tested by the combination of the precision study of various Higgs boson couplings at the LHC, the measurement of the triple Higgs boson coupling at future lepton colliders and the shape of the spectrum of gravitational wave detectable at future gravitational interferometers.
Full Field Scalar Measurements in a Pulsating Helium Jet using Rainbow Schlieren Deflectometry
NASA Technical Reports Server (NTRS)
Pasumarthi, Kasyap S.
2000-01-01
The flow structure of a pulsating helium jet was investigated using quantitative rainbow schlieren deflectometry. The operating parameters included the tube inside diameter, the jet Reynolds number and the jet Richardson number. The jet structure was characterized by the frequency spectrum, temporal evolution of the oscillations and mean and root-mean-square profiles of the species mole fraction, which in this case, was helium. Experiments were conducted using a variable nozzle facility. Angular deflection data were obtained using rainbow schlieren deflectometry across full field of color images taken at a temporal resolution of 60Hz. The flicker cycle was analyzed by instantaneous rainbow schlieren images, contour plots of deflection angle and helium mole fraction placed sequentially in time. Two observe the flow downstream, the tube was lowered with respect to the optical setup and images were taken at different axial planes. In this way, the laminar, transition and turbulent regions of the jet flow were observed. Abel inversion algorithm was utilized to reconstruct the refractive index field from the measurements of the beam deflection angle. The concentration field was then generated from the refractive index field. The phenomenon of vortex initiation and propagation in the flicker cycle was described by correlating the ray deflection angle and concentration contour plots. Experiments in the flickering jet reveal global oscillation in the flow field. The effect of jet exit Reynolds number and jet Richardson number on the flickering frequency was analyzed. The effect of jet Richardson number was more pronounced than that of the jet exit Reynolds number. The flow field was studies quantitatively in terms of temporal evolution and statistical description of helium mole fraction.
Nondiagonal Values of the Heat Kernel for Scalars in a Constant Electromagnetic Field
NASA Astrophysics Data System (ADS)
Kalinichenko, I. S.; Kazinski, P. O.
2017-03-01
An original method for finding the nondiagonal values of the heat kernel associated with the wave operator Fourier-transformed in time is proposed for the case of a constant external electromagnetic field. The connection of the trace of such a heat kernel to the one-loop correction to the grand thermodynamic potential is indicated. The structure of its singularities is analyzed.
NASA Astrophysics Data System (ADS)
Ghiti, M. F.; Mebarki, N.; Aissaoui, H.
2015-08-01
The noncommutative Bianchi I curved space-time vierbeins and spin connections are derived. Moreover, the corresponding noncommutative Dirac equation as well as its solutions are presented. As an application within the quantum field theory approach using Bogoliubov transformations, the von Neumann fermion-antifermion pair creation quantum entanglement entropy is studied. It is shown that its behavior is strongly dependent on the value of the noncommutativity θ parameter, k⊥-modes frequencies and the structure of the curved space-time. Various discussions of the obtained features are presented.
NASA Astrophysics Data System (ADS)
Grosse, Harald; Wulkenhaar, Raimar
2014-08-01
We study quartic matrix models with partition function exp(trace). The integral is over the space of Hermitean -matrices, the external matrix E encodes the dynamics, is a scalar coupling constant and the matrix J is used to generate correlation functions. For E not a multiple of the identity matrix, we prove a universal algebraic recursion formula which gives all higher correlation functions in terms of the 2-point function and the distinct eigenvalues of E. The 2-point function itself satisfies a closed non-linear equation which must be solved case by case for given E. These results imply that if the 2-point function of a quartic matrix model is renormalisable by mass and wavefunction renormalisation, then the entire model is renormalisable and has vanishing β-function. As the main application we prove that Euclidean -quantum field theory on four-dimensional Moyal space with harmonic propagation, taken at its self-duality point and in the infinite volume limit, is exactly solvable and non-trivial. This model is a quartic matrix model, where E has for the same spectrum as the Laplace operator in four dimensions. Using the theory of singular integral equations of Carleman type we compute (for and after renormalisation of ) the free energy density (1/volume) log exactly in terms of the solution of a non-linear integral equation. Existence of a solution is proved via the Schauder fixed point theorem. The derivation of the non-linear integral equation relies on an assumption which in subsequent work is verified for coupling constants.
NASA Astrophysics Data System (ADS)
Rybnikov, A. K.
2017-01-01
The paper is devoted to the investigation, using the method of Cartan-Laptev, of the differential-geometric structure associated with a Lagrangian L, depending on a function z of the variables t, x 1,..., x n and its partial derivatives. Lagrangians of this kind are considered in theoretical physics (in field theory). Here t is interpreted as time, and x 1,..., x n as spatial variables. The state of the field is characterized by a function z( t, x 1,..., x n ) (a field function) satisfying the Euler equation, which corresponds to the variational problem for the action integral. In the present paper, the variables z( t, x 1,..., x n are regarded as adapted local coordinates of a bundle of general type M with n-dimensional fibers and 1-dimensional base (here the variable t is simultaneously a local coordinate on the base). If we agree to call t time, and a typical fiber an n-dimensional space, then M can be called the spatiotemporal bundle manifold. We consider the variables t, x 1,..., x n , z (i.e., the variables t, x 1,..., x n with the added variable z) as adapted local coordinates in the bundle H over the fibered base M. The Lagrangian L, which is a coefficient in the differential form of the variational action integral in the integrand, is a relative invariant given on the manifold J 1 H (the manifold of 1-jets of the bundle H). In the present paper, we construct a tensor with components Λ00, Λ0 i , Λ ij (Λ ij = Λ ji ) which is generated by the fundamental object of the structure associated with the Lagrangian. This tensor is an invariant (with respect to admissible transformations the variables t, x 1,..., x n , z) analog of the energy-momentum tensor of the classical theory of physical fields. We construct an invariant I, a vector G i , and a bivalent tensor G jk generated by the Lagrangian. We also construct a relative invariant of E (in the paper, we call it the Euler relative invariant) such that the equation E = 0 is an invariant form of the Euler
NASA Astrophysics Data System (ADS)
Huang, Zhiming; Situ, Haozhen
2017-02-01
In this article, the dynamics of quantum correlation and coherence for two atoms interacting with a bath of fluctuating massless scalar field in the Minkowski vacuum is investigated. We firstly derive the master equation that describes the system evolution with initial Bell-diagonal state. Then we discuss the system evolution for three cases of different initial states: non-zero correlation separable state, maximally entangled state and zero correlation state. For non-zero correlation initial separable state, quantum correlation and coherence can be protected from vacuum fluctuations during long time evolution when the separation between the two atoms is relatively small. For maximally entangled initial state, quantum correlation and coherence overall decrease with evolution time. However, for the zero correlation initial state, quantum correlation and coherence are firstly generated and then drop with evolution time; when separation is sufficiently small, they can survive from vacuum fluctuations. For three cases, quantum correlation and coherence first undergo decline and then fluctuate to relatively stable values with the increasing distance between the two atoms. Specially, for the case of zero correlation initial state, quantum correlation and coherence occur periodically revival at fixed zero points and revival amplitude declines gradually with increasing separation of two atoms.
NASA Astrophysics Data System (ADS)
Li, Bohua; Shapiro, Paul R.; Rindler-Daller, Tanja
2017-01-01
We consider an alternative to WIMP cold dark matter (CDM), ultralight bosonic dark matter (m≥10-22 eV) described by a complex scalar field (SFDM), of which the comoving particle number density is conserved after particle production during standard reheating (w=p/ρ=0). In a ΛSFDM universe, SFDM starts relativistic, evolving from stiff (w=1) to radiation-like (w=1/3), before becoming nonrelativistic at late times (w=0). Thus, before the familiar radiation-dominated phase, there is an even earlier phase of stiff-SFDM-domination, during which the expansion rate is higher than in ΛCDM. The transitions between these phases, determined by SFDM particle mass m, and coupling strength λ, of a quartic self-interaction, are therefore constrained by cosmological observables, particularly Neff, the effective number of neutrino species during BBN, and zeq, the redshift of matter-radiation equality. Furthermore, since the homogeneous energy density contributed by the stochastic gravitational wave background (SGWB) from inflation is amplified during the stiff phase, relative to the other components, the SGWB can contribute a radiation-like component large enough to affect these observables. This same amplification makes possible detection of this SGWB at high frequencies by current laser interferometer experiments, e.g., aLIGO/Virgo, eLISA. For SFDM particle parameters that satisfy these cosmological constraints, the amplified SGWB is detectable by aLIGO, for values of tensor-to-scalar ratio r currently allowed by CMB polarization measurements, for a broad range of possible reheat temperatures Tre. For a given r, if SFDM parameters marginally satisfy cosmological constraints (maximizing total SGWB energy density), the SGWB is maximally detectable when modes that reenter the horizon when reheating ends have frequencies in the 10-50 Hz aLIGO band today. For example, if r=0.01, the maximally detectable model for (λ/(mc2)2, m)=(10-18 eV-1cm3, 8×10-20 eV) has Tre=104 GeV, for
Akarsu, Özgür; Kumar, Suresh; Myrzakulov, R.; Sami, M.; Xu, Lixin E-mail: sukuyd@gmail.com E-mail: samijamia@gmail.com
2014-01-01
In this paper, we consider a simple form of expansion history of Universe referred to as the hybrid expansion law - a product of power-law and exponential type of functions. The ansatz by construction mimics the power-law and de Sitter cosmologies as special cases but also provides an elegant description of the transition from deceleration to cosmic acceleration. We point out the Brans-Dicke realization of the cosmic history under consideration. We construct potentials for quintessence, phantom and tachyon fields, which can give rise to the hybrid expansion law in general relativity. We investigate observational constraints on the model with hybrid expansion law applied to late time acceleration as well as to early Universe a la nucleosynthesis.
Blaga, Robert
2015-12-07
We investigate the energy radiated by an inertial scalar charge evolving in the expanding Poincaré patch of de Sitter spacetime, in the framework of scalar QED perturbation theory. We approximate the transition amplitude in the small expansion parameter limit and show that the leading contribution to the radiated energy has the form of the energy radiated by an accelerated particle in Minkowski space.
Butera, P; Pernici, M
2012-02-01
High-temperature expansions are presently the only viable approach to the numerical calculation of the higher susceptibilities for the spin and the scalar-field models on high-dimensional lattices. The critical amplitudes of these quantities enter into a sequence of universal amplitude ratios that determine the critical equation of state. We have obtained a substantial extension, through order 24, of the high-temperature expansions of the free energy (in presence of a magnetic field) for the Ising models with spin s≥1/2 and for the lattice scalar-field theory with quartic self-interaction on the simple-cubic and the body-centered-cubic lattices in four, five, and six spatial dimensions. A numerical analysis of the higher susceptibilities obtained from these expansions yields results consistent with the widely accepted ideas, based on the renormalization group and the constructive approach to Euclidean quantum field theory, concerning the no-interaction ("triviality") property of the continuum (scaling) limit of spin-s Ising and lattice scalar-field models at and above the upper critical dimensionality.
Constraining spacetime noncommutativity with primordial nucleosynthesis
Horvat, Raul; Trampetic, Josip
2009-04-15
We discuss a constraint on the scale {lambda}{sub NC} of noncommutative (NC) gauge field theory arising from consideration of the big bang nucleosynthesis of light elements. The propagation of neutrinos in the NC background described by an antisymmetric tensor {theta}{sup {mu}}{sup {nu}} does result in a tree-level vectorlike coupling to photons in a generation-independent manner, raising thus a possibility to have an appreciable contribution of three light right-handed (RH) fields to the energy density of the Universe at nucleosynthesis time. Considering elastic scattering processes of the RH neutrinos off charged plasma constituents at a given cosmological epoch, we obtain for a conservative limit on an effective number of additional doublet neutrinos {delta}N{sub {nu}}=1, a bound {lambda}{sub NC} > or approx. 3 TeV. With a more stringent requirement, {delta}N{sub {nu}} < or approx. 0.2, the bound is considerably improved, {lambda}{sub NC} > or approx. 10{sup 3} TeV. For our bounds the {theta} expansion of the NC action stays always meaningful, since the decoupling temperature of the RH species is perseveringly much less than the inferred bound for the scale of noncommutativity.
On the regularity of the covariance matrix of a discretized scalar field on the sphere
NASA Astrophysics Data System (ADS)
Bilbao-Ahedo, J. D.; Barreiro, R. B.; Herranz, D.; Vielva, P.; Martínez-González, E.
2017-02-01
We present a comprehensive study of the regularity of the covariance matrix of a discretized field on the sphere. In a particular situation, the rank of the matrix depends on the number of pixels, the number of spherical harmonics, the symmetries of the pixelization scheme and the presence of a mask. Taking into account the above mentioned components, we provide analytical expressions that constrain the rank of the matrix. They are obtained by expanding the determinant of the covariance matrix as a sum of determinants of matrices made up of spherical harmonics. We investigate these constraints for five different pixelizations that have been used in the context of Cosmic Microwave Background (CMB) data analysis: Cube, Icosahedron, Igloo, GLESP and HEALPix, finding that, at least in the considered cases, the HEALPix pixelization tends to provide a covariance matrix with a rank closer to the maximum expected theoretical value than the other pixelizations. The effect of the propagation of numerical errors in the regularity of the covariance matrix is also studied for different computational precisions, as well as the effect of adding a certain level of noise in order to regularize the matrix. In addition, we investigate the application of the previous results to a particular example that requires the inversion of the covariance matrix: the estimation of the CMB temperature power spectrum through the Quadratic Maximum Likelihood algorithm. Finally, some general considerations in order to achieve a regular covariance matrix are also presented.
Vector and Scalar Field Visualization Techniques for Multispacecraft Space Physics Missions
NASA Astrophysics Data System (ADS)
Roberts, D. A.; Rezapkin, V.; Coleman, J.; Boller, R.
2003-12-01
We present a new way of visualizing data that makes it possible to view simultaneously a large number of measured time series on the orbits of a large number of spacecraft. We shall show examples of using our ``ViSBARD" software to illucidate the structure of the solar wind upstream of the Earth, as well as cases showing magnetic field and particle information from many spacecraft in the magnetosphere. Each measurement is presented by a glyph (symbol or vector) at each point in time and at the position it was measured in the 3-D space. The ecliptic plane and, if appropriate, magnetospheric surfaces are presented to provide context. The software allows scrolling and zooming in time; the usual pan, zoom, and rotate in space; scaling of the data variables; a choice of color palettes; and 2-D graphs that scroll and scale in concert with the 3-D representation to aid the interpretation of the 3-D visualization. As the interval of data changes, the resolution automatically adjusts to maintain rapid response and to limit memory usage. A kinematic projection of all quantities yields a ``spatial view" that is particularly effective in fast flows such as the solar wind. The center of rotation can be moved to any data point to allow a detailed examination of a particular region. The software supports stereo viewing. Future extensions will incorporate the viewing of images as well as the simultaneous viewing of data and models.
NASA Astrophysics Data System (ADS)
Rejon-Barrera, Fernando; Robbins, Daniel
2016-01-01
We work out all of the details required for implementation of the conformal bootstrap program applied to the four-point function of two scalars and two vectors in an abstract conformal field theory in arbitrary dimension. This includes a review of which tensor structures make appearances, a construction of the projectors onto the required mixed symmetry representations, and a computation of the conformal blocks for all possible operators which can be exchanged. These blocks are presented as differential operators acting upon the previously known scalar conformal blocks. Finally, we set up the bootstrap equations which implement crossing symmetry. Special attention is given to the case of conserved vectors, where several simplifications occur.
On the Chern-Gauss-Bonnet theorem for the noncommutative 4-sphere
NASA Astrophysics Data System (ADS)
Arnlind, Joakim; Wilson, Mitsuru
2017-01-01
We construct a differential calculus over the noncommutative 4-sphere in the framework of pseudo-Riemannian calculi, and show that for every metric in a conformal class of perturbations of the round metric, there exists a unique metric and torsion-free connection. Furthermore, we find a localization of the projective module corresponding to the space of vector fields, which allows us to formulate a Chern-Gauss-Bonnet type theorem for the noncommutative 4-sphere.
Regularization of two-dimensional supersymmetric Yang-Mills theory via non-commutative geometry
NASA Astrophysics Data System (ADS)
Valavane, K.
2000-11-01
The non-commutative geometry is a possible framework to regularize quantum field theory in a non-perturbative way. This idea is an extension of the lattice approximation by non-commutativity that allows us to preserve symmetries. The supersymmetric version is also studied and more precisely in the case of the Schwinger model on a supersphere. This paper is a generalization of this latter work to more general gauge groups.
NASA Astrophysics Data System (ADS)
Momeni, D.; Setare, M. R.; Myrzakulov, Ratbay
2012-09-01
We study analytical properties of the Stuckelberg holographic superconductors with Weyl corrections. We obtain the minimum critical temperature as a function of the mass of the scalar field m2. We show that in limit of the m2 = -3, T Minc≈ 0.158047√ [3]{ρ } which is close to the numerical estimate Tc Numerical≈ 0.170√ [3]{ρ }. Further we show that the mass of the scalar field is bounded from below by the m2mc^2 where mc2 = -5.40417. This lower bound is weaker and different from the previous lower bound m2 = -3 predicted by stability analysis. We show that in the Breitenlohner-Freedman bound, the critical temperature remains finite. Explicitly, we prove that here there exists a linear relation between
Numazaki, Kazuya; Imai, Hiromitsu; Morinaga, Atsuo
2010-03-15
The second-order Zeeman effect of the sodium clock transition in a weak magnetic field of less than 50 {mu}T was measured as the scalar Aharonov-Bohm phase by two-photon stimulated Raman atom interferometry. The ac Stark effect of the Raman pulse was canceled out by adopting an appropriate intensity ratio of two photons in the Raman pulse. The Ramsey fringes for the pulse separation of 7 ms were obtained with a phase uncertainty of {pi}/200 rad. The nondispersive feature of the scalar Aharonov-Bohm phase was clearly demonstrated through 18 fringes with constant amplitude. The Breit-Rabi formula of the sodium clock transition was verified to be {Delta}{nu}=(0.222{+-}0.003)x10{sup 12}xB{sup 1.998{+-}0.004} in a magnetic field of less than 50 {mu}T.
A perspective on non-commutative quantum gravity
NASA Astrophysics Data System (ADS)
Martins, Rachel A. D.
2015-06-01
In this paper, we present some of the concepts underlying a program of non-commutative quantum gravity and recall some of the results. This program includes a novel approach to spectral triple categorification and also a precise connection between Fell bundles and Connes' non-commutative geometry. Motivated by topics in quantization of the non-commutative standard model and introduction of algebraic techniques and concepts into quantum gravity (following for example Crane, Baez and Barrett), we define spectral C*-categories, which are deformed spectral triples in a sense made precise. This definition gives to representations of a C*-category on a small category of Hilbert spaces and bounded linear maps, the interpretation of a topological quantum field theory. The construction passes two mandatory tests: (i) there is a classical limit theorem reproducing a Riemannian spin manifold manifesting Connes' and Schücker's non-commutative counterpart of Einstein's equivalence principle, and (ii) there is consistency with the experimental fermion mass matrix. We also present an algebra invariant taking the form of a partition function arising from a C*-bundle dynamical system in connection with C*-subalgebra theory.
Noncommuting Momenta of Topological Solitons
NASA Astrophysics Data System (ADS)
Watanabe, Haruki; Murayama, Hitoshi
2014-05-01
We show that momentum operators of a topological soliton may not commute among themselves when the soliton is associated with the second cohomology H2 of the target space. The commutation relation is proportional to the winding number, taking a constant value within each topological sector. The noncommutativity makes it impossible to specify the momentum of a topological soliton, and induces a Magnus force.
NASA Astrophysics Data System (ADS)
Milton, Kimball A.; Fulling, Stephen A.; Parashar, Prachi; Kalauni, Pushpa; Murphy, Taylor
2016-04-01
Motivated by a desire to understand quantum fluctuation energy densities and stress within a spatially varying dielectric medium, we examine the vacuum expectation value for the stress tensor of a scalar field with arbitrary conformal parameter, in the background of a given potential that depends on only one spatial coordinate. We regulate the expressions by incorporating a temporal-spatial cutoff in the (imaginary) time and transverse-spatial directions. The divergences are captured by the zeroth- and second-order WKB approximations. Then the stress tensor is "renormalized" by omitting the terms that depend on the cutoff. The ambiguities that inevitably arise in this procedure are both duly noted and restricted by imposing certain physical conditions; one result is that the renormalized stress tensor exhibits the expected trace anomaly. The renormalized stress tensor exhibits no pressure anomaly, in that the principle of virtual work is satisfied for motions in a transverse direction. We then consider a potential that defines a wall, a one-dimensional potential that vanishes for z <0 and rises like zα, α >0 , for z >0 . Previously, the stress tensor had been computed outside of the wall, whereas now we compute all components of the stress tensor in the interior of the wall. The full finite stress tensor is computed numerically for the two cases where explicit solutions to the differential equation are available, α =1 and 2. The energy density exhibits an inverse linear divergence as the boundary is approached from the inside for a linear potential, and a logarithmic divergence for a quadratic potential. Finally, the interaction between two such walls is computed, and it is shown that the attractive Casimir pressure between the two walls also satisfies the principle of virtual work (i.e., the pressure equals the negative derivative of the energy with respect to the distance between the walls).
Zhang Xin
2009-05-15
In this work, we consider the cosmological constraints on the holographic Ricci dark energy proposed by Gao et al.[Phys. Rev. D 79, 043511 (2009)], by using the observational data currently available. The main characteristic of holographic Ricci dark energy is governed by a positive numerical parameter {alpha} in the model. When {alpha}<1/2, the holographic Ricci dark energy will exhibit a quintomlike behavior; i.e., its equation of state will evolve across the cosmological-constant boundary w=-1. The parameter {alpha} can be determined only by observations. Thus, in order to characterize the evolving feature of dark energy and to predict the fate of the Universe, it is of extraordinary importance to constrain the parameter {alpha} by using the observational data. In this paper, we derive constraints on the holographic Ricci dark energy model from the latest observational data including the Union sample of 307 type Ia supernovae, the shift parameter of the cosmic microwave background given by the five-year Wilkinson Microwave Anisotropy Probe observations, and the baryon acoustic oscillation measurement from the Sloan Digital Sky Survey. The joint analysis gives the best-fit results (with 1{sigma} uncertainty): {alpha}=0.359{sub -0.025}{sup +0.024} and {omega}{sub m0}=0.318{sub -0.024}{sup +0.026}. That is to say, according to the observations, the holographic Ricci dark energy takes on the quintom feature. Finally, in light of the results of the cosmological constraints, we discuss the issue of the scalar-field dark energy reconstruction, based on the scenario of the holographic Ricci vacuum energy.
Batalin-Fradkin-Tyutin embedding of noncommutative chiral bosons
Kim, Wontae; Park, Young-Jai; Shin, Hyeonjoon; Yoon, Myung Seok
2007-04-15
A two dimensional model of chiral bosons in noncommutative field space is considered in the framework of the Batalin-Fradkin-Tyutin Hamiltonian embedding method converting the second-class constrained system into the first-class one. The symmetry structure associated with the first-class constraints is explored and the propagation speed of fields is equivalent to that of the second-class constraint system.
Path-integral action of a particle in the noncommutative plane.
Gangopadhyay, Sunandan; Scholtz, Frederik G
2009-06-19
Noncommutative quantum mechanics can be viewed as a quantum system represented in the space of Hilbert-Schmidt operators acting on noncommutative configuration space. Taking this as a departure point, we formulate a coherent state approach to the path-integral representation of the transition amplitude. From this we derive an action for a particle moving in the noncommutative plane and in the presence of an arbitrary potential. We find that this action is nonlocal in time. However, this nonlocality can be removed by introducing an auxilary field, which leads to a second class constrained system that yields the noncommutative Heisenberg algebra upon quantization. Using this action, the propagator of the free particle and harmonic oscillator are computed explicitly.
NASA Astrophysics Data System (ADS)
Tsapalis, Antonios S.
This thesis deals with two topics in lattice field theories. In the first part we discuss aspects of renormalization group flow and non-perturbative improvement of actions for scalar theories regularized on a lattice. We construct a perfect action, an action which is free of lattice artifacts, for a given theory. It is shown how a good approximation to the perfect action-referred to as classically perfect-can be constructed based on a well-defined blocking scheme for the O(3) non-linear σ-model. We study the O(N) non- linear σ-model in the large-N limit and derive analytically its perfect action. This action is applied to the O(3) model on a square lattice. The Wolff cluster algorithm is used to simulate numerically the system. We perform scaling tests and discuss the scaling properties of the large- N inspired perfect action as opposed to the standard and the classically perfect action. In the second part we present a new formulation for a quantum field theory with Abelian gauge symmetry. A Hamiltonian is constructed on a four-dimensional Euclidean space-time lattice which is invariant under local transformations. The model is formulated as a 5- dimensional path integral of discrete variables. We argue that dimensional reduction will allow us to study the behavior of the standard compact U(1) gauge theory in 4-d. Based on the idea of the loop- cluster algorithm for quantum spins, we present the construction of a flux-cluster algorithm for the U(1) quantum link model for the spin-1/2 quantization of the electric flux. It is shown how improved estimators for Wilson loop expectation values can be defined. This is important because the Wilson loops are traditionally used to identify confining and Coulomb phases in gauge theories. Our study indicates that the spin-1/2 U(1) quantum link model is strongly coupled for all bare coupling values we examined. (Copies available exclusively from MIT Libraries, Rm. 14-0551, Cambridge, MA 02139-4307. Ph. 617-253-5668; Fax 617-253-1690.)
Noncommutativity from exact renormalization group dualities
NASA Astrophysics Data System (ADS)
Gangopadhyay, Sunandan; Scholtz, Frederik G.
2014-08-01
Here we demonstrate, first, the construction of dualities using the exact renormalization group approach and, second, that spatial noncommutativity can emerge as such a duality. This is done in a simple quantum mechanical setting that establishes an exact duality between the commutative and noncommutative quantum Hall systems with harmonic interactions. It is also demonstrated that this link can be understood as a blocking (coarse graining) transformation in time that relates commutative and noncommutative degrees of freedom.
Constrained inflaton due to a complex scalar
Budhi, Romy H. S.; Kashiwase, Shoichi; Suematsu, Daijiro
2015-09-14
We reexamine inflation due to a constrained inflaton in the model of a complex scalar. Inflaton evolves along a spiral-like valley of special scalar potential in the scalar field space just like single field inflation. Sub-Planckian inflaton can induce sufficient e-foldings because of a long slow-roll path. In a special limit, the scalar spectral index and the tensor-to-scalar ratio has equivalent expressions to the inflation with monomial potential φ{sup n}. The favorable values for them could be obtained by varying parameters in the potential. This model could be embedded in a certain radiative neutrino mass model.
Canonical quantum gravity on noncommutative space-time
NASA Astrophysics Data System (ADS)
Kober, Martin
2015-06-01
In this paper canonical quantum gravity on noncommutative space-time is considered. The corresponding generalized classical theory is formulated by using the Moyal star product, which enables the representation of the field quantities depending on noncommuting coordinates by generalized quantities depending on usual coordinates. But not only the classical theory has to be generalized in analogy to other field theories. Besides, the necessity arises to replace the commutator between the gravitational field operator and its canonical conjugated quantity by a corresponding generalized expression on noncommutative space-time. Accordingly the transition to the quantum theory has also to be performed in a generalized way and leads to extended representations of the quantum theoretical operators. If the generalized representations of the operators are inserted to the generalized constraints, one obtains the corresponding generalized quantum constraints including the Hamiltonian constraint as dynamical constraint. After considering quantum geometrodynamics under incorporation of a coupling to matter fields, the theory is transferred to the Ashtekar formalism. The holonomy representation of the gravitational field as it is used in loop quantum gravity opens the possibility to calculate the corresponding generalized area operator.
Non-commutative Nash inequalities
Kastoryano, Michael; Temme, Kristan
2016-01-15
A set of functional inequalities—called Nash inequalities—are introduced and analyzed in the context of quantum Markov process mixing. The basic theory of Nash inequalities is extended to the setting of non-commutative L{sub p} spaces, where their relationship to Poincaré and log-Sobolev inequalities is fleshed out. We prove Nash inequalities for a number of unital reversible semigroups.
Group theoretical construction of planar noncommutative phase spaces
Ngendakumana, Ancille Todjihoundé, Leonard; Nzotungicimpaye, Joachim
2014-01-15
Noncommutative phase spaces are generated and classified in the framework of centrally extended anisotropic planar kinematical Lie groups as well as in the framework of noncentrally abelian extended planar absolute time Lie groups. Through these constructions the coordinates of the phase spaces do not commute due to the presence of naturally introduced fields giving rise to minimal couplings. By symplectic realizations methods, physical interpretations of generators coming from the obtained structures are given.
Cosmological power spectrum in a noncommutative spacetime
NASA Astrophysics Data System (ADS)
Kothari, Rahul; Rath, Pranati K.; Jain, Pankaj
2016-09-01
We propose a generalized star product that deviates from the standard one when the fields are considered at different spacetime points by introducing a form factor in the standard star product. We also introduce a recursive definition by which we calculate the explicit form of the generalized star product at any number of spacetime points. We show that our generalized star product is associative and cyclic at linear order. As a special case, we demonstrate that our recursive approach can be used to prove the associativity of standard star products for same or different spacetime points. The introduction of a form factor has no effect on the standard Lagrangian density in a noncommutative spacetime because it reduces to the standard star product when spacetime points become the same. We show that the generalized star product leads to physically consistent results and can fit the observed data on hemispherical anisotropy in the cosmic microwave background radiation.
Noncommutativity in the early universe
NASA Astrophysics Data System (ADS)
Oliveira-Neto, G.; Silva de Oliveira, M.; Monerat, G. A.; Corrêa Silva, E. V.
In the present work, we study the noncommutative version of a quantum cosmology model. The model has a Friedmann-Robertson-Walker (FRW) geometry, the matter content is a radiative perfect fluid and the spatial sections have zero constant curvature. In this model, the scale factor takes values in a bounded domain. Therefore, its quantum mechanical version has a discrete energy spectrum. We compute the discrete energy spectrum and the corresponding eigenfunctions. The energies depend on a noncommutative parameter β. We compute the scale factor expected value () for several values of β. For all of them, oscillates between maxima and minima values and never vanishes. It gives an initial indication that those models are free from singularities, at the quantum level. We improve this result by showing that if we subtract a quantity proportional to the standard deviation of a from , this quantity is still positive. The behavior, for the present model, is a drastic modification of the behavior in the corresponding commutative version of the present model. There, grows without limits with the time variable. Therefore, if the present model may represent the early stages of the universe, the results of the present paper give an indication that may have been, initially, bounded due to noncommutativity. We also compute the Bohmian trajectories for a, which are in accordance with , and the quantum potential Q. From Q, we may understand why that model is free from singularities, at the quantum level.
Schwarzschild black holes can wear scalar wigs.
Barranco, Juan; Bernal, Argelia; Degollado, Juan Carlos; Diez-Tejedor, Alberto; Megevand, Miguel; Alcubierre, Miguel; Núñez, Darío; Sarbach, Olivier
2012-08-24
We study the evolution of a massive scalar field surrounding a Schwarzschild black hole and find configurations that can survive for arbitrarily long times, provided the black hole or the scalar field mass is small enough. In particular, both ultralight scalar field dark matter around supermassive black holes and axionlike scalar fields around primordial black holes can survive for cosmological times. Moreover, these results are quite generic in the sense that fairly arbitrary initial data evolve, at late times, as a combination of those long-lived configurations.
NASA Astrophysics Data System (ADS)
Bittencourt, E.; Moschella, U.; Novello, M.; Toniato, J. D.
2016-06-01
We discuss a class of models for gravity based on a scalar field. The models include and generalize the old approach by Nordström which predated and, in some ways, inspired general relativity. The class include also a model that we have recently introduced and discussed in terms of its cosmological aspects (GSG). We present here a complete characterization of the Schwarschild geometry as a vacuum solution of GSG and sketch a discussion of the first post-Newtonian approximation.
Burns, Sean P.; Sun, Jielun; Lenschow, D.H.; Oncley, S.P.; Stephens, B.B.; Yi, C.; Anderson, D.E.; Hu, Jiawen; Monson, Russell K.
2011-01-01
Air temperature Ta, specific humidity q, CO2 mole fraction ??c, and three-dimensional winds were measured in mountainous terrain from five tall towers within a 1 km region encompassing a wide range of canopy densities. The measurements were sorted by a bulk Richardson number Rib. For stable conditions, we found vertical scalar differences developed over a "transition" region between 0.05 < Rib < 0.5. For strongly stable conditions (Rib > 1), the vertical scalar differences reached a maximum and remained fairly constant with increasing stability. The relationships q and ??c have with Rib are explained by considering their sources and sinks. For winds, the strong momentum absorption in the upper canopy allows the canopy sublayer to be influenced by pressure gradient forces and terrain effects that lead to complex subcanopy flow patterns. At the dense-canopy sites, soil respiration coupled with wind-sheltering resulted in CO2 near the ground being 5-7 ??mol mol-1 larger than aloft, even with strong above-canopy winds (near-neutral conditions). We found Rib-binning to be a useful tool for evaluating vertical scalar mixing; however, additional information (e.g., pressure gradients, detailed vegetation/topography, etc.) is needed to fully explain the subcanopy wind patterns. Implications of our results for CO2 advection over heterogenous, complex terrain are discussed. ?? 2010 Springer Science+Business Media B.V.
Noncommutative de Sitter and FRW spaces
NASA Astrophysics Data System (ADS)
Burić, Maja; Madore, John
2015-10-01
Several versions of fuzzy four-dimensional de Sitter space are constructed using the noncommutative frame formalism. Although all noncommutative spacetimes which are found have commutative de Sitter metric as a classical limit, the algebras and the differential calculi which define them have many differences, which we derive and discuss.
Effective Potential in Noncommutative BTZ Black Hole
NASA Astrophysics Data System (ADS)
Sadeghi, Jafar; Shajiee, Vahid Reza
2016-02-01
In this paper, we investigated the noncommutative rotating BTZ black hole and showed that such a space-time is not maximally symmetric. We calculated effective potential for the massive and the massless test particle by geodesic equations, also we showed effect of non-commutativity on the minimum mass of BTZ black hole.
NASA Astrophysics Data System (ADS)
Egorov, A. I.; Kashargin, P. E.; Sushkov, Sergey V.
2016-09-01
In 1921 Bach and Weyl derived the method of superposition to construct new axially symmetric vacuum solutions of general relativity. In this paper we extend the Bach-Weyl approach to non-vacuum configurations with massless scalar fields. Considering a phantom scalar field with the negative kinetic energy, we construct a multi-wormhole solution describing an axially symmetric superposition of N wormholes. The solution found is static, everywhere regular and has no event horizons. These features drastically tell the multi-wormhole configuration from other axially symmetric vacuum solutions which inevitably contain gravitationally inert singular structures, such as ‘struts’ and ‘membranes’, that keep the two bodies apart making a stable configuration. However, the multi-wormholes are static without any singular struts. Instead, the stationarity of the multi-wormhole configuration is provided by the phantom scalar field with the negative kinetic energy. Anther unusual property is that the multi-wormhole spacetime has a complicated topological structure. Namely, in the spacetime there exist 2 N asymptotically flat regions connected by throats.
Scalar graviton as dark matter
NASA Astrophysics Data System (ADS)
Pirogov, Yu. F.
2015-06-01
The basics of the theory of unimodular bimode gravity built on the principles of unimodular gauge invariance/relativity and general covariance are exposed. Besides the massless tensor graviton of General Relativity, the theory includes an (almost) massless scalar graviton treated as the gravitational dark matter. A spherically symmetric vacuum solution describing the coherent scalar-graviton field for the soft-core dark halos, with the asymptotically flat rotation curves, is demonstrated as an example.
Scalar graviton as dark matter
Pirogov, Yu. F.
2015-06-15
The basics of the theory of unimodular bimode gravity built on the principles of unimodular gauge invariance/relativity and general covariance are exposed. Besides the massless tensor graviton of General Relativity, the theory includes an (almost) massless scalar graviton treated as the gravitational dark matter. A spherically symmetric vacuum solution describing the coherent scalar-graviton field for the soft-core dark halos, with the asymptotically flat rotation curves, is demonstrated as an example.
Inflation and the Higgs Scalar
Green, Dan
2014-12-05
This note makes a self-contained exposition of the basic facts of big bang cosmology as they relate to inflation. The fundamental problems with that model are then explored. A simple scalar model of inflation is evaluated which provides the solution of those problems and makes predictions which will soon be definitively tested. The possibility that the recently discovered fundamental Higgs scalar field drives inflation is explored.
NASA Astrophysics Data System (ADS)
Wang, Chun-Xiao; Liu, Mo-Lin; Liu, Hong-Ya
2008-10-01
As one exact candidate of the higher dimensional black hole, the 5D Ricci Qat Schwarzschild-de Sitter black string space presents something interesting. In this paper, we give a numerical solution to the real scalar field around the Nariai black hole by the polynomial approximation. Unlike the previous tangent approximation, this fitting function makes a perfect match in the leading intermediate region and gives a good description near both the event and the cosmological horizons. We can read from our results that the wave is close to a harmonic one with the tortoise coordinate. Furthermore, with the actual radial coordinate the waves pile up almost equally near the both horizons.
The first search for sub-eV scalar fields via four-wave mixing at a quasi-parallel laser collider
NASA Astrophysics Data System (ADS)
Homma, Kensuke; Hasebe, Takashi; Kume, Kazuki
2014-08-01
A search for sub-eV scalar fields coupling to two photons has been performed via four-wave mixing at a quasi-parallel laser collider for the first time. The experiment demonstrates the novel approach of searching for resonantly produced sub-eV scalar fields by combining two-color laser fields in the vacuum. The aim of this paper is to provide the concrete experimental setup and the analysis method based on specific combinations of polarization states between incoming and outgoing photons, which is extendable to higher-intensity laser systems operated at high repetition rates. No significant signal of four-wave mixing was observed by combining a 0.2 μ J/0.75 ns pulse laser and a 2 mW CW laser on the same optical axis. Based on the prescription developed for this particular experimental approach, we obtained the upper limit at a confidence level of 95% on the coupling-mass relation.
NASA Astrophysics Data System (ADS)
Pejhan, Hamed; Rahbardehghan, Surena
2016-09-01
In a previous work [S. Rahbardehghan and H. Pejhan, Phys. Lett. B 750, 627 (2015)], we considered a simple brane-world model: a single four-dimensional brane embedded in a five-dimensional de Sitter (dS) space-time. Then, by including a conformally coupled scalar field in the bulk, we studied the induced Casimir energy-momentum tensor. Technically, the Krein-Gupta-Bleuler quantization scheme as a covariant and renormalizable quantum field theory in dS space was used to perform the calculations. In the present paper, we generalize this study to a less idealized, but physically motivated, scenario; namely, we consider Friedmann-Robertson-Walker (FRW) space-time which behaves asymptotically as a dS space-time. More precisely, we evaluate a Casimir energy-momentum tensor for a system with two D -dimensional curved branes on background of D +1 -dimensional FRW space-time with negative spatial curvature and a conformally coupled bulk scalar field that satisfied the Dirichlet boundary condition on the branes.
Time-dependent Aharonov-Bohm effect on the noncommutative space
NASA Astrophysics Data System (ADS)
Ma, Kai; Wang, Jian-Hua; Yang, Huan-Xiong
2016-08-01
We study the time-dependent Aharonov-Bohm effect on the noncommutative space. Because there is no net Aharonov-Bohm phase shift in the time-dependent case on the commutative space, therefore, a tiny deviation from zero indicates new physics. Based on the Seiberg-Witten map we obtain the gauge invariant and Lorentz covariant Aharonov-Bohm phase shift in general case on noncommutative space. We find there are two kinds of contribution: momentum-dependent and momentum-independent corrections. For the momentum-dependent correction, there is a cancellation between the magnetic and electric phase shifts, just like the case on the commutative space. However, there is a non-trivial contribution in the momentum-independent correction. This is true for both the time-independent and time-dependent Aharonov-Bohm effects on the noncommutative space. However, for the time-dependent Aharonov-Bohm effect, there is no overwhelming background which exists in the time-independent Aharonov-Bohm effect on both commutative and noncommutative space. Therefore, the time-dependent Aharonov-Bohm can be sensitive to the spatial noncommutativity. The net correction is proportional to the product of the magnetic fluxes through the fundamental area represented by the noncommutative parameter θ, and through the surface enclosed by the trajectory of charged particle. More interestingly, there is an anti-collinear relation between the logarithms of the magnetic field B and the averaged flux Φ / N (N is the number of fringes shifted). This nontrivial relation can also provide a way to test the spatial noncommutativity. For BΦ / N ∼ 1, our estimation on the experimental sensitivity shows that it can reach the 10 GeV scale. This sensitivity can be enhanced by using stronger magnetic field strength, larger magnetic flux, as well as higher experimental precision on the phase shift.
Ripoll, Jorge
2011-08-01
In this paper the expression for the radiative transfer equation (RTE) commonly used when describing light propagation in biological tissues is derived directly from the equation of energy conservation of Maxwell's equations (Poynting's theorem) by making use of a volume-averaged expression for the time-averaged flow of energy. The derivation is presented step by step with Maxwell's equations as the starting point, analyzing all approximations taken in order to arrive at the expression of the scalar RTE employed in biomedical applications, which neglects particle nonsphericity and orientation, depolarization, and coherence effects.
NASA Astrophysics Data System (ADS)
Muniz, Sérgio R.; Bagnato, Vanderlei S.; Bhattacharya, M.
2015-06-01
In a region free of currents, magnetostatics can be described by the Laplace equation of a scalar magnetic potential, and one can apply the same methods commonly used in electrostatics. Here, we show how to calculate the general vector field inside a real (finite) solenoid, using only the magnitude of the field along the symmetry axis. Our method does not require integration or knowledge of the current distribution and is presented through practical examples, including a nonuniform finite solenoid used to produce cold atomic beams via laser cooling. These examples allow educators to discuss the nontrivial calculation of fields off-axis using concepts familiar to most students, while offering the opportunity to introduce themes of current modern research.
Chiavazza, Enrico; Kubala, Eugen; Gringeri, Concetta V; Düwel, Stephan; Durst, Markus; Schulte, Rolf F; Menzel, Marion I
2013-02-01
Scalar coupling relaxation, which is usually only associated with closely resonant nuclei (e.g., (79)Br-(13)C), can be a very effective relaxation mechanism. While working on hyperpolarized [5-(13)C]glutamine, fast liquid-state polarization decay during transfer to the MRI scanner was observed. This behavior could hypothetically be explained by substantial T(1) shortening due to a scalar coupling contribution (type II) to the relaxation caused by the fast-relaxing quadrupolar (14)N adjacent to the (13)C nucleus in the amide group. This contribution is only effective in low magnetic fields (i.e., less than 800 μT) and prevents the use of molecules bearing the (13)C-amide group as hyperpolarized MRS/MRI probes. In the present work, this hypothesis is explored both theoretically and experimentally. The results show that high hyperpolarization levels can be retained using either a (15)N-labeled amide or by applying a magnetic field during transfer of the sample from the polarizer to the MRI scanner.
Spontaneous Scalarization: Dead or Alive?
NASA Astrophysics Data System (ADS)
Berti, Emanuele; Crispino, Luis; Gerosa, Davide; Gualtieri, Leonardo; Horbatsch, Michael; Macedo, Caio; Okada da Silva, Hector; Pani, Paolo; Sotani, Hajime; Sperhake, Ulrich
2015-04-01
In 1993, Damour and Esposito-Farese showed that a wide class of scalar-tensor theories can pass weak-field gravitational tests and exhibit nonperturbative strong-field deviations away from General Relativity in systems involving neutron stars. These deviations are possible in the presence of ``spontaneous scalarization,'' a phase transition similar in nature to spontaneous magnetization in ferromagnets. More than twenty years after the original proposal, binary pulsar experiments have severely constrained the possibility of spontaneous scalarization occurring in nature. I will show that these experimental constraints have important implications for the torsional oscillation frequencies of neutron stars and for the so-called ``I-Love-Q'' relations in scalar-tensor theories. I will also argue that there is still hope to observe strong scalarization effects, despite the strong experimental bounds on the original mechanism. In particular, I will discuss two mechanisms that could produce strong scalarization in neutron stars: anisotropy and multiscalarization. This work was supported by NSF CAREER Award PHY-1055103.
NASA Astrophysics Data System (ADS)
Martinetti, P.; Wallet, J.-C.; Amelino-Camelia, G.
2015-08-01
The conference Conceptual and Technical Challenges for Quantum Gravity at Sapienza University of Rome, from 8 to 12 September 2014, has provided a beautiful opportunity for an encounter between different approaches and different perspectives on the quantum-gravity problem. It contributed to a higher level of shared knowledge among the quantum-gravity communities pursuing each specific research program. There were plenary talks on many different approaches, including in particular string theory, loop quantum gravity, spacetime noncommutativity, causal dynamical triangulations, asymptotic safety and causal sets. Contributions from the perspective of philosophy of science were also welcomed. In addition several parallel sessions were organized. The present volume collects contributions from the Noncommutative Geometry and Quantum Gravity parallel session4, with additional invited contributions from specialists in the field. Noncommutative geometry in its many incarnations appears at the crossroad of many researches in theoretical and mathematical physics: • from models of quantum space-time (with or without breaking of Lorentz symmetry) to loop gravity and string theory, • from early considerations on UV-divergencies in quantum field theory to recent models of gauge theories on noncommutative spacetime, • from Connes description of the standard model of elementary particles to recent Pati-Salam like extensions. This volume provides an overview of these various topics, interesting for the specialist as well as accessible to the newcomer. 4partially funded by CNRS PEPS /PTI ''Metric aspect of noncommutative geometry: from Monge to Higgs''
NASA Astrophysics Data System (ADS)
Lasukov, V. V.
2012-06-01
It is shown that negative Scalars can claim to be the object referred to as black holes, therefore observation of black holes means observation of Scalars. In contrast to blackholes, negative Scalars contain no singularity inside. Negative Scalars can be observed from the effect of generation of ordinary matter by the Lemaître primordial atom.
Towards understanding turbulent scalar mixing
NASA Technical Reports Server (NTRS)
Girimaji, Sharath S.
1992-01-01
In an effort towards understanding turbulent scalar mixing, we study the effect of molecular mixing, first in isolation and then by accounting for the effects of the velocity field. The chief motivation for this approach stems from the strong resemblance of the scalar probability density function (PDF) obtained from the scalar field evolving from the heat conduction equation that arises in a turbulent velocity field. However, the evolution of the scalar dissipation is different for the two cases. We attempt to account for these differences, which are due to the velocity field, using a Lagrangian frame analysis. After establishing the usefulness of this approach, we use the heat-conduction simulations (HCS), in lieu of the more expensive direct numerical simulations (DNS), to study many of the less understood aspects of turbulent mixing. Comparison between the HCS data and available models are made whenever possible. It is established that the beta PDF characterizes the evolution of the scalar PDF during mixing from all types of non-premixed initial conditions.
Duality and gauge invariance of non-commutative spacetime Podolsky electromagnetic theory
NASA Astrophysics Data System (ADS)
Abreu, Everton M. C.; Fernandes, Rafael L.; Mendes, Albert C. R.; Neto, Jorge Ananias; Neves, Mario, Jr.
2017-01-01
The interest in higher derivative field theories has its origin mainly in their influence concerning the renormalization properties of physical models and to remove ultraviolet divergences. In this paper, we have introduced the non-commutative (NC) version of the Podolsky theory and we investigated the effect of the non-commutativity over its original gauge invariance property. We have demonstrated precisely that the non-commutativity spoiled the primary gauge invariance of the original action under this primary gauge transformation. After that we have used the Noether dualization technique to obtain a dual and gauge invariant action. We have demonstrated that through the introduction of a Stueckelberg field in this NC model, we can also recover the primary gauge invariance. In this way, we have accomplished a comparison between both methods.
Noncommutative Riemannian geometry on graphs
NASA Astrophysics Data System (ADS)
Majid, Shahn
2013-07-01
We show that arising out of noncommutative geometry is a natural family of edge Laplacians on the edges of a graph. The family includes a canonical edge Laplacian associated to the graph, extending the usual graph Laplacian on vertices, and we find its spectrum. We show that for a connected graph its eigenvalues are strictly positive aside from one mandatory zero mode, and include all the vertex degrees. Our edge Laplacian is not the graph Laplacian on the line graph but rather it arises as the noncommutative Laplace-Beltrami operator on differential 1-forms, where we use the language of differential algebras to functorially interpret a graph as providing a 'finite manifold structure' on the set of vertices. We equip any graph with a canonical 'Euclidean metric' and a canonical bimodule connection, and in the case of a Cayley graph we construct a metric compatible connection for the Euclidean metric. We make use of results on bimodule connections on inner calculi on algebras, which we prove, including a general relation between zero curvature and the braid relations.
NASA Astrophysics Data System (ADS)
Antonov, N. V.; Malyshev, A. V.
2012-01-01
Infrared asymptotic behavior of a scalar field, passively advected by a random shear flow, is studied by means of the field theoretic renormalization group and the operator product expansion. The advecting velocity is Gaussian, white in time, with correlation function of the form ∝δ(t-t') / k_{bot}^{d-1+ξ}, where k ⊥=| k ⊥| and k ⊥ is the component of the wave vector, perpendicular to the distinguished direction (`direction of the flow')—the d-dimensional generalization of the ensemble introduced by Avellaneda and Majda (Commun. Math. Phys. 131:381, 1990). The structure functions of the scalar field in the infrared range exhibit scaling behavior with exactly known critical dimensions. It is strongly anisotropic in the sense that the dimensions related to the directions parallel and perpendicular to the flow are essentially different. In contrast to the isotropic Kraichnan's rapid-change model, the structure functions show no anomalous (multi)scaling and have finite limits when the integral turbulence scale tends to infinity. On the contrary, the dependence of the internal scale (or diffusivity coefficient) persists in the infrared range. Generalization to the velocity field with a finite correlation time is also obtained. Depending on the relation between the exponents in the energy spectrum {E} ∝ k_{bot}^{1-\\varepsilon} and in the dispersion law ω∝ k_{bot}^{2-η}, the infrared behavior of the model is given by the limits of vanishing or infinite correlation time, with the crossover at the ray η=0, ɛ>0 in the ɛ- η plane. The physical (Kolmogorov) point ɛ=8/3, η=4/3 lies inside the domain of stability of the rapid-change regime; there is no crossover line going through this point.
Space-Time Diffeomorphisms in Noncommutative Gauge Theories
NASA Astrophysics Data System (ADS)
Rosenbaum, Marcos; Vergara, J. David; Juarez, L. Román
2008-07-01
In previous work [Rosenbaum M. et al., J. Phys. A: Math. Theor. 40 (2007), 10367-10382] we have shown how for canonical parametrized field theories, where space-time is placed on the same footing as the other fields in the theory, the representation of space-time diffeomorphisms provides a very convenient scheme for analyzing the induced twisted deformation of these diffeomorphisms, as a result of the space-time noncommutativity. However, for gauge field theories (and of course also for canonical geometrodynamics) where the Poisson brackets of the constraints explicitely depend on the embedding variables, this Poisson algebra cannot be connected directly with a representation of the complete Lie algebra of space-time diffeomorphisms, because not all the field variables turn out to have a dynamical character [Isham C.J., Kuchar K.V., Ann. Physics 164 (1985), 288-315, 316-333]. Nonetheless, such an homomorphic mapping can be rec! uperated by first modifying the original action and then adding additional constraints in the formalism in order to retrieve the original theory, as shown by Kuchar and Stone for the case of the parametrized Maxwell field in [Kuchar K.V., Stone S.L., Classical Quantum Gravity 4 (1987), 319-328]. Making use of a combination of all of these ideas, we are therefore able to apply our canonical reparametrization approach in order to derive the deformed Lie algebra of the noncommutative space-time diffeomorphisms as well as to consider how gauge transformations act on the twisted algebras of gauge and particle fields. Thus, hopefully, adding clarification on some outstanding issues in the literature concerning the symmetries for gauge theories in noncommutative space-times.
Constraining noncommutative spacetime from GW150914
NASA Astrophysics Data System (ADS)
Kobakhidze, Archil; Lagger, Cyril; Manning, Adrian
2016-09-01
The gravitational wave signal GW150914, recently detected by LIGO and Virgo collaborations, is used to place a bound on the scale of quantum fuzziness of noncommutative space-time. We show that the leading noncommutative correction to the phase of the gravitational waves produced by a binary system appears at the second order of the post-Newtonian expansion. This correction is proportional to Λ2≡|θ0 i|2/(lPtP)2, where θμ ν is the antisymmetric tensor of noncommutativity. To comply with GW150914 data, we find that √{Λ }≲3.5 , namely at the order of the Planck scale. This is the most stringent bound on the noncommutative scale, exceeding the previous constraints from particle physics processes by ˜15 orders of magnitude.
Entropic force, noncommutative gravity, and ungravity
Nicolini, Piero
2010-08-15
After recalling the basic concepts of gravity as an emergent phenomenon, we analyze the recent derivation of Newton's law in terms of entropic force proposed by Verlinde. By reviewing some points of the procedure, we extend it to the case of a generic quantum gravity entropic correction to get compelling deviations to the Newton's law. More specifically, we study: (1) noncommutative geometry deviations and (2) ungraviton corrections. As a special result in the noncommutative case, we find that the noncommutative character of the manifold would be equivalent to the temperature of a thermodynamic system. Therefore, in analogy to the zero temperature configuration, the description of spacetime in terms of a differential manifold could be obtained only asymptotically. Finally, we extend the Verlinde's derivation to a general case, which includes all possible effects, noncommutativity, ungravity, asymptotically safe gravity, electrostatic energy, and extra dimensions, showing that the procedure is solid versus such modifications.
Cosmological perturbations of a perfect fluid and noncommutative variables
De Felice, Antonio; Gerard, Jean-Marc; Suyama, Teruaki
2010-03-15
We describe the linear cosmological perturbations of a perfect fluid at the level of an action, providing thus an alternative to the standard approach based only on the equations of motion. This action is suited not only to perfect fluids with a barotropic equation of state, but also to those for which the pressure depends on two thermodynamical variables. By quantizing the system we find that (1) some perturbation fields exhibit a noncommutativity quite analogous to the one observed for a charged particle moving in a strong magnetic field, (2) local curvature and pressure perturbations cannot be measured simultaneously, (3) ghosts appear if the null energy condition is violated.
NASA Astrophysics Data System (ADS)
Saharian, Aram; Kotanjyan, Anna; Sargsyan, Hayk; Simonyan, David
2016-07-01
The models with compact spatial dimensions appear in a number of fundamental physical theories. In particular, the idea of compactified dimensions has been extensively used in supergravity and superstring theories. In quantum field theory, the modification of the vacuum fluctuations spectrum by the periodicity conditions imposed on the field operator along compact dimensions leads to a number of interesting physical effects. A well known example of this kind, demonstrating the close relation between quantum phenomena and global geometry, is the topological Casimir effect. In models with extra compact dimensions, the Casimir energy creates a nontrivial potential for the compactification radius. This can serve as a stabilization mechanism for moduli fields and for the effective gauge couplings. The Casimir effect has also been considered as a possible origin for the dark energy in Kaluza-Klein-type and braneworld models. In the resent presentation we investigate the effects of the gravity and topology on the local properties of the quantum vacuum for a charged scalar field in the presence of a classical gauge field. Vacuum expectation value of the energy-momentum tensor and current density are investigated for a charged scalar field in dS spacetime with toroidally compact spatial dimensions in the presence of a classical constant gauge field. Due to the nontrivial topology, the latter gives rise to Aharonov-Bohm-like effect on the vacuum characteristics. The vacuum current density, energy density and stresses are even periodic functions of the magnetic flux enclosed by compact dimensions. For small values of the comoving lengths of compact dimensions, compared with the dS curvature radius, the effects of gravity on the topological contributions are small and the expectation values are expressed in terms of the corresponding quantities in the Minkowski bulk by the standard conformal relation. For large values of the comoving lengths, depending on the field mass, two
Scalar excursions in large-eddy simulations
NASA Astrophysics Data System (ADS)
Matheou, Georgios; Dimotakis, Paul E.
2016-12-01
The range of values of scalar fields in turbulent flows is bounded by their boundary values, for passive scalars, and by a combination of boundary values, reaction rates, phase changes, etc., for active scalars. The current investigation focuses on the local conservation of passive scalar concentration fields and the ability of the large-eddy simulation (LES) method to observe the boundedness of passive scalar concentrations. In practice, as a result of numerical artifacts, this fundamental constraint is often violated with scalars exhibiting unphysical excursions. The present study characterizes passive-scalar excursions in LES of a shear flow and examines methods for diagnosis and assesment of the problem. The analysis of scalar-excursion statistics provides support of the main hypothesis of the current study that unphysical scalar excursions in LES result from dispersive errors of the convection-term discretization where the subgrid-scale model (SGS) provides insufficient dissipation to produce a sufficiently smooth scalar field. In the LES runs three parameters are varied: the discretization of the convection terms, the SGS model, and grid resolution. Unphysical scalar excursions decrease as the order of accuracy of non-dissipative schemes is increased, but the improvement rate decreases with increasing order of accuracy. Two SGS models are examined, the stretched-vortex and a constant-coefficient Smagorinsky. Scalar excursions strongly depend on the SGS model. The excursions are significantly reduced when the characteristic SGS scale is set to double the grid spacing in runs with the stretched-vortex model. The maximum excursion and volume fraction of excursions outside boundary values show opposite trends with respect to resolution. The maximum unphysical excursions increase as resolution increases, whereas the volume fraction decreases. The reason for the increase in the maximum excursion is statistical and traceable to the number of grid points (sample size
Effective action for noncommutative Bianchi I model
Rosenbaum, M.; Vergara, J. D.; Minzoni, A. A.
2013-06-12
Quantum Mechanics, as a mini-superspace of Field Theory has been assumed to provide physically relevant information on quantum processes in Field Theory. In the case of Quantum Gravity this would imply using Cosmological models to investigate quantum processes at distances of the order of the Planck scale. However because of the Stone-von Neuman Theorem, it is well known that quantization of Cosmological models by the Wheeler-DeWitt procedure in the context of a Heisenberg-Weyl group with piecewise continuous parameters leads irremediably to a volume singularity. In order to avoid this information catastrophe it has been suggested recently the need to introduce in an effective theory of the quantization some form of reticulation in 3-space. On the other hand, since in the geometry of the General Relativistic formulation of Gravitation space can not be visualized as some underlying static manifold in which the physical system evolves, it would be interesting to investigate whether the effective reticulation which removes the singularity in such simple cosmologies as the Bianchi models has a dynamical origin manifested by a noncommutativity of the generators of the Heisenberg-Weyl algebra, as would be expected from an operational point of view at the Planck length scale.
Effective action for noncommutative Bianchi I model
NASA Astrophysics Data System (ADS)
Rosenbaum, M.; Vergara, J. D.; Minzoni, A. A.
2013-06-01
Quantum Mechanics, as a mini-superspace of Field Theory has been assumed to provide physically relevant information on quantum processes in Field Theory. In the case of Quantum Gravity this would imply using Cosmological models to investigate quantum processes at distances of the order of the Planck scale. However because of the Stone-von Neuman Theorem, it is well known that quantization of Cosmological models by the Wheeler-DeWitt procedure in the context of a Heisenberg-Weyl group with piecewise continuous parameters leads irremediably to a volume singularity. In order to avoid this information catastrophe it has been suggested recently the need to introduce in an effective theory of the quantization some form of reticulation in 3-space. On the other hand, since in the geometry of the General Relativistic formulation of Gravitation space can not be visualized as some underlying static manifold in which the physical system evolves, it would be interesting to investigate whether the effective reticulation which removes the singularity in such simple cosmologies as the Bianchi models has a dynamical origin manifested by a noncommutativity of the generators of the Heisenberg-Weyl algebra, as would be expected from an operational point of view at the Planck length scale.
Visualization of scalar topology for structural enhancement
Bajaj, C.L.; Pascucci, V.; Schikore, D.R.
1998-09-22
Scalar fields arise in every scientific application. Existing scalar visualization techniques require that the user infer the global scalar structure from what is frequently an insufficient display of information. We present a visualization technique which numerically detects the structure at all scales, removing from the user the responsibility of extracting information implicit in the data, and presenting the structure explicitly for analysis. We further demonstrate how scalar topology detection proves useful for correct visualization and image processing applications such as image co-registration, isocontouring, and mesh compression.