Asymptotic dynamics of the exceptional Bianchi cosmologies
NASA Astrophysics Data System (ADS)
Hewitt, C. G.; Horwood, J. T.; Wainwright, J.
2003-05-01
In this paper we give, for the first time, a qualitative description of the asymptotic dynamics of a class of non-tilted spatially homogeneous (SH) cosmologies, the so-called exceptional Bianchi cosmologies, which are of Bianchi type VI$_{-1/9}$. This class is of interest for two reasons. Firstly, it is generic within the class of non-tilted SH cosmologies, being of the same generality as the models of Bianchi types VIII and IX. Secondly, it is the SH limit of a generic class of spatially inhomogeneous $G_{2}$ cosmologies. Using the orthonormal frame formalism and Hubble-normalized variables, we show that the exceptional Bianchi cosmologies differ from the non-exceptional Bianchi cosmologies of type VI$_{h}$ in two significant ways. Firstly, the models exhibit an oscillatory approach to the initial singularity and hence are not asymptotically self-similar. Secondly, at late times, although the models are asymptotically self-similar, the future attractor for the vacuum-dominated models is the so-called Robinson-Trautman SH model instead of the vacuum SH plane wave models.
Quantum supersymmetric Bianchi IX cosmology
NASA Astrophysics Data System (ADS)
Damour, Thibault; Spindel, Philippe
2014-11-01
We study the quantum dynamics of a supersymmetric squashed three-sphere by dimensionally reducing (to one timelike dimension) the action of D =4 simple supergravity for a S U (2 ) -homogeneous (Bianchi IX) cosmological model. The quantization of the homogeneous gravitino field leads to a 64-dimensional fermionic Hilbert space. After imposition of the diffeomorphism constraints, the wave function of the Universe becomes a 64-component spinor of spin(8,4) depending on the three squashing parameters, which satisfies Dirac-like, and Klein-Gordon-like, wave equations describing the propagation of a "quantum spinning particle" reflecting off spin-dependent potential walls. The algebra of the supersymmetry constraints and of the Hamiltonian one is found to close. One finds that the quantum Hamiltonian is built from operators that generate a 64-dimensional representation of the (infinite-dimensional) maximally compact subalgebra of the rank-3 hyperbolic Kac-Moody algebra A E3 . The (quartic-in-fermions) squared-mass term μ^ 2 entering the Klein-Gordon-like equation has several remarkable properties: (i) it commutes with all the other (Kac-Moody-related) building blocks of the Hamiltonian; (ii) it is a quadratic function of the fermion number NF; and (iii) it is negative in most of the Hilbert space. The latter property leads to a possible quantum avoidance of the singularity ("cosmological bounce"), and suggests imposing the boundary condition that the wave function of the Universe vanish when the volume of space tends to zero (a type of boundary condition which looks like a final-state condition when considering the big crunch inside a black hole). The space of solutions is a mixture of "discrete-spectrum states" (parametrized by a few constant parameters, and known in explicit form) and of continuous-spectrum states (parametrized by arbitrary functions entering some initial-value problem). The predominantly negative values of the squared-mass term lead to a "bottle
Bianchi IX cosmologies and the golden ratio
NASA Astrophysics Data System (ADS)
Bryant, M. S.; Hobill, D. W.
2017-06-01
Special solutions to the Einstein equations in the asymptotic limit for the Bianchi IX cosmologies in the vacuum are examined using Ellis-MacCallum-Wainwright (‘expansion-normalized’) variables. Using an iterative map (the B-map) obeyed by two of the dynamical variables (the normalized shear components) in the ‘asymptotic regime’ close to the cosmological singularity, two period 3 solutions are constructed. These are the simplest of an infinite number of periodic solutions and represent the transition from one vacuum Bianchi I Kasner solution to another. It is shown that the full 3-cycle solutions for the remaining variables (the logarithms of the normalized curvatures) generate a set of self-similar golden rectangles in a graphical time series representation of their dynamics as the normalized time parameter is run backwards towards the initial singularity.
Higher-dimensional Bianchi type-VIh cosmologies
NASA Astrophysics Data System (ADS)
Lorenz-Petzold, D.
1985-09-01
The higher-dimensional perfect fluid equations of a generalization of the (1 + 3)-dimensional Bianchi type-VIh space-time are discussed. Bianchi type-V and Bianchi type-III space-times are also included as special cases. It is shown that the Chodos-Detweiler (1980) mechanism of cosmological dimensional-reduction is possible in these cases.
Bianchi-I cosmology from causal thermodynamics
NASA Astrophysics Data System (ADS)
Bittencourt, Eduardo; Gomes, Leandro G.; Klippert, Renato
2017-02-01
We investigate diagonal Bianchi-I spacetimes in the presence of viscous fluids by using the shear and the anisotropic pressure components as the basic variables, where the viscosity is driven by the (second-order) causal thermodynamics. A few exact solutions are presented, among which we mention the anisotropic versions of de Sitter/anti-de Sitter geometries as well as an asymptotically isotropic spacetime presenting an effectively constant cosmic acceleration without any cosmological constant. The qualitative analysis of the solutions for barotropic fluids with linear equations of state suggests that the behaviour is quite general.
Bayesian analysis of anisotropic cosmologies: Bianchi VIIh and WMAP
NASA Astrophysics Data System (ADS)
McEwen, J. D.; Josset, T.; Feeney, S. M.; Peiris, H. V.; Lasenby, A. N.
2013-12-01
We perform a definitive analysis of Bianchi VIIh cosmologies with Wilkinson Microwave Anisotropy Probe (WMAP) observations of the cosmic microwave background (CMB) temperature anisotropies. Bayesian analysis techniques are developed to study anisotropic cosmologies using full-sky and partial-sky masked CMB temperature data. We apply these techniques to analyse the full-sky internal linear combination (ILC) map and a partial-sky masked W-band map of WMAP 9 yr observations. In addition to the physically motivated Bianchi VIIh model, we examine phenomenological models considered in previous studies, in which the Bianchi VIIh parameters are decoupled from the standard cosmological parameters. In the two phenomenological models considered, Bayes factors of 1.7 and 1.1 units of log-evidence favouring a Bianchi component are found in full-sky ILC data. The corresponding best-fitting Bianchi maps recovered are similar for both phenomenological models and are very close to those found in previous studies using earlier WMAP data releases. However, no evidence for a phenomenological Bianchi component is found in the partial-sky W-band data. In the physical Bianchi VIIh model, we find no evidence for a Bianchi component: WMAP data thus do not favour Bianchi VIIh cosmologies over the standard Λ cold dark matter (ΛCDM) cosmology. It is not possible to discount Bianchi VIIh cosmologies in favour of ΛCDM completely, but we are able to constrain the vorticity of physical Bianchi VIIh cosmologies at (ω/H)0 < 8.6 × 10-10 with 95 per cent confidence.
Bianchi Type V Cosmological Models with Varying Cosmological Term
NASA Astrophysics Data System (ADS)
Tiwari, R. K.; Singh, Rameshwar
2015-05-01
We have analyzed a new class of spatially homogeneous and anisotropic Bianchi type-V cosmological models with perfect fluid distribution in presence of time varying cosmological and gravitational constants in the framework of general relativity. Exact solutions of Einstein's field equations are obtained for two types of cosmologies viz. m ≠ 3 and m = 3 respectively. We propose an alternate variation law in which the anisotropy ( σ/ 𝜃) per unit expansion scalar ( 𝜃) is proportional to a function of scale factor R i.e. (where σ is a shear scalar) Tiwari (The African Review of Physics, 8, 437-447 2013). Physical properties of the models are discussed in detail. The models isotropize at late times. Some cosmological distance parameters for both the models have also been presented. We also discussed state finder parameters and observe that our solutions favor Λ C D M model.
Anisotropic Bianchi types VIII and IX locally rotationally symmetric cosmologies
Assad, M.J.D.; Soares, I.D.
1983-10-15
We present a class of exact cosmological solutions of Einstein-Maxwell equations, which are anisotropic and spatially homogeneous of Bianchi types VIII and IX, and class IIIb in the Stewart-Ellis classification of locally rotationally symmetric models. If we take the electromagnetic field equal to zero, a class of Bianchi types VIII/IX spatially homogeneous anisotropic cosmological solutions with perfect fluid is obtained.
Loop quantum cosmology of Bianchi IX: effective dynamics
NASA Astrophysics Data System (ADS)
Corichi, Alejandro; Montoya, Edison
2017-03-01
We study solutions to the effective equations for the Bianchi IX class of spacetimes within loop quantum cosmology (LQC). We consider Bianchi IX models whose matter content is a massless scalar field, by numerically solving the loop quantum cosmology effective equations, with and without inverse triad corrections. The solutions are classified using certain geometrically motivated classical observables. We show that both effective theories—with lapse N = V and N = 1—resolve the big bang singularity and reproduce the classical dynamics far from the bounce. Moreover, due to the positive spatial curvature, there is an infinite number of bounces and recollapses. We study the limit of large field momentum and show that both effective theories reproduce the same dynamics, thus recovering general relativity. We implement a procedure to identify amongst the Bianchi IX solutions, those that behave like k = 0,1 FLRW as well as Bianchi I, II, and VII0 models. The effective solutions exhibit Bianchi I phases with Bianchi II transitions and also Bianchi VII0 phases, which had not been studied before. We comment on the possible implications of these results for a quantum modification to the classical BKL behaviour.
Loop quantum cosmology of Bianchi type IX models
Wilson-Ewing, Edward
2010-08-15
The loop quantum cosmology 'improved dynamics' of the Bianchi type IX model are studied. The action of the Hamiltonian constraint operator is obtained via techniques developed for the Bianchi type I and type II models, no new input is required. It is shown that the big bang and big crunch singularities are resolved by quantum gravity effects. We also present effective equations which provide quantum geometry corrections to the classical equations of motion.
Loop quantum cosmology of Bianchi type IX models
NASA Astrophysics Data System (ADS)
Wilson-Ewing, Edward
2010-08-01
The loop quantum cosmology “improved dynamics” of the Bianchi type IX model are studied. The action of the Hamiltonian constraint operator is obtained via techniques developed for the Bianchi type I and type II models, no new input is required. It is shown that the big bang and big crunch singularities are resolved by quantum gravity effects. We also present effective equations which provide quantum geometry corrections to the classical equations of motion.
Bianchi-I cosmological model and crossing singularities
NASA Astrophysics Data System (ADS)
Kamenshchik, Alexander Yu.; Pozdeeva, Ekaterina O.; Vernov, Sergey Yu.; Tronconi, Alessandro; Venturi, Giovanni
2017-04-01
We consider a rather simple method for the description of the big bang-big crunch cosmological singularity crossing. For the flat Friedmann universe this method gives the same results as more complicated methods, using Weyl symmetry or the transitions between the Jordan and Einstein frames. It is then easily generalized for the case of a Bianchi-I anisotropic universe. We also present early-time and late-time asymptotic solutions for a Bianchi-I universe, filled with a conformally coupled massless scalar field.
NASA Astrophysics Data System (ADS)
Körpinar, Talat; Ünlütürk, Yasin
2015-11-01
Anisotropic Bianchi type-I magnetized string cosmological models are obtained in decaying vacuum energy density proposed by Pradhan (Commun Theor Phys 55:931-941, 2011). In this study, we obtain some physical and geometrical properties of biharmonic particles of a new spacetime using Bianchi type-I (B-I) cosmological model. We use solution of the Einstein's field equations for biharmonic particles. Some important features of the model have been discussed. Established the existence of string cosmological models for biharmonic particles, unlike the earlier authors, in this theory and studied some physical and geometrical properties.
Spectral action for Bianchi type-IX cosmological models
NASA Astrophysics Data System (ADS)
Fan, Wentao; Fathizadeh, Farzad; Marcolli, Matilde
2015-10-01
A rationality result previously proved for Robertson-Walker metrics is extended to a homogeneous anisotropic cosmological model, namely the Bianchi type-IX minisuperspace. It is shown that the Seeley-de Witt coefficients appearing in the expansion of the spectral action for the Bianchi type-IX geometry are expressed in terms of polynomials with rational coefficients in the cosmic evolution factors w 1( t) , w 2( t) , w 3( t) , and their higher derivates with respect to time. We begin with the computation of the Dirac operator of this geometry and calculate the coefficients a 0 ,a 2 ,a 4 of the spectral action by using heat kernel methods and parametric pseudodifferential calculus. An efficient method is devised for computing the Seeley-de Witt coefficients of a geometry by making use of Wodzicki's noncommutative residue, and it is confirmed that the method checks out for the cosmological model studied in this article. The advantages of the new method are discussed, which combined with symmetries of the Bianchi type-IX metric, yield an elegant proof of the rationality result.
Bianchi type I cosmologies in arbitrary dimensional dilaton gravities
NASA Astrophysics Data System (ADS)
Chen, Chiang-Mei; Harko, T.; Mak, M. K.
2000-12-01
We study the low energy string effective action with an exponential type dilaton potential and vanishing torsion in a Bianchi type I space-time geometry. In the Einstein and string frames the general solution of the gravitational field equations can be expressed in an exact parametric form. Depending on the values of the dilaton coupling constant and of the coefficient in the exponential, the obtained cosmological models can be generically divided into three classes, leading to both singular and non-singular behaviors. The effect of the potential on the time evolution of the mean anisotropy parameter is also considered in detail, and it is shown that a Bianchi type I universe isotropizes only in the presence of a dilaton field potential or a central deficit charge.
Generalized uncertainty principle in Bianchi type I quantum cosmology
NASA Astrophysics Data System (ADS)
Vakili, B.; Sepangi, H. R.
2007-07-01
We study a quantum Bianchi type I model in which the dynamical variables of the corresponding minisuperspace obey the generalized Heisenberg algebra. Such a generalized uncertainty principle has its origin in the existence of a minimal length suggested by quantum gravity and sting theory. We present approximate analytical solutions to the corresponding Wheeler DeWitt equation in the limit where the scale factor of the universe is small and compare the results with the standard commutative and noncommutative quantum cosmology. Similarities and differences of these solutions are also discussed.
The general solution of Bianchi type III vacuum cosmology
NASA Astrophysics Data System (ADS)
Christodoulakis, T.; Terzis, Petros A.
2007-02-01
The second-order ordinary differential equation which describes the unknown part of the solution space of some vacuum Bianchi cosmologies is completely integrated for type III, thus obtaining the general solution to Einstein's field equations for this case, with the aid of the sixth Painlevé transcendent PVI. For particular representations of PVI we obtain the known Kinnersley two-parameter spacetime and a solution of Euclidean signature. The imposition of the spacetime generalization of a 'hidden' symmetry of the generic type III spatial slice enables us to retrieve the two-parameter subfamily without considering the Painlevé transcendent.
NASA Astrophysics Data System (ADS)
Roy, S. R.; Banerjee, S. K.
1992-11-01
A homogeneous Bianchi type VIh cosmological model filled with perfect fluid, null electromagnetic field and streaming neutrinos is obtained for which the free gravitational field is of the electric type. The barotropic equation of statep = (γ-1)ɛ is imposed in the particular case of Bianchi VI0 string models. Various physical and kinematical properties of the models are discussed.
Bianchi type-I cosmological model with quadratic equation of state
NASA Astrophysics Data System (ADS)
Reddy, D. R. K.; Adhav, K. S.; Purandare, M. A.
2015-05-01
Bianchi type-I cosmological model containing perfect fluid with quadratic equation of state has been studied in general theory of relativity. The general solutions of the Einstein's field equations for Bianchi type-I space-time have been obtained under the assumption of quadratic equation of state (EoS) p= αρ 2- ρ, where α is constant and strictly α≠0. The physical and geometrical aspects of the model are discussed.
Loop quantum cosmology of Bianchi IX: Inclusion of inverse triad corrections
NASA Astrophysics Data System (ADS)
Corichi, Alejandro; Karami, Asieh
2016-06-01
We consider the loop quantization of the (diagonal) Bianchi type IX cosmological model. We explore different quantization prescriptions that extend the work of Wilson-Ewing and Singh. In particular, we study two different ways of implementing the so-called inverse triad corrections. We construct the corresponding Hamiltonian constraint operators and show that the singularity is formally resolved. We find the effective equations associated with the different quantization prescriptions, and study the relation with the isotropic k = 1 model that, classically, is contained within the Bianchi IX model. Somewhat surprisingly, we find the most natural quantization does not reduce to the k = 1 model. We use geometrically defined scalar observables to explore the physical implications of each of these theories. This is the first part in a series of papers analyzing different aspects of the Bianchi IX model, with inverse corrections, within loop quantum cosmology (LQC).
Bianchi type-I magnetized radiating cosmological model in self creation theory of gravitation
NASA Astrophysics Data System (ADS)
Jain, Vimal Chand; Jain, Nikhil
2015-06-01
We have investigated Bianchi type-I cosmological model in the presence of magnetized field with disordered radiation in Barber's second self-creation theory of gravitation. To obtain exact solution we assume that the component of shear tensor is proportional to expansion ( θ). Some geometrical and physical properties of the model have also been discussed.
Bianchi Type-I cosmological model in Einstein-Cartan theory
NASA Astrophysics Data System (ADS)
Manna, B.; Sinha, S.; Sahoo, S.
2017-08-01
In this paper, we obtain a solution of Bianchi Type-I cosmological model using Einstein-Cartan theory for perfect fluid distribution with the improved stress-energy-momentum tensor of Ray and Smalley. Here, we use a special law of variation for Hubble's parameter proposed by Bermann (Nuovo Cim B 74:182, 1983). Some physical behaviours of the cosmological model are also studied.
NASA Astrophysics Data System (ADS)
Kotambkar, S.; Singh, G. P.; Kelkar, R.; Bishi, Binaya K.
2017-02-01
This paper deals with study of generalized Chaplygin gas model with dynamical gravitational and cosmological constants. In this paper a new set of exact solutions of Einstein field equations for spatially homogeneous and anisotropic Bianchi type I space-time have been obtained. The solutions of the Einstein’s field equations are obtained by considering (i) the power law relation between Hubble parameter H and scale factor R and (ii) scale factor of the form R = ‑1/t + t 2, t > 1. The assumptions lead to constant and variable deceleration parameter respectively. The physical and dynamical behaviors of the models have been discussed with the help of graphical representations. Also we have discussed the stability and physical acceptability of solutions for solution type-I and solution type-II.
Loop quantum cosmology of diagonal Bianchi type I model: Simplifications and scaling problems
Szulc, Lukasz
2008-09-15
A simplified theory of the diagonal Bianchi type I model coupled with a massless scalar field in loop quantum cosmology is constructed according to the {mu} scheme. Kinematical and physical sectors of the theory are under good analytical control as well as the scalar constraint operator. Although it is possible to compute numerically the nonsingular evolution of the three gravitational degrees of freedom, the naive implementation of the {mu} scheme to the diagonal Bianchi type I model is problematic. The lack of the full invariance of the theory with respect to the fiducial cell and fiducial metric scaling causes serious problems in the semiclassical limit of the theory. Because of this behavior it is very difficult to extract reasonable physics from the model. The weaknesses of the implementation of the {mu} scheme to the Bianchi I model do not imply limitations of the {mu} scheme in the isotropic case.
NASA Astrophysics Data System (ADS)
Pradhan, A.; Saha, B.; Rikhvitsky, V.
2015-05-01
The Einstein's field equations with variable gravitational and cosmological "constants" for a spatially homogeneous and anisotropic Bianchi type-I space-time are obtained in present study. To study the transit behaviour of Universe, we consider a law of variation of scale factor a(t) = ( tk et) ^{1/n}, which yields a time dependent deceleration parameter q = -1 + nk/(k + t)2, comprising a class of models that depicts a transition of the universe from the early decelerated phase to the recent accelerating phase. We find that the time dependent deceleration parameter is reasonable for the present day Universe and gives an appropriate description of the evolution of the universe. For n = 0.27k, we obtain q0 = -0.73, which is similar to observed value of deceleration parameter at present epoch. It is also observed that for n ≥ 2 and k = 1, we obtain a class of transit models of the universe from early decelerating to present accelerating phase. For k = 0, the universe has non-singular origin. In these models, we arrive at the decision that, from the structure of the field equations, the behaviour of cosmological and gravitational constants and are related. Taking into consideration the observational data, we conclude that the cosmological constant behaves as a positive decreasing function of time, whereas gravitational constant is increasing and tends to a constant value at late time. H(z)/(1+z) data (32 points) and model prediction as a function of redshift for different k and n are successfully presented by using recent data. Some physical and geometric properties of the models are also discussed.
Hořava–Lifshitz gravity inspired Bianchi-II cosmology and the mixmaster universe
NASA Astrophysics Data System (ADS)
Giani, Leonardo; Kamenshchik, Alexander Y.
2017-04-01
We study different aspects of the Hořava-Lifshitz inspired Bianchi-II cosmology and its relations with the mixmaster universe model. First, we present exact solutions for a toy model, where only the cubic in spatial curvature terms are present in the action; then we briefly discuss some exotic singularities, which can appear in this toy model. We study also the toy model where only the quadratic in spatial curvature terms are present in the action. We establish relations between our results and those obtained by using the Hamiltonian formalism. Finally, we apply the results obtained by studying Bianchi-II cosmology to describe the evolution of the mixmaster universe in terms of the Belinsky–Khalatnikov–Lifshitz formalism. Generally, our analysis gives some arguments in favour of the existence of the oscillatory approach to the singularity in a universe governed by the Hořava–Lifshitz type gravity.
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.
Bianchi I solutions of the Einstein-Boltzmann system with a positive cosmological constant
NASA Astrophysics Data System (ADS)
Lee, Ho; Nungesser, Ernesto
2017-09-01
In this paper, we study the future global existence and late-time behaviour of the Einstein-Boltzmann system with Bianchi I symmetry and a positive cosmological constant Λ >0 . For the Boltzmann equation, we consider the scattering kernel of Israel particles which are the relativistic counterpart of Maxwellian particles. Under a smallness assumption on initial data in a suitable norm, we show that solutions exist globally in time and isotropize at late times.
Big-bounce cosmology from quantum gravity: The case of a cyclical Bianchi I universe
NASA Astrophysics Data System (ADS)
Moriconi, Riccardo; Montani, Giovanni; Capozziello, Salvatore
2016-07-01
We analyze the classical and quantum dynamics of a Bianchi I model in the presence of a small negative cosmological constant characterizing its evolution in term of the dust-time dualism. We demonstrate that in a canonical metric approach, the cosmological singularity is removed in correspondence to a positive defined value of the dust energy density. Furthermore, the quantum big bounce is connected to the Universe's turning point via a well-defined semiclassical limit. Then we can reliably infer that the proposed scenario is compatible with a cyclical universe picture. We also show how, when the contribution of the dust energy density is sufficiently high, the proposed scenario can be extended to the Bianchi IX cosmology and therefore how it can be regarded as a paradigm for the generic cosmological model. Finally, we investigate the origin of the observed cutoff on the cosmological dynamics, demonstrating how the big-bounce evolution can be mimicked by the same semiclassical scenario, where the negative cosmological constant is replaced via a polymer discretization of the Universe's volume. A direct proportionality law between these two parameters is then established.
Chaos-order transition in Bianchi type I non-Abelian Born-Infeld cosmology
NASA Astrophysics Data System (ADS)
Dyadichev, Vladimir V.; Gal'Tsov, Dmitri V.; Moniz, Paulo Vargas
2005-10-01
We investigate the Bianchi I cosmology with the homogeneous SU(2) Yang-Mills field governed by the non-Abelian Born-Infeld action. A similar system with the standard Einstein-Yang-Mills (EYM) action is known to exhibit chaotic behavior induced by the Yang-Mills field. When the action is replaced by the Born-Infeld type non-Abelian action (NBI), the chaos-order transition is observed in the high-energy region. This is interpreted as a smothering effect due to (nonperturbative in α') string corrections to the classical EYM action. We give numerical evidence for the chaos-order transition and present an analytical proof of regularity of color oscillations in the limit of strong Born-Infeld nonlinearity. We also perform a general analysis of the Bianchi I NBI cosmology and derive an exact solution in the case of only the U(1) component excited. Our new exact solution generalizes the Rosen solution of the Bianchi I Einstein-Maxwell cosmology to the U(1) Einstein-Born-Infeld theory.
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.
A Dynamical Systems Approach to Geodesics in Bianchi Cosmologies
NASA Astrophysics Data System (ADS)
Nilsson, Ulf S.; Uggla, Claes; Wainwright, John
2000-10-01
To understand the observational properties of cosmological models, in particular, the temperature of the cosmic microwave background radiation, it is necessary to study their null geodesics. Dynamical systems theory, in conjunction with the orthonormal frame approach, has proved to be an invaluable tool for analyzing spatially homogeneous cosmologies. It is thus natural to use such techniques to study the geodesics of these models. We therefore augment the Einstein field equations with the geodesic equations, all written in dimensionless form, obtaining an extended system of first-order ordinary differential equations that simultaneously describes the evolution of the gravitational field and the behavior of the associated geodesics. It is shown that the extended system is a powerful tool for investigating the effect of space-time anisotropies on the temperature of the cosmic microwave background radiation, and that it can also be used for studying geodesic chaos.
Bianchi type-VIh string cloud cosmological models with bulk viscosity
NASA Astrophysics Data System (ADS)
Tripathy, Sunil K.; Behera, Dipanjali
2010-11-01
String cloud cosmological models are studied using spatially homogeneous and anisotropic Bianchi type VIh metric in the frame work of general relativity. The field equations are solved for massive string cloud in presence of bulk viscosity. A general linear equation of state of the cosmic string tension density with the proper energy density of the universe is considered. The physical and kinematical properties of the models have been discussed in detail and the limits of the anisotropic parameter responsible for different phases of the universe are explored.
NASA Astrophysics Data System (ADS)
D'Ambroise, Jennie; Williams, Floyd L.
2010-06-01
In some interesting work of James Lidsey, the dynamics of Friedmann-Lemaître-Robertson-Walker (FLRW) cosmology with positive curvature and a perfect fluid matter source is shown to be modeled in terms of a time-dependent, harmonically trapped Bose-Einstein condensate. In the present work, we extend this dynamic correspondence to both FLRW and Bianchi I cosmologies in arbitrary dimension, especially when a cosmological constant is present.
D'Ambroise, Jennie; Williams, Floyd L.
2010-06-15
In some interesting work of James Lidsey, the dynamics of Friedmann-Lemaitre-Robertson-Walker (FLRW) cosmology with positive curvature and a perfect fluid matter source is shown to be modeled in terms of a time-dependent, harmonically trapped Bose-Einstein condensate. In the present work, we extend this dynamic correspondence to both FLRW and Bianchi I cosmologies in arbitrary dimension, especially when a cosmological constant is present.
Behavior of nonlinear anisotropies in bouncing Bianchi I models of loop quantum cosmology
Chiou, D.-W.; Vandersloot, Kevin
2007-10-15
In homogeneous and isotropic loop quantum cosmology, gravity can behave repulsively at Planckian energy densities leading to the replacement of the big bang singularity with a big bounce. Yet in any bouncing scenario it is important to include nonlinear effects from anisotropies which typically grow during the collapsing phase. We investigate the dynamics of a Bianchi I anisotropic model within the framework of loop quantum cosmology. Using effective semiclassical equations of motion to study the dynamics, we show that the big bounce is still predicted with only differences in detail arising from the inclusion of anisotropies. We show that the anisotropic shear term grows during the collapsing phase, but remains finite through the bounce. Immediately following the bounce, the anisotropies decay and with the inclusion of matter with equation of state w<+1, the universe isotropizes in the expanding phase.
Homoclinic chaos in axisymmetric Bianchi-IX cosmological models with an ad hoc quantum potential
Correa, G. C.; Stuchi, T. J.; Joras, S. E.
2010-04-15
In this work we study the dynamics of the axisymmetric Bianchi-IX cosmological model with a term of quantum potential added. As it is well known, this class of Bianchi-IX models is homogeneous and anisotropic with two scale factors, A(t) and B(t), derived from the solution of Einstein's equation for general relativity. The model we use in this work has a cosmological constant and the matter content is dust. To this model we add a quantum-inspired potential that is intended to represent short-range effects due to the general relativistic behavior of matter in small scales and play the role of a repulsive force near the singularity. We find that this potential restricts the dynamics of the model to positive values of A(t) and B(t) and alters some qualitative and quantitative characteristics of the dynamics studied previously by several authors. We make a complete analysis of the phase space of the model finding critical points, periodic orbits, stable/unstable manifolds using numerical techniques such as Poincare section, numerical continuation of orbits, and numerical globalization of invariant manifolds. We compare the classical and the quantum models. Our main result is the existence of homoclinic crossings of the stable and unstable manifolds in the physically meaningful region of the phase space [where both A(t) and B(t) are positive], indicating chaotic escape to inflation and bouncing near the singularity.
Twisted C⋆-algebra formulation of quantum cosmology with application to the Bianchi I model
NASA Astrophysics Data System (ADS)
Rosenbaum, Marcos; Vergara, J. David; Juárez, Román; Minzoni, A. A.
2014-04-01
A twisted C⋆-algebra of the extended (noncommutative) Heisenberg-Weyl group has been constructed which takes into account the uncertainty principle for coordinates in the Planck-length regime. This general construction is then used to generate an appropriate Hilbert space and observables for the noncommutative theory which, when applied to the Bianchi I cosmology, leads to a new set of equations that describe the quantum evolution of the Universe. We find that this formulation matches theories based on a reticular Heisenberg-Weyl algebra in the bouncing and expanding regions of a collapsing Bianchi universe. There is, however, an additional effect introduced by the dynamics generated by the noncommutativity. This is an oscillation in the spectrum of the volume operator of the Universe, within the bouncing region of the commutative theories. We show that this effect is generic and produced by the noncommutative momentum exchange between the degrees of freedom in the cosmology. We give asymptotic and numerical solutions which show the above mentioned effects of the noncommutativity.
Bianchi type I cyclic cosmology from Lie-algebraically deformed phase space
Vakili, Babak; Khosravi, Nima
2010-11-15
We study the effects of noncommutativity, in the form of a Lie-algebraically deformed Poisson commutation relations, on the evolution of a Bianchi type I cosmological model with a positive cosmological constant. The phase space variables turn out to correspond to the scale factors of this model in x, y, and z directions. According to the conditions that the structure constants (deformation parameters) should satisfy, we argue that there are two types of noncommutative phase space with Lie-algebraic structure. The exact classical solutions in commutative and type I noncommutative cases are presented. In the framework of this type of deformed phase space, we investigate the possibility of building a Bianchi I model with cyclic scale factors in which the size of the Universe in each direction experiences an endless sequence of contractions and reexpansions. We also obtain some approximate solutions for the type II noncommutative structure by numerical methods and show that the cyclic behavior is repeated as well. These results are compared with the standard commutative case, and similarities and differences of these solutions are discussed.
NASA Astrophysics Data System (ADS)
Chaubey, R.; Shukla, A. K.; Raushan, Rakesh
2017-04-01
The general class of Bianchi cosmological models with dark energy in the form of modified Chaplygin gas with variable Λ and G and bulk viscosity have been considered. We discuss three types of average scale factor by using a special law for deceleration parameter which is linear in time with negative slope. The exact solutions to the corresponding field equations are obtained. We obtain the solution of bulk viscosity ( ξ), cosmological constant (Λ), gravitational parameter ( G) and deceleration parameter ( q) for different equations of state. The model describes an accelerating Universe for large value of time t, wherein the effective negative pressure induced by Chaplygin gas and bulk viscous pressure are driving the acceleration.
Bianchi type-I model with cosmological constant in a generalized scalar-tensor theory of gravitation
Banerjee, A.; Duttachoudhury, S.B.; Banerjee, N.
1985-12-15
Bianchi type-I cosmological models are discussed in the Bergmann-Wagoner-Nordtvedt scalar-tensor theory where both the so-called cosmological constant ..lambda.. and the coupling parameter ..omega.. are taken to be functions of the scalar field phi. Exact solutions are obtained in Dicke's revised units assuming a very simple relationship between ..lambda.. and phi. The properties of the models are discussed in special cases.
Anisotropic matter in cosmology: locally rotationally symmetric Bianchi I and VII o models
NASA Astrophysics Data System (ADS)
Sloan, David
2016-05-01
We examine the behaviour of homogeneous, anisotropic space-times, specifically the locally rotationally symmetric Bianchi types I and VII o in the presence of anisotropic matter. By finding an appropriate constant of the motion, and transforming the equations of motion we are able to provide exact solutions in the presence of perfect fluids with anisotropic pressures. The solution space covers matter consisting of a single perfect fluid which satisfies the weak energy condition and is rich enough to contain solutions which exhibit behaviour which is qualitatively distinct from the isotropic sector. Thus we find that there is more ‘matter that matters’ close to a homogeneous singularity than the usual stiff fluid. Example metrics are given for cosmologies whose matter sources are magnetic fields, relativistic particles, cosmic strings and domain walls.
LRS Bianchi type-II string cosmological models in a modified theory of gravitation
NASA Astrophysics Data System (ADS)
Kanakavalli, T.; Ananda Rao, G.; Reddy, D. R. K.
2017-03-01
This paper is devoted to the investigation of spatially homogeneous anisotropic LRS Bianchi type-II cosmological models with string source in a modified theory of gravitation formulated by Harko et al. (Phys. Rev. D 84:024020, 2011) which is universally known as f( R, T) gravity. Here R is the Ricci scalar and T is the trace of the energy momentum tensor. By solving the field equation we have presented massive string and Takabyasi or p-string models in this theory. However it is interesting to note that geometric string in this space-time does not exist in this theory. Physical and geometrical properties of the strings obtained are also discussed.
Cosmological dynamics of magnetic Bianchi I in viable f(R) models of gravity
NASA Astrophysics Data System (ADS)
Liu, Xuyang; Channuie, Phongpichit; Samart, Daris
2017-09-01
Standard dynamical system analysis of Einstein-Maxwell equation in f(R) theories is considered in this work. We investigate cosmological dynamics of a uniform magnetic field in the Orthogonal Spatially Homogeneous (OSH) Bianchi I universe with viable f(R) models of gravity. In this work, the f(R) = R - αRn and f(R) =(Rb - Λ) c models are examined by using our dynamical system analysis. Our results show that both of two f(R) models have a viable cosmological consequence identical to the analysis present in Amendola and Tsujikawa (2008) for the FLRW background. Contrary to Amendola and Tsujikawa (2008), we discover in our models that there is an additional anisotropic and non-zero cosmological magnetic fields fixed point emerging before the present of the standard matter epoch. This means that the universe has initially isotropic stage with the intermediated epoch as the anisotropic background and it ends up with the isotropic late-time acceleration. The primordial magnetic fields play a crucial role of the shear evolutions obtained from these two models which have the same scaling of the cosmic time as σ ∼t - 1/3, instead of σ ∼t-1 for the absence of the primordial magnetic cases.
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.
Effective dynamics, big bounces, and scaling symmetry in Bianchi type I loop quantum cosmology
Chiou, D.-W.
2007-12-15
The detailed formulation for loop quantum cosmology (LQC) in the Bianchi I model with a scalar massless field has been constructed. In this paper, its effective dynamics is studied in two improved strategies for implementing the LQC discreteness corrections. Both schemes show that the big bang is replaced by the big bounces, which take place up to 3 times, once in each diagonal direction, when the area or volume scale factor approaches the critical values in the Planck regime measured by the reference of the scalar field momentum. These two strategies give different evolutions: In one scheme, the effective dynamics is independent of the choice of the finite sized cell prescribed to make Hamiltonian finite; in the other, the effective dynamics reacts to the macroscopic scales introduced by the boundary conditions. Both schemes reveal interesting symmetries of scaling, which are reminiscent of the relational interpretation of quantum mechanics and also suggest that the fundamental spatial scale (area gap) may give rise to a temporal scale.
Effective dynamics, big bounces, and scaling symmetry in Bianchi type I loop quantum cosmology
NASA Astrophysics Data System (ADS)
Chiou, Dah-Wei
2007-12-01
The detailed formulation for loop quantum cosmology (LQC) in the Bianchi I model with a scalar massless field has been constructed. In this paper, its effective dynamics is studied in two improved strategies for implementing the LQC discreteness corrections. Both schemes show that the big bang is replaced by the big bounces, which take place up to 3 times, once in each diagonal direction, when the area or volume scale factor approaches the critical values in the Planck regime measured by the reference of the scalar field momentum. These two strategies give different evolutions: In one scheme, the effective dynamics is independent of the choice of the finite sized cell prescribed to make Hamiltonian finite; in the other, the effective dynamics reacts to the macroscopic scales introduced by the boundary conditions. Both schemes reveal interesting symmetries of scaling, which are reminiscent of the relational interpretation of quantum mechanics and also suggest that the fundamental spatial scale (area gap) may give rise to a temporal scale.
Bianchi IX dynamics in bouncing cosmologies: homoclinic chaos and the BKL conjecture
NASA Astrophysics Data System (ADS)
Maier, Rodrigo; Damião Soares, Ivano; Valentino Tonini, Eduardo
2015-12-01
We examine the dynamics of a Bianchi IX model with three scale factors on a 4-dim Lorentzian brane embedded in a 5-dim conformally flat empty bulk with a timelike extra dimension. The matter content is a pressureless perfect fluid restricted to the brane, with the embedding consistently satisfying the Gauss-Codazzi equations. The 4-dim Einstein equations on the brane reduce to a 6-dim Hamiltonian dynamical system with additional terms (due to the bulk-brane interaction) that avoid the singularity and implement nonsingular bounces in the model. We examine the complex Bianchi IX dynamics in its approach to the neighborhood of the bounce which replaces the cosmological singularity of general relativity. The phase space of the model presents (i) two critical points (a saddle-center-center and a center-center-center) in a finite region of phase space, (ii) two asymptotic de Sitter critical points at infinity, one acting as an attractor to late-time acceleration and (iii) a 2-dim invariant plane, which together organize the dynamics of the phase space. The saddle-center-center engenders in the phase space the topology of stable and unstable 4-dim cylinders R × S 3, where R is a saddle direction and S 3 is the center manifold of unstable periodic orbits, the latter being the nonlinear extension of the center-center sector. By a proper canonical transformation the degrees of freedom of the dynamics are separated into one degree connected with the expansion/contraction of the scales of the model, and two rotational degrees of freedom associated with the center manifold S 3. The typical dynamical flow is thus an oscillatory mode about the orbits of the invariant plane. The stable and unstable cylinders are spanned by oscillatory orbits about the separatrix towards the bounce, leading to the homoclinic transversal intersection of the cylinders, as shown numerically in two distinct simulations. The homoclinic intersection manifold has the topology of R × S 2 consisting of
Ayissi, Raoul Domingo Noutchegueme, Norbert
2015-01-15
Global solutions regular for the Einstein-Boltzmann equation on a magnetized Bianchi type-I cosmological model with the cosmological constant are investigated. We suppose that the metric is locally rotationally symmetric. The Einstein-Boltzmann equation has been already considered by some authors. But, in general Bancel and Choquet-Bruhat [Ann. Henri Poincaré XVIII(3), 263 (1973); Commun. Math. Phys. 33, 83 (1973)], they proved only the local existence, and in the case of the nonrelativistic Boltzmann equation. Mucha [Global existence of solutions of the Einstein-Boltzmann equation in the spatially homogeneous case. Evolution equation, existence, regularity and singularities (Banach Center Publications, Institute of Mathematics, Polish Academy of Science, 2000), Vol. 52] obtained a global existence result, for the relativistic Boltzmann equation coupled with the Einstein equations and using the Yosida operator, but confusing unfortunately with the nonrelativistic case. Noutchegueme and Dongho [Classical Quantum Gravity 23, 2979 (2006)] and Noutchegueme, Dongho, and Takou [Gen. Relativ. Gravitation 37, 2047 (2005)], have obtained a global solution in time, but still using the Yosida operator and considering only the uncharged case. Noutchegueme and Ayissi [Adv. Stud. Theor. Phys. 4, 855 (2010)] also proved a global existence of solutions to the Maxwell-Boltzmann system using the characteristic method. In this paper, we obtain using a method totally different from those used in the works of Noutchegueme and Dongho [Classical Quantum Gravity 23, 2979 (2006)], Noutchegueme, Dongho, and Takou [Gen. Relativ. Gravitation 37, 2047 (2005)], Noutchegueme and Ayissi [Adv. Stud. Theor. Phys. 4, 855 (2010)], and Mucha [Global existence of solutions of the Einstein-Boltzmann equation in the spatially homogeneous case. Evolution equation, existence, regularity and singularities (Banach Center Publications, Institute of Mathematics, Polish Academy of Science, 2000), Vol. 52] the
NASA Astrophysics Data System (ADS)
Ayissi, Raoul Domingo; Noutchegueme, Norbert
2015-01-01
Global solutions regular for the Einstein-Boltzmann equation on a magnetized Bianchi type-I cosmological model with the cosmological constant are investigated. We suppose that the metric is locally rotationally symmetric. The Einstein-Boltzmann equation has been already considered by some authors. But, in general Bancel and Choquet-Bruhat [Ann. Henri Poincaré XVIII(3), 263 (1973); Commun. Math. Phys. 33, 83 (1973)], they proved only the local existence, and in the case of the nonrelativistic Boltzmann equation. Mucha [Global existence of solutions of the Einstein-Boltzmann equation in the spatially homogeneous case. Evolution equation, existence, regularity and singularities (Banach Center Publications, Institute of Mathematics, Polish Academy of Science, 2000), Vol. 52] obtained a global existence result, for the relativistic Boltzmann equation coupled with the Einstein equations and using the Yosida operator, but confusing unfortunately with the nonrelativistic case. Noutchegueme and Dongho [Classical Quantum Gravity 23, 2979 (2006)] and Noutchegueme, Dongho, and Takou [Gen. Relativ. Gravitation 37, 2047 (2005)], have obtained a global solution in time, but still using the Yosida operator and considering only the uncharged case. Noutchegueme and Ayissi [Adv. Stud. Theor. Phys. 4, 855 (2010)] also proved a global existence of solutions to the Maxwell-Boltzmann system using the characteristic method. In this paper, we obtain using a method totally different from those used in the works of Noutchegueme and Dongho [Classical Quantum Gravity 23, 2979 (2006)], Noutchegueme, Dongho, and Takou [Gen. Relativ. Gravitation 37, 2047 (2005)], Noutchegueme and Ayissi [Adv. Stud. Theor. Phys. 4, 855 (2010)], and Mucha [Global existence of solutions of the Einstein-Boltzmann equation in the spatially homogeneous case. Evolution equation, existence, regularity and singularities (Banach Center Publications, Institute of Mathematics, Polish Academy of Science, 2000), Vol. 52] the
Bianchi type-V bulk viscous string cosmological model in a self-creation theory of gravitation
NASA Astrophysics Data System (ADS)
Bhaskara Rao, M. P. V. V.; Reddy, D. R. K.; Sobhan Babu, K.
2015-10-01
A spatially homogenous and anisotropic Bianchi type space-time is considered in the frame work of second self-creation theory of gravitation proposed by Barber (Gen. Relativ. Gravit. 14:117, 1982) in the presence of bulk viscous fluid containing one dimensional cosmic strings. Solving the field equations of this theory an exact cosmological model is obtained using some physically plausible conditions. It is observed that strings in this model do not survive. Some physical and kinematical properties of the model are also discussed.
Bianchi Type VI1 Viscous Fluid Cosmological Model in Wesson´s Theory of Gravitation
NASA Astrophysics Data System (ADS)
Khadekar, G. S.; Avachar, G. R.
2007-03-01
Field equations of a scale invariant theory of gravitation proposed by Wesson [1, 2] are obtained in the presence of viscous fluid with the aid of Bianchi type VIh space-time with the time dependent gauge function (Dirac gauge). It is found that Bianchi type VIh (h = 1) space-time with viscous fluid is feasible in this theory, whereas Bianchi type VIh (h = -1, 0) space-times are not feasible in this theory, even in the presence of viscosity. For the feasible case, by assuming a relation connecting viscosity and metric coefficient, we have obtained a nonsingular-radiating model. We have discussed some physical and kinematical properties of the models.
Symmetry structure of a wave equation on some classes of Bianchi cosmological models
NASA Astrophysics Data System (ADS)
Jamal, S.; Kara, A. H.; Narain, R.; Shabbir, G.
2015-04-01
Nonlinear wave equations are constructed on certain Bianchi models and a symmetry analysis of these equations are performed to construct some exact solutions. Conservation laws of the respective wave equations are also obtained by the application of Noether's theorem. We show how a knowledge of these contributes to the reduction of the wave equation on this manifold.
NASA Technical Reports Server (NTRS)
Ryan, M. P., Jr.
1971-01-01
The investigation of expanding, rotating, shearing Bianchi type IX universes is extended to the most general case possible. Use is made of the techniques of Arnowitt et al. (1962). It is shown that the conclusion reached by Arnowitt et al. regarding the small effect of rotation on the singularity of type IX universes is true in general. The superspace approach to the motion of the universe is discussed in an appendix.
Inhomogeneous generalization of some Bianchi models
NASA Astrophysics Data System (ADS)
Carmeli, M.; Charach, Ch.
1980-02-01
Vacuum Bianchi models which can be transformed to the Einstein-Rosen metric are considered. The models are used in order to construct new inhomogeneous universes, which are generalizations of Bianchi cosmologies of types III, V and VIh. Recent generalizations of these Bianchi models, considered by Wainwright et al., are also discussed.
Dynamics of Bianchi I cosmologies in f( R) gravity in the Palatini formalism
NASA Astrophysics Data System (ADS)
Banik, D. K.; Banik, S. K.; Bhuyan, K.
2017-01-01
A detailed analysis of the dynamics of homogeneous and anisotropic Bianchi I geometries has been performed in f( R) gravity theory in the Palatini formalism, using dynamical systems approach. The exact solutions have been found and the behavior and stability of these solutions have been studied for three different models based on f( R) gravity. These models can produce a sequence of radiation-dominated, matter-dominated and de-Sitter periods. The analysis shows that stable solutions exist which correspond to accelerated expansion at late times. The solutions corresponding to radiation-dominated and matter-dominated era are found to be unstable. Solutions have also been found corresponding to decelerated expansion.
Supersymmetry of Bianchi attractors in gauged supergravity
NASA Astrophysics Data System (ADS)
Chakrabarty, Bidisha; Inbasekar, Karthik; Samanta, Rickmoy
2017-09-01
Bianchi attractors are near horizon geometries with homogeneous symmetries in spatial directions. We construct supersymmetric Bianchi attractors in N =2 ,d =4 , 5 gauged supergravity. In d =4 , we consider gauged supergravity coupled to vector and hypermultiplets. In d =5 , we consider gauged supergravity coupled to vector multiplets with a generic gauging of symmetries of the scalar manifold and the U (1 )R gauging of the R -symmetry. Analyzing the gaugino conditions, we show that when the fermionic shifts do not vanish, there are no supersymmetric Bianchi attractors. This is analogous to the known condition that for maximally supersymmetric solutions, all of the fermionic shifts must vanish. When the central charge satisfies an extremization condition, some of the fermionic shifts vanish and supersymmetry requires that the symmetries of the scalar manifold are not gauged. This allows supersymmetric Bianchi attractors sourced by massless gauge fields and a cosmological constant. In five dimensions in the Bianchi I class, we show that the anisotropic AdS3×R2 solution is 1 /2 BPS (Bogomol'nyi-Prasad-Sommerfield). We also construct a new class of 1 /2 BPS Bianchi III geometries labeled by the central charge. When the central charge takes a special value, the Bianchi III geometry reduces to the known AdS3×H2 solution. For the Bianchi V and VII classes, the radial spinor breaks all of supersymmetry. We briefly discuss the conditions for possible massive supersymmetric Bianchi solutions by generalizing the matter content to include tensor, hypermultiplets, and a generic gauging on the R -symmetry.
Camci, Ugur; Kucukakca, Yusuf
2007-10-15
We consider some scalar-coupled theories of gravity, including induced gravity, and study the Noether symmetries of Bianchi I, Bianchi III, and Kantowski-Sachs cosmological models for this theory. For various forms of coupling of the scalar field with gravity, some potentials are found in these cosmological models under the assumption that the Lagrangian admits Noether symmetry. The solutions of the field equations for the considered models are presented by using the results obtained from the Noether symmetry. We also find the explicit form of the scalar field in terms of the conformal time for Bianchi I, III, and Kantowski-Sachs models.
A Class of Homogeneous Scalar Tensor Cosmologies with a Radiation Fluid
NASA Astrophysics Data System (ADS)
Yazadjiev, Stoytcho S.
We present a new class of exact homogeneous cosmological solutions with a radiation fluid for all scalar tensor theories. The solutions belong to Bianchi type VIh cosmologies. Explicit examples of nonsingular homogeneous scalar tensor cosmologies are also given.
NASA Astrophysics Data System (ADS)
Harrison, Edward
2000-03-01
Cosmology: The Science of the Universe is a broad introduction to the science of modern cosmology, with emphasis on its historical origins. The first edition of this best-selling book received worldwide acclaim for its lucid style and wide-ranging exploration of the universe. This eagerly awaited second edition updates and greatly extends the first with seven new chapters that explore early scientific cosmology, Cartesian and Newtonian world systems, cosmology after Newton and before Einstein, special relativity, observational cosmology, inflation and creation of the universe. All chapters conclude with a section entitled Reflections containing provocative topics that will foster lively debate. The new Projects section, also at the end of each chapter, raises questions and issues to challenge the reader.
A dynamical systems approach to the tilted Bianchi models of solvable type
NASA Astrophysics Data System (ADS)
Coley, Alan; Hervik, Sigbjørn
2005-02-01
We use a dynamical systems approach to analyse the tilting spatially homogeneous Bianchi models of solvable type (e.g., types VIh and VIIh) with a perfect fluid and a linear barotropic γ-law equation of state. In particular, we study the late-time behaviour of tilted Bianchi models, with an emphasis on the existence of equilibrium points and their stability properties. We briefly discuss the tilting Bianchi type V models and the late-time asymptotic behaviour of irrotational Bianchi type VII0 models. We prove the important result that for non-inflationary Bianchi type VIIh models vacuum plane-wave solutions are the only future attracting equilibrium points in the Bianchi type VIIh invariant set. We then investigate the dynamics close to the plane-wave solutions in more detail, and discover some new features that arise in the dynamical behaviour of Bianchi cosmologies with the inclusion of tilt. We point out that in a tiny open set of parameter space in the type IV model (the loophole) there exist closed curves which act as attracting limit cycles. More interestingly, in the Bianchi type VIIh models there is a bifurcation in which a set of equilibrium points turns into closed orbits. There is a region in which both sets of closed curves coexist, and it appears that for the type VIIh models in this region the solution curves approach a compact surface which is topologically a torus.
The closure constraint for the hyperbolic tetrahedron as a Bianchi identity
NASA Astrophysics Data System (ADS)
Charles, Christoph; Livine, Etera R.
2017-07-01
The closure constraint is a central piece of the mathematics of loop quantum gravity. It encodes the gauge invariance of the spin network states of quantum geometry and provides them with a geometrical interpretation: each decorated vertex of a spin network is dual to a quantized polyhedron in R3. For instance, a 4-valent vertex is interpreted as a tetrahedron determined by the four normal vectors of its faces. We develop a framework where the closure constraint is re-interpreted as a Bianchi identity, with the normals defined as holonomies around the polyhedron faces of a connection (constructed from the spinning geometry interpretation of twisted geometries). This allows us to define closure constraints for hyperbolic tetrahedra (living in the 3-hyperboloid of unit future-oriented spacelike vectors in R^{3,1}) in terms of normals living all in SU(2) or in SB(2,C). The latter fits perfectly with the classical phase space developed for q-deformed loop quantum gravity supposed to account for a non-vanishing cosmological constant Λ >0. This allows the interpretation of q-deformed twisted geometries as actual discrete hyperbolic triangulations for 4d quantum gravity.
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.
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.
Quantum gravitational Kasner transitions in Bianchi-I spacetime
NASA Astrophysics Data System (ADS)
Gupt, Brajesh; Singh, Parampreet
2012-07-01
Because of nonperturbative quantum gravitational effects, the classical big bang singularity is replaced by a quantum big bounce of the mean scale factor in loop quantization of Bianchi-I spacetime. An important issue is to understand the various differences in the physical properties of the spacetime across the bounce. We investigate this issue in the context of various geometrical structures, identified by the Kasner exponents of the metric, which arise on approach to the singularity in the classical theory. Using an effective spacetime description of the Bianchi-I model in loop quantum cosmology with dust, radiation and stiff matter, we find that as in the classical theory, geometrical structures such as a cigar or a pancake form, but they are finite and nonsingular. Depending on the initial conditions of the matter and anisotropies, different geometric structures are possible in the pre- and post-bounce phases in physical evolution. Thus, quantum gravitational effects can cause a Kasner transition in Bianchi-I spacetime, which is not possible at the classical level. Interestingly, we find that not all transitions are allowed at the level of effective dynamics in loop quantum cosmology. We find the selection rules and underlying conditions for all allowed and forbidden transitions. The selection rules suggest that for a given set of initial conditions on anisotropies, the occurrence of Kasner transitions follows a distinct pattern, and certain transitions are more favored than others.
NASA Astrophysics Data System (ADS)
Clancy, Dominic; Feinstein, Alexander; Lidsey, James E.; Tavakol, Reza
1999-04-01
Global symmetries of the string effective action are employed to generate tilted, homogeneous Bianchi type VIh string cosmologies from a previously known stiff perfect fluid solution to Einstein gravity. The dilaton field is not constant on the surfaces of homogeneity. The future asymptotic state of the models is interpreted as a plane wave and is itself an exact solution to the string equations of motion to all orders in the inverse string tension. An inhomogeneous generalization of the Bianchi type III model is also found.
Vertex expansion for the Bianchi type I model
Campiglia, Miguel; Henderson, Adam; Nelson, William
2010-09-15
A perturbative expansion of loop quantum cosmological transitions amplitudes of Bianchi I models is performed. Following the procedure outlined in [1,2] for isotropic models, it is shown that the resulting expansion can be written in the form of a series of amplitudes each with a fixed number of transitions mimicking a spin foam expansion. This analogy is more complete than in the isotropic case, since there are now the additional anisotropic degrees of freedom which play the role of 'coloring' of the spin foams. Furthermore, the isotropic expansion is recovered by integrating out the anisotropies.
Planimetric Martian triangulations
NASA Technical Reports Server (NTRS)
Arthur, D. W. G.; Mcmacken, D. K.
1977-01-01
Narrow-angle photographs, which have severe drawbacks for stereophotogrammetry, have advantages for simple plane triangulations. Rectified narrow-angle pictures corrected for map projection effects can be combined in the map plane in relatively accurate planimetric triangulations. Provided the strict precepts of least squares are not followed, these triangulations can incorporate considerable overdetermination without increase in the labor of solving the equations. These plane triangulations have been used successfully in the cartography of Mars and are illustrated here by a triangulation of the environs of the prime Martian landing site.
Inflation from supersymmetric quantum cosmology
Socorro, J.; D'Oleire, Marco
2010-08-15
We derive a special scalar field potential using the anisotropic Bianchi type I cosmological model from canonical quantum cosmology under determined conditions in the evolution to anisotropic variables {beta}{sub {+-}}. In the process, we obtain a family of potentials that has been introduced by hand in the literature to explain cosmological data. Considering supersymmetric quantum cosmology, this family is scanned, fixing the exponential potential as more viable in the inflation scenario V({phi})=V{sub 0}e{sup -{radical}(3){phi}}.
Bianchi type-I universe in f(R, T) modified gravity with quark matter and Λ
NASA Astrophysics Data System (ADS)
Ćaǧlar, Halife; Aygün, Sezgin
2017-02-01
In this study, we investigate homogeneous and anisotropic Bianchi type I universe in the presence of quark matter source in f(R, T) gravity (Harko et al. in Phys. Rev. D 84:024020, 2011) with cosmological constant Λ (where R is the Ricci scalar and T is the trace of the energy momentum tensor). For this aim we have used the anisotropy feature of Bianchi type I universe and equation of states (EoS) of quark matter. We explore the exact solution f(R,T)=R+2f(T) model for Bianchi type I universe model. When t→∞, we get very small cosmological constant value, this result agrees with recent observations.
Geodesic-light-cone coordinates and the Bianchi I spacetime
NASA Astrophysics Data System (ADS)
Fleury, Pierre; Nugier, Fabien; Fanizza, Giuseppe
2016-06-01
The geodesic-light-cone (GLC) coordinates are a useful tool to analyse light propagation and observations in cosmological models. In this article, we propose a detailed, pedagogical, and rigorous introduction to this coordinate system, explore its gauge degrees of freedom, and emphasize its interest when geometric optics is at stake. We then apply the GLC formalism to the homogeneous and anisotropic Bianchi I cosmology. More than a simple illustration, this application (i) allows us to show that the Weinberg conjecture according to which gravitational lensing does not affect the proper area of constant-redshift surfaces is significantly violated in a globally anisotropic universe; and (ii) offers a glimpse into new ways to constrain cosmic isotropy from the Hubble diagram.
Cosmic anisotropic doomsday in Bianchi type I universes
NASA Astrophysics Data System (ADS)
Cataldo, Mauricio; Cid, Antonella; Labraña, Pedro; Mella, Patricio
2016-11-01
In this paper we study finite time future singularities in anisotropic Bianchi type I models. It is shown that there exist future singularities similar to Big Rip ones (which appear in the framework of phantom Friedmann-Robertson-Walker cosmologies). Specifically, in an ellipsoidal anisotropic scenario or in a fully anisotropic scenario, the three directional and average scale factors may diverge at a finite future time, together with energy densities and anisotropic pressures. We call these singularities "Anisotropic Big Rip Singularities." We show that there also exist Bianchi type I models filled with matter, where one or two directional scale factors may diverge. Another type of future anisotropic singularities is shown to be present in vacuum cosmologies, i.e., Kasner spacetimes. These singularities are induced by the shear scalar, which also blows up at a finite time. We call such a singularity "Vacuum Rip." In this case one directional scale factor blows up, while the other two and average scale factors tend to zero.
Late-time behaviour of the tilted Bianchi type VIh models
NASA Astrophysics Data System (ADS)
Hervik, S.; van den Hoogen, R. J.; Lim, W. C.; Coley, A. A.
2007-08-01
We study tilted perfect fluid cosmological models with a constant equation of state parameter in spatially homogeneous models of Bianchi type VIh using dynamical systems methods and numerical experimentation, with an emphasis on their future asymptotic evolution. We determine all of the equilibrium points of the type VIh state space (which correspond to exact self-similar solutions of the Einstein equations, some of which are new), and their stability is investigated. We find that there are vacuum plane-wave solutions that act as future attractors. In the parameter space, a 'loophole' is shown to exist in which there are no stable equilibrium points. We then show that a Hopf-bifurcation can occur resulting in a stable closed orbit (which we refer to as the Mussel attractor) corresponding to points both inside the loophole and points just outside the loophole; in the former case the closed curves act as late-time attractors while in the latter case these attracting curves will co-exist with attracting equilibrium points. In the special Bianchi type III case, centre manifold theory is required to determine the future attractors. Comprehensive numerical experiments are carried out to complement and confirm the analytical results presented. We note that the Bianchi type VIh case is of particular interest in that it contains many different subcases which exhibit many of the different possible future asymptotic behaviours of Bianchi cosmological models.
A new way to derive the Taub-NUT metric with positive cosmological constant
NASA Astrophysics Data System (ADS)
Osuga, Kento; Page, Don N.
2017-08-01
We investigate a biaxial Bianchi IX model with positive cosmological constant, which is sometimes called the Λ -Taub-NUT spacetime, whose exact solution is well known. The minisuperspace of biaxial Bianchi IX models admits two non-trivial Killing tensors that play an important role for deriving the Taub-NUT metric.
NASA Technical Reports Server (NTRS)
Fennelly, A. J.; Evans, C. R.
1980-01-01
Magnetohydrodynamic (MHD) perturbations in flat Robertson-Walker universes were analyzed, emphasizing their effects on galaxy formation. The Newtonian approximation is used. There is no increase in the growth rates beyond those of the usual perturbed Robertson-Walker models; the MHD modes extract as much energy as they contribute. Some global properties of fully MHD Bianchi I relativistic models are analyzed including vorticity, fluid accelerations, and dissipative effects. The time dependence of perturbations of a fully MHD diagonal Bianchi I cosmology is studied, with an enhanced growth rate of the density contrast of t found which is still not exponential Jeans-type growth. This indicates that a more detailed analysis is needed if a solution to the galaxy formation problem in MHD cosmologies is to be found.
NASA Astrophysics Data System (ADS)
Socorro, J.; Toledo Sesma, L.
2016-03-01
In this work we construct an effective four-dimensional model by compactifying a ten-dimensional theory of gravity coupled with a real scalar dilaton field on a time-dependent torus without the contributions of fluxes as first approximation. This approach is applied to anisotropic cosmological Bianchi type II model for which we study the classical coupling of the anisotropic scale factors with the two real scalar moduli produced by the compactification process. Also, we present some solutions to the corresponding Wheeler-DeWitt (WDW) equation in the context of Standard Quantum Cosmology and we claim that these quantum solution are generic in the moduli scalar field for all Bianchi Class A models. Also we give the relation to these solutions for asymptotic behavior to large argument in the corresponding quantum solution in the gravitational variables and compare with Bohm's solutions, finding that this corresponds to the lowest-order WKB approximation.
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.
ERIC Educational Resources Information Center
Denzin, Norman K.
2012-01-01
The author's thesis is simple and direct. Those in the mixed methods qualitative inquiry community need a new story line, one that does not confuse pragmatism for triangulation, and triangulation for mixed methods research (MMR). A different third way is required, one that inspires generative politics and dialogic democracy and helps shape…
ERIC Educational Resources Information Center
Denzin, Norman K.
2012-01-01
The author's thesis is simple and direct. Those in the mixed methods qualitative inquiry community need a new story line, one that does not confuse pragmatism for triangulation, and triangulation for mixed methods research (MMR). A different third way is required, one that inspires generative politics and dialogic democracy and helps shape…
Anisotropic Bianchi type-III model in Palatini f (R) gravity
NASA Astrophysics Data System (ADS)
Banik, Debika Kangsha; Banik, Sebika Kangsha; Bhuyan, Kalyan
2017-03-01
We derive exact solutions for anisotropic Bianchi type-III cosmological model in the Palatini formalism of f (R) gravity using Dynamical System Approach. For the f (R) of the form f(R) =R-β /Rn and f(R) =R+α Rm , we have found the fixed points describing the radiation-dominated, matter dominated and de Sitter evolution periods. Fixed points have also been found which have non-vanishing shear playing a very significant role in describing the anisotropy present in the early universe. In addition, we have also found that the spatial curvature affect isotropisation of this cosmological model.
Noether symmetries of Bianchi type II spacetimes
NASA Astrophysics Data System (ADS)
Hickman, Mark; Yazdan, Shair-a.
2017-05-01
This paper is devoted to investigate Noether symmetries of Bianchi type II spacetimes. We use the reduced involutive form of the determining equations to classify their possible algebras. We show that Noether symmetries contain both Killing vectors and homothetic motions.
Triangulation of NURBS Surfaces
NASA Technical Reports Server (NTRS)
Samareh-Abolhassani, Jamshid
1994-01-01
A technique is presented for triangulation of NURBS surfaces. This technique is built upon an advancing front technique combined with grid point projection. This combined approach has been successfully implemented for structured and unstructured grids.
Inhomogeneous Einstein-Rosen string cosmology
NASA Astrophysics Data System (ADS)
Clancy, Dominic; Feinstein, Alexander; Lidsey, James E.; Tavakol, Reza
1999-08-01
Families of anisotropic and inhomogeneous string cosmologies containing non-trivial dilaton and axion fields are derived by applying the global symmetries of the string effective action to a generalized Einstein-Rosen metric. The models exhibit a two-dimensional group of Abelian isometries. In particular, two classes of exact solutions are found that represent inhomogeneous generalizations of the Bianchi type VIh cosmology. The asymptotic behavior of the solutions is investigated and further applications are briefly discussed.
Bianchi class A models in Sàez-Ballester's theory
NASA Astrophysics Data System (ADS)
Socorro, J.; Espinoza-García, Abraham
2012-08-01
We apply the Sàez-Ballester (SB) theory to Bianchi class A models, with a barotropic perfect fluid in a stiff matter epoch. We obtain exact classical solutions à la Hamilton for Bianchi type I, II and VIh=-1 models. We also find exact quantum solutions to all Bianchi Class A models employing a particular ansatz for the wave function of the universe.
Anisotropic spinfoam cosmology
NASA Astrophysics Data System (ADS)
Rennert, Julian; Sloan, David
2014-01-01
The dynamics of a homogeneous, anisotropic universe are investigated within the context of spinfoam cosmology. Transition amplitudes are calculated for a graph consisting of a single node and three links—the ‘Daisy graph’—probing the behaviour a classical Bianchi I spacetime. It is shown further how the use of such single node graphs gives rise to a simplification of states such that all orders in the spin expansion can be calculated, indicating that it is the vertex expansion that contains information about quantum dynamics.
Unstable anisotropic loop quantum cosmology
Nelson, William; Sakellariadou, Mairi
2009-09-15
We study stability conditions of the full Hamiltonian constraint equation describing the quantum dynamics of the diagonal Bianchi I model in the context of loop quantum cosmology. Our analysis has shown robust evidence of an instability in the explicit implementation of the difference equation, implying important consequences for the correspondence between the full loop quantum gravity theory and loop quantum cosmology. As a result, one may question the choice of the quantization approach, the model of lattice refinement, and/or the role of the ambiguity parameters; all these should, in principle, be dictated by the full loop quantum gravity theory.
Zhang, Qianggong; Chin, Tat-Jun
2017-09-11
Multiple-view triangulation by l∞ minimisation has become established in computer vision. State-of-the-art l∞ triangulation algorithms exploit the quasiconvexity of the cost function to derive iterative update rules that deliver the global minimum. Such algorithms, however, can be computationally costly for large problem instances that contain many image measurements, e.g., from web-based photo sharing sites or long-term video recordings. In this paper, we prove that l∞ triangulation admits a coreset approximation scheme, which seeks small representative subsets of the input data called coresets. A coreset possesses the special property that the error of the l∞ solution on the coreset is within known bounds from the global minimum. We establish the necessary mathematical underpinnings of the coreset algorithm, specifically, by enacting the stopping criterion of the algorithm and proving that the resulting coreset gives the desired approximation accuracy. On large-scale triangulation problems, our method provides theoretically sound approximate solutions. Iterated until convergence, our coreset algorithm is also guaranteed to reach the true optimum. On practical datasets, we show that our technique can in fact attain the global minimiser much faster than current methods.
Triangulation in aetiological epidemiology.
Lawlor, Debbie A; Tilling, Kate; Davey Smith, George
2016-12-01
Triangulation is the practice of obtaining more reliable answers to research questions through integrating results from several different approaches, where each approach has different key sources of potential bias that are unrelated to each other. With respect to causal questions in aetiological epidemiology, if the results of different approaches all point to the same conclusion, this strengthens confidence in the finding. This is particularly the case when the key sources of bias of some of the approaches would predict that findings would point in opposite directions if they were due to such biases. Where there are inconsistencies, understanding the key sources of bias of each approach can help to identify what further research is required to address the causal question. The aim of this paper is to illustrate how triangulation might be used to improve causal inference in aetiological epidemiology. We propose a minimum set of criteria for use in triangulation in aetiological epidemiology, summarize the key sources of bias of several approaches and describe how these might be integrated within a triangulation framework. We emphasize the importance of being explicit about the expected direction of bias within each approach, whenever this is possible, and seeking to identify approaches that would be expected to bias the true causal effect in different directions. We also note the importance, when comparing results, of taking account of differences in the duration and timing of exposures. We provide three examples to illustrate these points. © The Author 2017. Published by Oxford University Press on behalf of the International Epidemiological Association.
NASA Astrophysics Data System (ADS)
Belinchón, José Antonio
2008-06-01
In this paper we study how to attack, through different techniques, a perfect fluid Bianchi I model with variable G, c and Λ, “but” taking into account the effects of a “ c-variable” into the curvature tensor. We study the model under the assumption, div( T)=0. These tactics are: Lie groups method (LM), imposing a particular symmetry, self-similarity (SS), matter collineations (MC) and kinematical self-similarity (KSS). We compare both tactics since they are quite similar (symmetry principles). We arrive to the conclusion that the LM is too restrictive and brings us to get only the flat FRW solution. The SS, MC and KSS approaches bring us to obtain all the quantities depending on ( ∫ c( t) dt). Therefore, in order to study their behavior we impose some physical restrictions like for example the condition q<0 (accelerating universe). In this way we find that c is a growing time function and Λ is a decreasing time function whose sing depends on the equation of state ω, while the exponents of the scale factor must satisfy the conditions ∑{/i=1 3} α i =1 and ∑{/i=1 3} α {/i 2}<1, ∀ ω, i.e. for all equation of state, relaxing in this way the Kasner conditions. The behavior of G depends on two parameters, the equation of state ω and ɛ, a parameter that controls the behavior of c( t), therefore G may be growing or decreasing. We also show that through the Lie method, there is no difference between to study the field equations under the assumption of a c-var affecting to the curvature tensor which the other one where it is not considered such effects. Nevertheless, it is essential to consider such effects in the cases studied under the SS, MC, and KSS hypotheses.
Evolution in bouncing quantum cosmology
NASA Astrophysics Data System (ADS)
Mielczarek, Jakub; Piechocki, Włodzimierz
2012-03-01
We present the method of describing an evolution in quantum cosmology in the framework of the reduced phase space quantization of loop cosmology. We apply our method to the flat Friedmann-Robertson-Walker model coupled to a massless scalar field. We identify the physical quantum Hamiltonian that is positive-definite and generates globally a unitary evolution of the considered quantum system. We examine the properties of expectation values of physical observables in the process of the quantum big bounce transition. The dispersion of evolved observables is studied for the Gaussian state. Calculated relative fluctuations enable an examination of the semi-classicality conditions and possible occurrence of the cosmic forgetfulness. Preliminary estimations based on the cosmological data suggest that there was no cosmic amnesia. Presented results are analytical, and numerical computations are only used for the visualization purposes. Our method may be generalized to sophisticated cosmological models including the Bianchi-type universes.
Gravitational Energy-Momentum Density in Bianchi Type II Space-Times
NASA Astrophysics Data System (ADS)
Aydogdu, Oktay
In this paper, using Einstein, Landau and Lifshitz's energy-momentum complexes both in general relativity and teleparallel gravity, we calculate the total energy distribution (due to matter and fields, including gravitation) associated with locally rotationally symmetric (LRS) Bianchi type II cosmological models. We show that energy densities in these different gravitation theories are the same, so they agree with each other. We obtain the result that the total energy is zero. This result agrees with previous works of Cooperstock and Israelit, Rosen, Johri et al., Banerjee and Sen, Vargas, Aydogdu and Saltı. Moreover, our result supports the viewpoints of Albrow and Tryon.
Study of Bianchi type-I model in f(R,Tψ) gravity
NASA Astrophysics Data System (ADS)
Sharif, M.; Siddiqa, Aisha
2017-03-01
We study the cosmological behavior of locally rotationally symmetric (LRS) Bianchi type-I universe model in f (R ,Tψ) gravity. For this purpose, we evaluate Hubble parameter, effective equation of state parameter (ωeff) and potential of scalar field (ψ) as a function of time using the assumption H = W (ψ). The behavior of these parameters is investigated for different models of W (ψ). It is concluded that exponential form of W (ψ) leads to time independent ωeff which corresponds to different stages of evolution while for the other two models, they correspond to stiff fluid stage.
Bianchi type-I universe in Lyra manifold with quadratic equation of state
NASA Astrophysics Data System (ADS)
Şen, R.; Aygün, S.
2017-02-01
In this study, we have solved Einstein field equations for Bianchi type I universe model in Lyra manifold with quadratic equation of state (EoS) p = ap(t)2 - ρ(t). Where α ≠0 is an important constant. Cosmic pressure, density and displacement vector (β2) are related with α constant. In this study β2 is a decreasing function of time and behaves like a cosmological constant. These solutions agree with the studies of Halford, Pradhan and Singh, Aygün et al., Agarwal et al., Yadav and Haque as well as SN Ia observations.
Spinor fields in Bianchi type-I universe
NASA Astrophysics Data System (ADS)
Saha, B.
2006-12-01
A system of minimally coupled nonlinear spinor and scalar fields within the scope of a Bianchi type-I (BI) cosmological model in the presence of a perfect fluid and a cosmological constant (Λ term) is studied, and solutions to the corresponding field equations are obtained. The problem of initial singularity and the asymptotical isotropization process of the Universe are thoroughly studied. The effect of the Λ term on the character of evolution is analyzed. It is shown that some special choice of spinor field nonlinearity generates a regular solution, but the absence of singularity results in violating the dominant energy condition in the Hawking-Penrose theorem. It is also shown that a positive Λ, which denotes an additional gravitational force in our case, gives rise to an oscillatory or a non-periodic mode of expansion of the Universe depending on the choice of problem parameter. The regular oscillatory mode of expansion violets the dominant energy condition if the spinor field nonlinearity occurs as a result of self-action, whereas, in the case of a linear spinor field or nonlinear one that occurs due to interaction with a scalar field, the dominant condition remains unbroken. A system with time-varying gravitational (G) and cosmological (Λ) constants is also studied to some extent. The introduction of magneto-fluid in the system generates nonhomogeneity in the energy-momentum tensor and can be exactly solved only under some additional condition. Though in this case, we indeed deal with all four known fields, i.e., spinor, scalar, electromagnetic, and gravitational, the over-all picture of evolution remains unchanged.
Problems with Chaos in String Cosmology
NASA Astrophysics Data System (ADS)
Dąbrowski, Mariusz P.
I review the main ideas of the pre-big-bang cosmology scenario emphasizing the role of different boundary conditions in comparison to the standard ones which appear in quantum cosmology. My main issue is duality symmetry - a very general feature of string theory - and its role in suppressing chaos in Bianchi type IX "Mixmaster" universes within the framework of the tree-level low-energy-effectiveactions for strings. Finally, I discuss the ways to possibly `generate' chaos in string cosmology by admitting dilaton potential/massive string modes, more spacetime dimensions or nonlinear Yang-Mills-Lorentz-Chern-Simons terms into the action.
Triangulating Trimmed NURBS Surfaces
2000-01-01
Curve and Surface Design: Saint-Malo 1999 381 Pierre-Jean Laurent, Paul Sablonnibre, and Larry L. Schumaker ( eds .), pp. 381-388. Copyright 0 2000 by...the boundary of its neighboring surface. References 1. Baehmann, P. L., S. L. Wittchen , M. S. Shephard, K. R. Grice and M. A. Yerry, Robust...and D. Eppstein, Mesh generation and optimal triangulation, in Computing in Euclidean Geometry, 2nd ed ., D.-Z. Du and F. K. Hwang, ( eds .), World
Advanced Triangulation Displacement Sensors
NASA Technical Reports Server (NTRS)
Poteet, Wade M.; Cauthen, Harold K.
1996-01-01
Advanced optoelectronic triangulation displacement sensors undergoing development. Highly miniaturized, more stable, more accurate, and relatively easy to use. Incorporate wideband electronic circuits suitable for real-time monitoring and control of displacements. Measurements expected to be accurate to within nanometers. In principle, sensors mass-produced at relatively low unit cost. Potential applications numerous. Possible industrial application in measuring runout of rotating shaft or other moving part during fabrication in "zero-defect" manufacturing system, in which measured runout automatically corrected.
Advanced Triangulation Displacement Sensors
NASA Technical Reports Server (NTRS)
Poteet, Wade M.; Cauthen, Harold K.
1996-01-01
Advanced optoelectronic triangulation displacement sensors undergoing development. Highly miniaturized, more stable, more accurate, and relatively easy to use. Incorporate wideband electronic circuits suitable for real-time monitoring and control of displacements. Measurements expected to be accurate to within nanometers. In principle, sensors mass-produced at relatively low unit cost. Potential applications numerous. Possible industrial application in measuring runout of rotating shaft or other moving part during fabrication in "zero-defect" manufacturing system, in which measured runout automatically corrected.
Inhomogeneous anisotropic cosmology
NASA Astrophysics Data System (ADS)
Kleban, Matthew; Senatore, Leonardo
2016-10-01
In homogeneous and isotropic Friedmann-Robertson-Walker cosmology, the topology of the universe determines its ultimate fate. If the Weak Energy Condition is satisfied, open and flat universes must expand forever, while closed cosmologies can recollapse to a Big Crunch. A similar statement holds for homogeneous but anisotropic (Bianchi) universes. Here, we prove that arbitrarily inhomogeneous and anisotropic cosmologies with ``flat'' (including toroidal) and ``open'' (including compact hyperbolic) spatial topology that are initially expanding must continue to expand forever at least in some region at a rate bounded from below by a positive number, despite the presence of arbitrarily large density fluctuations and/or the formation of black holes. Because the set of 3-manifold topologies is countable, a single integer determines the ultimate fate of the universe, and, in a specific sense, most 3-manifolds are ``flat'' or ``open''. Our result has important implications for inflation: if there is a positive cosmological constant (or suitable inflationary potential) and initial conditions for the inflaton, cosmologies with ``flat'' or ``open'' topology must expand forever in some region at least as fast as de Sitter space, and are therefore very likely to begin inflationary expansion eventually, regardless of the scale of the inflationary energy or the spectrum and amplitude of initial inhomogeneities and gravitational waves. Our result is also significant for numerical general relativity, which often makes use of periodic (toroidal) boundary conditions.
Inhomogeneous anisotropic cosmology
Kleban, Matthew; Senatore, Leonardo
2016-10-12
In homogeneous and isotropic Friedmann-Robertson-Walker cosmology, the topology of the universe determines its ultimate fate. If the Weak Energy Condition is satisfied, open and flat universes must expand forever, while closed cosmologies can recollapse to a Big Crunch. A similar statement holds for homogeneous but anisotropic (Bianchi) universes. Here, we prove that arbitrarily inhomogeneous and anisotropic cosmologies with “flat” (including toroidal) and “open” (including compact hyperbolic) spatial topology that are initially expanding must continue to expand forever at least in some region at a rate bounded from below by a positive number, despite the presence of arbitrarily large density fluctuations and/or the formation of black holes. Because the set of 3-manifold topologies is countable, a single integer determines the ultimate fate of the universe, and, in a specific sense, most 3-manifolds are “flat” or “open”. Our result has important implications for inflation: if there is a positive cosmological constant (or suitable inflationary potential) and initial conditions for the inflaton, cosmologies with “flat” or “open” topology must expand forever in some region at least as fast as de Sitter space, and are therefore very likely to begin inflationary expansion eventually, regardless of the scale of the inflationary energy or the spectrum and amplitude of initial inhomogeneities and gravitational waves. Our result is also significant for numerical general relativity, which often makes use of periodic (toroidal) boundary conditions.
Inhomogeneous anisotropic cosmology
Kleban, Matthew; Senatore, Leonardo
2016-10-12
In homogeneous and isotropic Friedmann-Robertson-Walker cosmology, the topology of the universe determines its ultimate fate. If the Weak Energy Condition is satisfied, open and flat universes must expand forever, while closed cosmologies can recollapse to a Big Crunch. A similar statement holds for homogeneous but anisotropic (Bianchi) universes. Here in this paper, we prove that arbitrarily inhomogeneous and anisotropic cosmologies with "flat'' (including toroidal) and "open'' (including compact hyperbolic) spatial topology that are initially expanding must continue to expand forever at least in some region at a rate bounded from below by a positive number, despite the presence of arbitrarilymore » large density fluctuations and/or the formation of black holes. Because the set of 3-manifold topologies is countable, a single integer determines the ultimate fate of the universe, and, in a specific sense, most 3-manifolds are "flat" or "open". Our result has important implications for inflation: if there is a positive cosmological constant (or suitable inflationary potential) and initial conditions for the inflaton, cosmologies with "flat'' or "open" topology must expand forever in some region at least as fast as de Sitter space, and are therefore very likely to begin inflationary expansion eventually, regardless of the scale of the inflationary energy or the spectrum and amplitude of initial inhomogeneities and gravitational waves. Our result is also significant for numerical general relativity, which often makes use of periodic (toroidal) boundary conditions.« less
Inhomogeneous anisotropic cosmology
Kleban, Matthew; Senatore, Leonardo
2016-10-12
In homogeneous and isotropic Friedmann-Robertson-Walker cosmology, the topology of the universe determines its ultimate fate. If the Weak Energy Condition is satisfied, open and flat universes must expand forever, while closed cosmologies can recollapse to a Big Crunch. A similar statement holds for homogeneous but anisotropic (Bianchi) universes. Here in this paper, we prove that arbitrarily inhomogeneous and anisotropic cosmologies with "flat'' (including toroidal) and "open'' (including compact hyperbolic) spatial topology that are initially expanding must continue to expand forever at least in some region at a rate bounded from below by a positive number, despite the presence of arbitrarily large density fluctuations and/or the formation of black holes. Because the set of 3-manifold topologies is countable, a single integer determines the ultimate fate of the universe, and, in a specific sense, most 3-manifolds are "flat" or "open". Our result has important implications for inflation: if there is a positive cosmological constant (or suitable inflationary potential) and initial conditions for the inflaton, cosmologies with "flat'' or "open" topology must expand forever in some region at least as fast as de Sitter space, and are therefore very likely to begin inflationary expansion eventually, regardless of the scale of the inflationary energy or the spectrum and amplitude of initial inhomogeneities and gravitational waves. Our result is also significant for numerical general relativity, which often makes use of periodic (toroidal) boundary conditions.
Loop quantum cosmology: Anisotropies and inhomogeneities
NASA Astrophysics Data System (ADS)
Wilson-Ewing, Edward
In this dissertation we extend the improved dynamics of loop quantum cosmology from the homogeneous and isotropic Friedmann-Lemaitre-Robertson-Walker space-times to cosmological models which allow anisotropies and inhomogeneities. Specifically, we consider the cases of the homogeneous but anisotropic Bianchi type I, II and IX models with a massless scalar field as well as the vacuum, inhomogeneous, linearly polarized Gowdy T3 model. For each case, we derive the Hamiltonian constraint operator and study its properties. In particular, we show how in all of these models the classical big bang and big crunch singularities are resolved due to quantum gravity effects. Since the Bianchi models play a key role in the Belinskii, Khalatnikov and Lifshitz conjecture regarding the nature of generic space-like singularities in general relativity, the quantum dynamics of the Bianchi cosmologies are likely to provide considerable intuition about the fate of such singularities in quantum gravity. In addition, the results obtained here provide an important step toward the full loop quantization of cosmological space-times that allow generic inhomogeneities; this would provide falsifiable predictions that could be compared to observations.
Inhomogeneous loop quantum cosmology: Hybrid quantization of the Gowdy model
NASA Astrophysics Data System (ADS)
Garay, L. J.; Martín-Benito, M.; Mena Marugán, G. A.
2010-08-01
The Gowdy cosmologies provide a suitable arena to further develop loop quantum cosmology, allowing the presence of inhomogeneities. For the particular case of Gowdy spacetimes with the spatial topology of a three-torus and a content of linearly polarized gravitational waves, we detail a hybrid quantum theory in which we combine a loop quantization of the degrees of freedom that parametrize the subfamily of homogeneous solutions, which represent Bianchi I spacetimes, and a Fock quantization of the inhomogeneities. Two different theories are constructed and compared, corresponding to two different schemes for the quantization of the Bianchi I model within the improved dynamics formalism of loop quantum cosmology. One of these schemes has been recently put forward by Ashtekar and Wilson-Ewing. We address several issues, including the quantum resolution of the cosmological singularity, the structure of the superselection sectors in the quantum system, or the construction of the Hilbert space of physical states.
The use of triangulation in qualitative research.
Carter, Nancy; Bryant-Lukosius, Denise; DiCenso, Alba; Blythe, Jennifer; Neville, Alan J
2014-09-01
Triangulation refers to the use of multiple methods or data sources in qualitative research to develop a comprehensive understanding of phenomena (Patton, 1999). Triangulation also has been viewed as a qualitative research strategy to test validity through the convergence of information from different sources. Denzin (1978) and Patton (1999) identified four types of triangulation: (a) method triangulation, (b) investigator triangulation, (c) theory triangulation, and (d) data source triangulation. The current article will present the four types of triangulation followed by a discussion of the use of focus groups (FGs) and in-depth individual (IDI) interviews as an example of data source triangulation in qualitative inquiry.
Anisotropic Cosmology and Curvature Invariants.
NASA Astrophysics Data System (ADS)
Skea, James E. F.
Available from UMI in association with The British Library. In Part 1 of this thesis we study the phase-planes of two classes of Kaluza-Klein (higher-dimensional) cosmologies, namely those containing a barotropic (p = nrho ) perfect fluid in a product-space of two flat manifolds, and those with a vacuum energy-momentum tensor in a product -space of one flat and one curved manifold. For the first class, we determine some general characteristics of the phase-plane--the number of types of solution possible is almost always found to be six, seven and three for the cases where the higher-dimensional cosmological constant (|{Lambda}) is zero, positive and negative respectively; the only stable solutions correspond to generalisations of the Einstein -De-Sitter solutions and De-Sitter solutions when |{Lambda} = 0 and |{Lambda} > 0 respectively; there are no stable solutions when |{Lambda} < 0. We identify higher-dimensional generalisations of barotropic fluids of particular cosmological interest and classify the different types of solution in terms of the asymptotic behaviour of the Hubble factors of the manifolds. Having identified criteria for compatibility of the cosmologies with observation, we check whether the proposed fluids satisfy these criteria, and find that only a very restricted subset of the fluids permit feasible cosmologies. Those fluids which do not conform to the general classification scheme are identified and their phase-planes studied. In Part 2, we evaluate the effects of the production of free particles on the Bianchi type I, VIII and IX homogeneous cosmologies. The theoretical predictions in the axisymmetric Bianchi I model are calculated, and comparison made with both the theory of Lukash and Starobinskii and subsequent numerical integrations of the Field Equations. From the numerical integrations, we find that isotropisation time will be a factor 50 greater than previously expected for axisymmetric models, and can be a further factor of 10 ^3
Birefringent light propagation on anisotropic cosmological backgrounds
NASA Astrophysics Data System (ADS)
Asenjo, Felipe A.; Hojman, Sergio A.
2017-08-01
Exact electromagnetic wave solutions to Maxwell equations on anisotropic Bianchi I cosmological spacetime backgrounds are studied. The waves evolving on Bianchi I spacetimes exhibit birefringence (associated with linear polarization) and dispersion. The particular case of a vacuum-dominated anisotropic Universe, which reproduces a Friedmann-Robertson-Walker Universe (for late times)—while, for earlier times, it matches a Kasner Universe—is studied. The electromagnetic waves do not, in general, follow null geodesics. This produces a modification of the cosmological redshift, which is then dependent on light polarization, its dispersion, and its non-null geodesic behavior. New results presented here may help to tackle some issues related to the "horizon" problem.
NASA Astrophysics Data System (ADS)
Hehl, Friedrich W.; McCrea, J. Dermott
1986-03-01
Automatic conservation of energy-momentum and angular momentum is guaranteed in a gravitational theory if, via the field equations, the conservation laws for the material currents are reduced to the contracted Bianchi identities. We first execute an irreducible decomposition of the Bianchi identities in a Riemann-Cartan space-time. Then, starting from a Riemannian space-time with or without torsion, we determine those gravitational theories which have automatic conservation: general relativity and the Einstein-Cartan-Sciama-Kibble theory, both with cosmological constant, and the nonviable pseudoscalar model. The Poincaré gauge theory of gravity, like gauge theories of internal groups, has no automatic conservation in the sense defined above. This does not lead to any difficulties in principle. Analogies to 3-dimensional continuum mechanics are stressed throughout the article.
Effect of inflation on anisotropic cosmologies
Jensen, L.G.; Stein-Schabes, J.A.
1986-03-01
The effects of anisotropic cosmologies on inflation are studied. By properly formulating the field equations it is possible to show that any model that undergoes sufficient inflation will become isotropic on scales greater than the horizon today. Furthermore, we shall show that it takes a very long time for anisotropies to become visible in the observable part of the Universe. It is interesting to note that the time scale will be independent of the Bianchi Model and of the initial anisotropy. 6 refs.
Inhomogeneous generalizations of Bianchi type VIh models with perfect fluid
NASA Astrophysics Data System (ADS)
Roy, S. R.; Prasad, A.
1991-07-01
Inhomogeneous universes admitting an Abelian G2 of isometry and filled with perfect fluid have been derived. These contain as special cases exact homogeneous universes of Bianchi type VIh. Many of these universes asymptotically tend to homogeneous Bianchi VIh universes. The models have been discussed for their physical and kinematical behaviors.
Unitary evolution for anisotropic quantum cosmologies: models with variable spatial curvature
NASA Astrophysics Data System (ADS)
Pandey, Sachin; Banerjee, Narayan
2016-11-01
Contrary to the general belief, there has recently been quite a few examples of unitary evolution of quantum cosmological models. The present work gives more examples, namely Bianchi type VI and type II. These examples are important as they involve varying spatial curvature unlike the most talked about homogeneous but anisotropic cosmological models like Bianchi I, V and IX. We exhibit either an explicit example of the unitary solutions of the Wheeler-DeWitt equation, or at least show that a self-adjoint extension is possible.
The Maxwell-Chern-Simons gravity, and its cosmological implications
NASA Astrophysics Data System (ADS)
Haghani, Zahra; Harko, Tiberiu; Shahidi, Shahab
2017-08-01
We consider the cosmological implications of a gravitational theory containing two vector fields coupled via a generalized Chern-Simons term. One of the vector fields is the usual Maxwell field, while the other is a constrained vector field with constant norm included in the action via a Lagrange multiplier. The theory admits a de Sitter type solution, with healthy cosmological perturbations. We also show that there are seven degrees of freedom that propagate on top of de Sitter space-time, consisting of two tensor polarizations, four degrees of freedom related to the two vector fields, and a scalar degree of freedom that makes one of the vector fields massive. We investigate the cosmological evolution of Bianchi type I space-time, by assuming that the matter content of the Universe can be described by the stiff and dust. The cosmological evolution of the Bianchi type I Universe strongly depends on the initial conditions of the physical quantities, as well as on the model parameters. The mean anisotropy parameter, and the deceleration parameter, are also studied, and we show that independently of the matter equation of state the cosmological evolution of the Bianchi type I Universe always ends in an isotropic de Sitter type phase.
Lindstrom, P
2009-12-23
We describe a simple and efficient algorithm for two-view triangulation of 3D points from approximate 2D matches based on minimizing the L2 reprojection error. Our iterative algorithm improves on the one by Kanatani et al. by ensuring that in each iteration the epipolar constraint is satisfied. In the case where the two cameras are pointed in the same direction, the method provably converges to an optimal solution in exactly two iterations. For more general camera poses, two iterations are sufficient to achieve convergence to machine precision, which we exploit to devise a fast, non-iterative method. The resulting algorithm amounts to little more than solving a quadratic equation, and involves a fixed, small number of simple matrixvector operations and no conditional branches. We demonstrate that the method computes solutions that agree to very high precision with those of Hartley and Sturm's original polynomial method, though achieves higher numerical stability and 1-4 orders of magnitude greater speed.
Issues in using methodological triangulation in research.
Casey, Dympna; Murphy, Kathy
2009-01-01
This paper describes how methodological triangulation was used in two nursing research studies. The literature identified a number of principles in reporting studies that used triangulation, including giving the rationale for using triangulation, detailing the process used to assist with triangulation and explaining how rigour was maintained. A brief review of triangulated studies revealed that few adhered fully to these principles. A 'within method' and an 'across method' study are used to illustrate how methodological triangulation was used, and the ways in which rigour was addressed are also described. In addition, the different contributions of triangulation to nursing research are highlighted.
An intrinsic and exterior form of the Bianchi identities
NASA Astrophysics Data System (ADS)
Do, Thoan; Prince, Geoff
2017-09-01
We give an elegant formulation of the structure equations (of Cartan) and the Bianchi identities in terms of exterior calculus without reference to a particular basis and without the exterior covariant derivative. This approach allows both structure equations and the Bianchi identities to be expressed in terms of forms of arbitrary degree. We demonstrate the relationship with both the conventional vector version of the Bianchi identities and to the exterior covariant derivative approach. Contact manifolds, codimension one foliations and the Cartan form of classical mechanics are studied as examples of its flexibility and utility.
Helical phase of chiral nematic liquid crystals as the Bianchi VII0 group manifold.
Gibbons, G W; Warnick, C M
2011-09-01
We show that the optical structure of the helical phase of a chiral nematic is naturally associated with the Bianchi VII(0) group manifold, of which we give a full account. The Joets-Ribotta metric governing propagation of the extraordinary rays is invariant under the simply transitive action of the universal cover E(2) of the three-dimensional Euclidean group of two dimensions. Thus extraordinary light rays are geodesics of a left-invariant metric on this Bianchi type VII(0) group. We are able to solve, by separation of variables, both the wave equation and the Hamilton-Jacobi equation for this metric. The former reduces to Mathieu's equation, and the latter to the quadrantal pendulum equation. We discuss Maxwell's equations for uniaxial optical materials where the configuration is invariant under a group action and develop a formalism to take advantage of these symmetries. The material is not assumed to be impedance matched, thus going beyond the usual scope of transformation optics. We show that for a chiral nematic in its helical phase Maxwell's equations reduce to a generalized Mathieu equation. Our results may also be relevant to helical phases of some magnetic materials and to light propagation in certain cosmological models.
Quantum Gowdy model within the new loop quantum cosmology improved dynamics
NASA Astrophysics Data System (ADS)
Martín-Benito, M.; Garay, L. J.; Mena Marugán, G. A.
2011-09-01
The linearly polarized Gowdy T3 model can be regarded as compact Bianchi I cosmologies with inhomogeneous modes allowed to travel in one direction. We study a hybrid quantization of this model that combines the loop quantization of the Bianchi I background, adopting the improved dynamics scheme put forward by Ashtekar and Wilson-Ewing, with a Fock quantization for the inhomogeneities. The Hamiltonian constraint operator provides a resolution of the cosmological singularity and superselects separable sectors. We analyze the complicated structure of these sectors. In any of them the Hamiltonian constraint provides an evolution equation with respect to the volume of the associated Bianchi I universe, with a well posed initial value problem. This fact allows us to construct the Hilbert space of physical states and to show that we recover the standard quantum field theory for the inhomogeneities.
Triangulation of cubic panorama for view synthesis.
Zhang, Chunxiao; Zhao, Yan; Wu, Falin
2011-08-01
An unstructured triangulation approach, new to our knowledge, is proposed to apply triangular meshes for representing and rendering a scene on a cubic panorama (CP). It sophisticatedly converts a complicated three-dimensional triangulation into a simple three-step triangulation. First, a two-dimensional Delaunay triangulation is individually carried out on each face. Second, an improved polygonal triangulation is implemented in the intermediate regions of each of two faces. Third, a cobweblike triangulation is designed for the remaining intermediate regions after unfolding four faces to the top/bottom face. Since the last two steps well solve the boundary problem arising from cube edges, the triangulation with irregular-distribution feature points is implemented in a CP as a whole. The triangular meshes can be warped from multiple reference CPs onto an arbitrary viewpoint by face-to-face homography transformations. The experiments indicate that the proposed triangulation approach provides a good modeling for the scene with photorealistic rendered CPs.
Sequential triangulation of orbital photography
NASA Technical Reports Server (NTRS)
Rajan, M.; Junkins, J. L.; Turner, J. D.
1979-01-01
The feasibility of structuring the satellite photogrammetric triangulation as an iterative Extended Kalman estimation algorithm is demonstrated. Comparative numerical results of the sequential against batch estimation algorithm are presented. Difficulty of accurately modeling of the attitude motion is overcome by utilizing the on-board angular rate measurements. Solutions of the differential equations and the evaluation of state transition matrix are carried out numerically.
Approaches to high aspect ratio triangulations
NASA Technical Reports Server (NTRS)
Posenau, M.-A.
1993-01-01
In aerospace computational fluid dynamics calculations, high aspect ratio, or stretched, triangulations are necessary to adequately resolve the features of a viscous flow around bodies. In this paper, we explore alternatives to the Delaunay triangulation which can be used to generate high aspect ratio triangulations of point sets. The method is based on a variation of the lifting map concept which derives Delaunay triangulations from convex hull calculations.
Delaunay triangulation and computational fluid dynamics meshes
NASA Technical Reports Server (NTRS)
Posenau, Mary-Anne K.; Mount, David M.
1992-01-01
In aerospace computational fluid dynamics (CFD) calculations, the Delaunay triangulation of suitable quadrilateral meshes can lead to unsuitable triangulated meshes. Here, we present case studies which illustrate the limitations of using structured grid generation methods which produce points in a curvilinear coordinate system for subsequent triangulations for CFD applications. We discuss conditions under which meshes of quadrilateral elements may not produce a Delaunay triangulation suitable for CFD calculations, particularly with regard to high aspect ratio, skewed quadrilateral elements.
Some properties of n-dimensional triangulations
NASA Technical Reports Server (NTRS)
Lawson, C. L.
1985-01-01
A number of mathematical results relevant to the problem of constructing a triangulation, i.e., a simplicial tessellation, of the convex hull of an arbitrary finite set of points in n-space are described. The principal results achieved are: (1) a set of n+2 points in n-space may be triangulated in at most 2 different ways; (2) the sphere test defined in this report selects a preferred one of these two triangulations; (3) a set of parameters is defined that permits the characterization and enumeration of all sets of n+2 points in n-space that are significantly different from the point of view of their possible triangulation; (4) the local sphere test induces a global sphere test property for a triangulation; and (5) a triangulation satisfying the global sphere property is dual to the n-dimensional Dirichlet tesselation, i.e., it is a Delaunay triangulation.
Temperature and polarization patterns in anisotropic cosmologies
Sung, Rockhee; Coles, Peter E-mail: Peter.Coles@astro.cf.ac.uk
2011-06-01
We study the coherent temperature and polarization patterns produced in homogeneous but anisotropic cosmological models. We show results for all Bianchi types with a Friedman-Robertson-Walker limit (i.e. Types I, V, VII{sub 0}, VII{sub h} and IX) to illustrate the range of possible behaviour. We discuss the role of spatial curvature, shear and rotation in the geodesic equations for each model and establish some basic results concerning the symmetries of the patterns produced. We also give examples of the time-evolution of these patterns in terms of the Stokes parameters I, Q and U.
Stability of the anisotropically inflating Bianchi type VI expanding solutions
Kao, W. F.; Lin, Ing-Chen
2011-03-15
A special class of the Bianchi type VI expanding solutions was speculated to break the cosmic no-hair theorem that will not approach the late-time de Sitter solution. We will show that an unstable mode always exists when the perturbation of the field equations is applied to the system. In addition to a model-independent perturbation formula, a simplification is also achieved by the introduction of a {delta}R=0 solution good for quadratic models in all Bianchi spaces. The result shows that this special class of anisotropically expanding solutions is unstable.
Stability conditions for the Bianchi type II anisotropically inflating universes
Kao, W.F.; Lin, Ing-Chen E-mail: g9522528@oz.nthu.edu.tw
2009-01-15
Stability conditions for a class of anisotropically inflating solutions in the Bianchi type II background space are shown explicitly in this paper. These inflating solutions were known to break the cosmic no-hair theorem such that they do not approach the de Sitter universe at large times. It can be shown that unstable modes of the anisotropic perturbations always exist for this class of expanding solutions. As a result, we show that these set of anisotropically expanding solutions are unstable against anisotropic perturbations in the Bianchi type II space.
Inflation in a renormalizable cosmological model and the cosmic no hair conjecture
NASA Technical Reports Server (NTRS)
Maeda, Kei-Ichi; Stein-Schabes, Jaime A.; Futamase, Toshifumi
1988-01-01
The possibility of having inflation in a renormalizable cosmological model is investigated. The Cosmic No Hair Conjecture is proved to hold for all Bianchi types except Bianchi IX. By the use of a conformal transformation on the metric it is shown that these models are equivalent to the ones described by the Einstein-Hilbert action for gravity minimally coupled to a set of scalar fields with inflationary potentials. Henceforth, it is proven that inflationary solutions behave as attractors in solution space, making it a natural event in the evolution of such models.
Precision cosmology, Accuracy cosmology and Statistical cosmology
NASA Astrophysics Data System (ADS)
Verde, Licia
2014-05-01
The avalanche of data over the past 10-20 years has propelled cosmology into the ``precision era''. The next challenge cosmology has to meet is to enter the era of accuracy. Because of the intrinsic nature of studying the Cosmos and the sheer amount of data available now and coming soon, the only way to meet this challenge is by developing suitable and specific statistical techniques. The road from precision Cosmology to accurate Cosmology goes through statistical Cosmology. I will outline some open challenges and discuss some specific examples.
Cosmological constant Λ in f(R,T) modified gravity
NASA Astrophysics Data System (ADS)
Singh, Gyan Prakash; Bishi, Binaya Kumar; Sahoo, Pradyumn Kumar
2016-04-01
In this paper, we have studied the Bianchi type-III cosmological model in the presence of cosmological constant in the context of f(R,T) modified theory of gravity. Here, we have discussed two classes of f(R,T) gravity, i.e. f(R,T) = R + f(T) and f(R,T) = f1(R) + f2(T). In both classes, the modified field equations are solved by the relation expansion scalar θ that is proportional to shear scalar σ which gives A = Cn, where A and C are metric potentials. Also we have discussed some physical and kinematical properties of the models.
The anisotropic cosmological models in f( R, T) gravity with Λ(T)
NASA Astrophysics Data System (ADS)
Chaubey, R.; Shukla, A. K.
2017-04-01
The general class of anisotropic Bianchi cosmological models in f( R, T) modified theories of gravity with Λ( T) has been considered. This paper deals with f( R, T) modified theories of gravity, where the gravitational Lagrangian is given by an arbitrary function of Ricci scalar R and the trace of the stress-energy tensor T has been investigated for a specific choice of f( R, T) = f 1( R) + f 2( T). The exact solutions to the corresponding field equations are obtained in quadrature form. We have discussed three types of solutions of the average scale factor for the general class of Bianchi cosmological models by using a special law for deceleration parameter which is linear in time with a negative slope. The solutions to the Einstein field equations are obtained for three different physical viable cosmologies. All physical parameters are calculated and discussed in each model.
Energy Distribution of the Bianchi Type i Solution
NASA Astrophysics Data System (ADS)
Radinschi, Irina
We calculate the energy of an anisotropic model of universe based on the Bianchi type I metric in the Mo ller prescription. The total energy due to the matter and gravitational field is zero. This result supports the importance of the energy-momentum complexes in the localization of energy.
Statistical properties of cosmological billiards
NASA Astrophysics Data System (ADS)
Damour, Thibault; Lecian, Orchidea Maria
2011-02-01
Belinski, Khalatnikov, and Lifshitz pioneered the study of the statistical properties of the never-ending oscillatory behavior (among successive Kasner epochs) of the geometry near a spacelike singularity. We show how the use of a “cosmological billiard” description allows one to refine and deepen the understanding of these statistical properties. Contrary to previous treatments, we do not quotient the dynamics by its discrete symmetry group (of order 6), thereby uncovering new phenomena, such as correlations between the successive billiard corners in which the oscillations take place. Starting from the general integral invariants of Hamiltonian systems, we show how to construct invariant measures for various projections of the cosmological-billiard dynamics. In particular, we exhibit, for the first time, a (non-normalizable) invariant measure on the “Kasner circle” which parametrizes the exponents of successive Kasner epochs. Finally, we discuss the relation between: (i) the unquotiented dynamics of the Bianchi-IX (a, b, c or mixmaster) model; (ii) its quotienting by the group of permutations of (a, b, c); and (iii) the billiard dynamics that arose in recent studies suggesting the hidden presence of Kac-Moody symmetries in cosmological billiards.
Diffeomorphism invariant cosmological symmetry in full quantum gravity
NASA Astrophysics Data System (ADS)
Beetle, Christopher; Engle, Jonathan S.; Hogan, Matthew E.; Mendonça, Phillip
2016-06-01
This paper summarizes a new proposal to define rigorously a sector of loop quantum gravity at the diffeomorphism invariant level corresponding to homogeneous and isotropic cosmologies, thereby enabling a detailed comparison of results in loop quantum gravity and loop quantum cosmology. The key technical steps we have completed are (a) to formulate conditions for homogeneity and isotropy in a diffeomorphism covariant way on the classical phase-space of general relativity, and (b) to translate these conditions consistently using well-understood techniques to loop quantum gravity. Some additional steps, such as constructing a specific embedding of the Hilbert space of loop quantum cosmology into a space of (distributional) states in the full theory, remain incomplete. However, we also describe, as a proof of concept, a complete analysis of an analogous embedding of homogeneous and isotropic loop quantum cosmology into the quantum Bianchi I model of Ashtekar and Wilson-Ewing. Details will appear in a pair of forthcoming papers.
The simplest possible bouncing quantum cosmological model
NASA Astrophysics Data System (ADS)
Peter, Patrick; Vitenti, Sandro D. P.
2016-06-01
We present and expand the simplest possible quantum cosmological bouncing model already discussed in previous works: the trajectory formulation of quantum mechanics applied to cosmology (through the Wheeler-De Witt equation) in the Friedmann-Lemaître-Robertson-Walker (FLRW) minisuperspace without spatial curvature. The initial conditions that were previously assumed were such that the wave function would not change its functional form but instead provide a dynamics to its parameters. Here, we consider a more general situation, in practice consisting of modified Gaussian wave functions, aiming at obtaining a nonsingular bounce from a contracting phase. Whereas previous works consistently obtain very symmetric bounces, we find that it is possible to produce highly non-symmetric solutions, and even cases for which multiple bounces naturally occur. We also introduce a means of treating the shear in this category of models by quantizing in the Bianchi I minisuperspace.
Nonvacuum taub-type cosmological model
NASA Astrophysics Data System (ADS)
Carmeli, M.; Manor, R.
1990-05-01
The Einstein universe is a simple model describing a static cosmological spacetime, having a constant radius and a constant curvature, and, as is well known, it does not describe our universe. We propose a model which is an extension of Einstein's. Our metric, having R × S 3 topology, describes a nonisotropic homogeneous closed (finite) universe of Bianchi type IX. This metric is similar to that of Taub, but is simpler. Unlike the Taub solution (which is a cosmological extension of the NUT solution), however, the universe described by our metric contains matter. Like the Taub metric, our metric has two positive constants ( τ, T). The gravitational red shift calculated from our metric is given. Similarly to the Schwarzschild metric, which has a “singularity” at r = 2m, this metric has the same kind of “singularity” at t = 2τ. The maximal extension of the coordinates in our metric is fairly analogous to that of the Schwarzschild metric.
Covariant approach to parametrized cosmological perturbations
NASA Astrophysics Data System (ADS)
Tattersall, Oliver J.; Lagos, Macarena; Ferreira, Pedro G.
2017-09-01
We present a covariant formulation for constructing general quadratic actions for cosmological perturbations, invariant under a given set of gauge symmetries for a given field content. This approach allows us to analyze scalar, vector, and tensor perturbations at the same time in a straightforward manner. We apply the procedure to diffeomorphism invariant single-tensor, scalar-tensor, and vector-tensor theories and show explicitly the full covariant form of the quadratic actions in such cases, in addition to the actions determining the evolution of vector and tensor perturbations. We also discuss the role of the symmetry of the background in identifying the set of cosmologically relevant free parameters describing these classes of theories, including calculating the relevant free parameters for an axisymmetric Bianchi-I vacuum universe.
Mixed Methods, Triangulation, and Causal Explanation
ERIC Educational Resources Information Center
Howe, Kenneth R.
2012-01-01
This article distinguishes a disjunctive conception of mixed methods/triangulation, which brings different methods to bear on different questions, from a conjunctive conception, which brings different methods to bear on the same question. It then examines a more inclusive, holistic conception of mixed methods/triangulation that accommodates…
Mixed Methods, Triangulation, and Causal Explanation
ERIC Educational Resources Information Center
Howe, Kenneth R.
2012-01-01
This article distinguishes a disjunctive conception of mixed methods/triangulation, which brings different methods to bear on different questions, from a conjunctive conception, which brings different methods to bear on the same question. It then examines a more inclusive, holistic conception of mixed methods/triangulation that accommodates…
Properties of n-dimensional triangulations
NASA Technical Reports Server (NTRS)
Lawson, Charles L.
1986-01-01
This paper establishes a number of mathematical results relevant to the problem of constructing a triangulation, i.e., a simplical tessellation of the convex hull of an arbitrary finite set of points in n-space. The principal results of the present paper are: (1) a set of n + 2 points in n-space may be triangulated in at most 2 different ways; (2) the 'sphere test' defined in this paper selects a preferred one of these two triangulations; (3) a set of parameters is defined that permits the characterization and enumeration of all sets on n + 2 points in n-space that are significantly different from the point of view of their possible triangulations; and (4) the local sphere test induces a global sphere test property for a triangulation.
Properties of n-dimensional triangulations
NASA Technical Reports Server (NTRS)
Lawson, Charles L.
1986-01-01
This paper establishes a number of mathematical results relevant to the problem of constructing a triangulation, i.e., a simplical tessellation of the convex hull of an arbitrary finite set of points in n-space. The principal results of the present paper are: (1) a set of n + 2 points in n-space may be triangulated in at most 2 different ways; (2) the 'sphere test' defined in this paper selects a preferred one of these two triangulations; (3) a set of parameters is defined that permits the characterization and enumeration of all sets on n + 2 points in n-space that are significantly different from the point of view of their possible triangulations; and (4) the local sphere test induces a global sphere test property for a triangulation.
Bianchi-IX, Darboux-Halphen and Chazy-Ramanujan
NASA Astrophysics Data System (ADS)
Chanda, Sumanto; Guha, Partha; Roychowdhury, Raju
2016-02-01
Bianchi-IX four metrics are SU(2) invariant solutions of vacuum Einstein equation, for which the connection-wise self-dual case describes the Euler top, while the curvature-wise self-dual case yields the Ricci flat classical Darboux-Halphen system. It is possible to see such a solution exhibiting Ricci flow. The classical Darboux-Halphen system is a special case of the generalized one that arises from a reduction of the self-dual Yang-Mills equation and the solutions to the related homogeneous quadratic differential equations provide the desired metric. A few integrable and near-integrable dynamical systems related to the Darboux-Halphen system and occurring in the study of Bianchi-IX gravitational instanton have been listed as well. We explore in details whether self-duality implies integrability.
Methodological triangulation: an approach to understanding data.
Bekhet, Abir K; Zauszniewski, Jaclene A
2012-01-01
To describe the use of methodological triangulation in a study of how people who had moved to retirement communities were adjusting. Methodological triangulation involves using more than one kind of method to study a phenomenon. It has been found to be beneficial in providing confirmation of findings, more comprehensive data, increased validity and enhanced understanding of studied phenomena. While many researchers have used this well-established technique, there are few published examples of its use. The authors used methodological triangulation in their study of people who had moved to retirement communities in Ohio, US. A blended qualitative and quantitative approach was used. The collected qualitative data complemented and clarified the quantitative findings by helping to identify common themes. Qualitative data also helped in understanding interventions for promoting 'pulling' factors and for overcoming 'pushing' factors of participants. The authors used focused research questions to reflect the research's purpose and four evaluative criteria--'truth value', 'applicability', 'consistency' and 'neutrality'--to ensure rigour. This paper provides an example of how methodological triangulation can be used in nursing research. It identifies challenges associated with methodological triangulation, recommends strategies for overcoming them, provides a rationale for using triangulation and explains how to maintain rigour. Methodological triangulation can be used to enhance the analysis and the interpretation of findings. As data are drawn from multiple sources, it broadens the researcher's insight into the different issues underlying the phenomena being studied.
Power-Law Type Solutions of Fourth-Order Gravity for Multidimensional Bianchi i Universes
NASA Astrophysics Data System (ADS)
Caprasse, H.; Demaret, J.; Gatermann, K.; Melenk, H.
This paper is devoted to the application of computer algebra to the study of solutions of the field equations derived from a non-linear Lagrangian, as suggested by recently proposed unified theories. More precisely, we restrict ourselves to the most general quadratic Lagrangian, i.e. containing quadratic contributions in the different curvature tensors exclusively. The corresponding field equations are then fourth-order in the metric tensor components. The cosmological models studied are the simplest ones in the class of spatially homogeneous but anisotropic models, i.e. Bianchi I models. For these models, we consider only power-law type solutions of the field equations. All the solutions of the associated system of algebraic equations are found, using computer algebra, from a search of its Groebner bases. While, in space dimension d=3, the Einsteinian-Kasner metric is still the most general power-law type solution, for d>3, no solution, other than the Minkowski space-time, is common to the three systems of equations corresponding to the three contributions to the Lagrangian density. In the case of a pure Riemann-squared contribution to the Lagrangian (suggested by a recent calculation of the effective action for the heterotic string), the possibility exists to realize a splitting of the d-dimensional space into a (d-3)-dimensional internal space and a physical 3-dimensional space, the latter expanding in time as a power bigger than 2 (about 4.5 when d=9).
NASA Astrophysics Data System (ADS)
Girdhar, Parth; Kobakhidze, Archil
2013-10-01
We describe a new phenomenon of zitterbewegung of a free Dirac particle in cosmological spacetimes. Unlike the similar effect theorized by Schrödinger in 1930, the cosmological zitterbewegung is a real, physically attainable effect, which originates from the mixing of positive and negative frequency modes of a field operator in cosmological spacetimes. We briefly discuss the potential for observing this effect in laboratory experiments with trapped ions.
Linear-size nonobtuse triangulation of polygons
Bern, M.; Mitchell, S.; Ruppert, J.
1994-05-01
We give an algorithm for triangulating n-vertex polygonal regions (with holes) so that no angle in the final triangulation measures more than {pi}/2. The number of triangles in the triangulation is only 0(n), improving a previous bound of 0(n{sup 2}), and the worst-case running time is 0(n log{sup 2} n). The basic technique used in the algorithm, recursive subdivision by disks, is new and may have wider application in mesh generation. We also report on an implementation of our algorithm.
Bianchi Type-I Anisotropic Dark Energy Model with Constant Deceleration Parameter
NASA Astrophysics Data System (ADS)
Pradhan, Anirudh; Amirhashchi, H.; Saha, Bijan
2011-09-01
A new dark energy model in anisotropic Bianchi type-I (B-I) space-time with time dependent equation of state (EoS) parameter and constant deceleration parameter has been investigated in the present paper. The Einstein's field equations have been solved by applying a variation law for generalized Hubble's parameter (Berman in Il Nuovo Cimento B 74:182, 1983) which generates two types of solutions, one is of power-law type and other is of the exponential form. The existing range of the dark energy EoS parameter ω for derived model is found to be in good agreement with the three recent observations (i) SNe Ia data (Knop et al. in Astrophys. J. 598:102, 2003), (ii) SNe Ia data collaborated with CMBR anisotropy and galaxy clustering statistics (Tegmark et al. in Astrophys. J. 606:702, 2004) and (iii) a combination of cosmological datasets coming from CMB anisotropies, luminosity distances of high redshift type Ia supernovae and galaxy clustering (Hinshaw et al. in Astrophys. J. Suppl. Ser. 180:225, 2009 and Komatsu et al. in Astrophys. J. Suppl. Ser. 180:330, 2009). The cosmological constant Λ is found to be a decreasing function of time and it approaches a small positive value at the present epoch which is corroborated by results from recent supernovae Ia observations. It has also been suggested that the dark energy that explains the observed accelerating universe may arise due to the contribution to the vacuum energy of the EoS in a time dependent background. Geometric and kinematic properties of the model and the behaviour of the anisotropy of the dark energy have been carried out.
NASA Astrophysics Data System (ADS)
Jones, Bernard J. T.
2017-04-01
Preface; Notation and conventions; Part I. 100 Years of Cosmology: 1. Emerging cosmology; 2. The cosmic expansion; 3. The cosmic microwave background; 4. Recent cosmology; Part II. Newtonian Cosmology: 5. Newtonian cosmology; 6. Dark energy cosmological models; 7. The early universe; 8. The inhomogeneous universe; 9. The inflationary universe; Part III. Relativistic Cosmology: 10. Minkowski space; 11. The energy momentum tensor; 12. General relativity; 13. Space-time geometry and calculus; 14. The Einstein field equations; 15. Solutions of the Einstein equations; 16. The Robertson–Walker solution; 17. Congruences, curvature and Raychaudhuri; 18. Observing and measuring the universe; Part IV. The Physics of Matter and Radiation: 19. Physics of the CMB radiation; 20. Recombination of the primeval plasma; 21. CMB polarisation; 22. CMB anisotropy; Part V. Precision Tools for Precision Cosmology: 23. Likelihood; 24. Frequentist hypothesis testing; 25. Statistical inference: Bayesian; 26. CMB data processing; 27. Parametrising the universe; 28. Precision cosmology; 29. Epilogue; Appendix A. SI, CGS and Planck units; Appendix B. Magnitudes and distances; Appendix C. Representing vectors and tensors; Appendix D. The electromagnetic field; Appendix E. Statistical distributions; Appendix F. Functions on a sphere; Appendix G. Acknowledgements; References; Index.
Phenomenological dynamics of loop quantum cosmology in Kantowski-Sachs spacetime
Chiou, D.-W.
2008-08-15
The fundamental theory and the semiclassical description of loop quantum cosmology (LQC) have been studied in the Friedmann-Robertson-Walker and Bianchi I models. As an extension to include both anisotropy and intrinsic curvature, this paper investigates the cosmological model of Kantowski-Sachs spacetime with a free massless scalar field at the level of phenomenological dynamics with the LQC discreteness corrections. The LQC corrections are implemented in two different improved quantization schemes. In both schemes, the big bang and big crunch singularities of the classical solution are resolved and replaced by the big bounces when the area or volume scale factor approaches the critical values in the Planck regime measured by the reference of the scalar field momentum. Symmetries of scaling are also noted and suggest that the fundamental spatial scale (area gap) may give rise to a temporal scale. The bouncing scenarios are in an analogous fashion of the Bianchi I model, naturally extending the observations obtained previously.
Testing different approaches to quantum gravity with cosmology: An overview
NASA Astrophysics Data System (ADS)
Barrau, Aurélien
2017-03-01
Among the available quantum gravity proposals, string theory, loop quantum gravity, non-commutative geometry, group field theory, causal sets, asymptotic safety, causal dynamical triangulation, emergent gravity are the best motivated models. As an introductory summary to this dossier of Comptes Rendus Physique, I explain how those different theories can be tested or constrained by cosmological observations.
Image encoding with triangulation wavelets
NASA Astrophysics Data System (ADS)
Hebert, D. J.; Kim, HyungJun
1995-09-01
We demonstrate some wavelet-based image processing applications of a class of simplicial grids arising in finite element computations and computer graphics. The cells of a triangular grid form the set of leaves of a binary tree and the nodes of a directed graph consisting of a single cycle. The leaf cycle of a uniform grid forms a pattern for pixel image scanning and for coherent computation of coefficients of splines and wavelets. A simple form of image encoding is accomplished with a 1D quadrature mirror filter whose coefficients represent an expansion of the image in terms of 2D Haar wavelets with triangular support. A combination the leaf cycle and an inherent quadtree structure allow efficient neighbor finding, grid refinement, tree pruning and storage. Pruning of the simplex tree yields a partially compressed image which requires no decoding, but rather may be rendered as a shaded triangulation. This structure and its generalization to n-dimensions form a convenient setting for wavelet analysis and computations based on simplicial grids.
A Triangulation Methodology in Research on Social Cultures.
ERIC Educational Resources Information Center
Owens, Robert G.; And Others
The purpose of this research was to develop, test, and demonstrate a systematic methodology of triangulation. Triangulation is a technique used to establish credibility of data gathered in qualitative ways. Triangulated conclusions are more stable than any of the individual vantage points from which they were triangulated. Using a previous study…
Dynamics of anisotropic power-law f( R) cosmology
NASA Astrophysics Data System (ADS)
Shamir, M. F.
2016-12-01
Modified theories of gravity have attracted much attention of the researchers in the recent years. In particular, the f( R) theory has been investigated extensively due to important f( R) gravity models in cosmological contexts. This paper is devoted to exploring an anisotropic universe in metric f( R) gravity. A locally rotationally symmetric Bianchi type I cosmological model is considered for this purpose. Exact solutions of modified field equations are obtained for a well-known f( R) gravity model. The energy conditions are also discussed for the model under consideration. The viability of the model is investigated via graphical analysis using the present-day values of cosmological parameters. The model satisfies null energy, weak energy, and dominant energy conditions for a particular range of the anisotropy parameter while the strong energy condition is violated, which shows that the anisotropic universe in f( R) gravity supports the crucial issue of accelerated expansion of the universe.
Dynamics of anisotropic power-law f(R) cosmology
Shamir, M. F.
2016-12-15
Modified theories of gravity have attracted much attention of the researchers in the recent years. In particular, the f(R) theory has been investigated extensively due to important f(R) gravity models in cosmological contexts. This paper is devoted to exploring an anisotropic universe in metric f(R) gravity. A locally rotationally symmetric Bianchi type I cosmological model is considered for this purpose. Exact solutions of modified field equations are obtained for a well-known f(R) gravity model. The energy conditions are also discussed for the model under consideration. The viability of the model is investigated via graphical analysis using the present-day values of cosmological parameters. The model satisfies null energy, weak energy, and dominant energy conditions for a particular range of the anisotropy parameter while the strong energy condition is violated, which shows that the anisotropic universe in f(R) gravity supports the crucial issue of accelerated expansion of the universe.
An Introduction to General Relativity and Cosmology
NASA Astrophysics Data System (ADS)
Plebanski, Jerzy; Krasinski, Andrzej
2012-09-01
1. How the theory of relativity came into being (a brief historical sketch); Part I. Elements of Differential Geometry: 2. A short sketch of two-dimensional differential geometries; 3. Tensors, tensor densities; 4. Covariant derivatives; 5. Parallel transport and geodesic lines; 6. Curvature of a manifold: flat manifolds; 7. Riemannian geometry; 8. Symmetries of Rieman spaces, invariance of tensors; 9. Methods to calculate the curvature quickly - Cartan forms and algebraic computer programs; 10. The spatially homogeneous Bianchi-type spacetimes; 11. The Petrov classification by the spinor method; Part II. The Gravitation Theory: 12. The Einstein equations and the sources of a gravitational field; 13. The Maxwell and Einstein-Maxwell equations and the Kaluza-Klein theory; 14. Spherically symmetric gravitational field of isolated objects; 15. Relativistic hydrodynamics and thermodynamics; 16. Relativistic cosmology I: general geometry; 17. Relativistic cosmology II: the Robertson-Walker geometry; 18. Relativistic cosmology III: the Lemaître-Tolman geometry; 19. Relativistic cosmology IV: generalisations of L-T and related geometries; 20. The Kerr solution; 21. Subjects omitted in this book; References.
An Introduction to General Relativity and Cosmology
NASA Astrophysics Data System (ADS)
Plebanski, Jerzy; Krasinski, Andrzej
2006-08-01
1. How the theory of relativity came into being (a brief historical sketch); Part I. Elements of Differential Geometry: 2. A short sketch of two-dimensional differential geometries; 3. Tensors, tensor densities; 4. Covariant derivatives; 5. Parallel transport and geodesic lines; 6. Curvature of a manifold: flat manifolds; 7. Riemannian geometry; 8. Symmetries of Rieman spaces, invariance of tensors; 9. Methods to calculate the curvature quickly - Cartan forms and algebraic computer programs; 10. The spatially homogeneous Bianchi-type spacetimes; 11. The Petrov classification by the spinor method; Part II. The Gravitation Theory: 12. The Einstein equations and the sources of a gravitational field; 13. The Maxwell and Einstein-Maxwell equations and the Kaluza-Klein theory; 14. Spherically symmetric gravitational field of isolated objects; 15. Relativistic hydrodynamics and thermodynamics; 16. Relativistic cosmology I: general geometry; 17. Relativistic cosmology II: the Robertson-Walker geometry; 18. Relativistic cosmology III: the Lemaître-Tolman geometry; 19. Relativistic cosmology IV: generalisations of L-T and related geometries; 20. The Kerr solution; 21. Subjects omitted in this book; References.
Accelerating anisotropic cosmological model in f(R,T) theory of gravity
NASA Astrophysics Data System (ADS)
Santhi Kumar, R.; Satyannarayana, B.
2017-10-01
Field equations in a modified theory of gravitation proposed by Harko et al. (Phys Rev D 84:024020, 8) are obtained with the aid of a spatially homogeneous and anisotropic LRS Bianchi type-I metric. Cosmological models corresponding to false vacuum and dust universe are obtained. Some physical and kinematical properties of each of the models are discussed. These models may be physically significant for discussion at an early stage of evolution of the universe.
Triangulating stapling technique for reconstruction after colectomy.
Fukunaga, Y; Higashino, M; Tanimura, S; Osugi, Harushi
2007-03-01
To retrospectively compare the triangulating stapling technique for colocolonic anastomosis with hand-sewn anastomosis and functional end-to-end anastomosis. Data from 646 patients who underwent colectomy for cancer from 1993 to 2004 were extracted by chart review. Patients were divided into three groups based on the type of anastomosis: handsewn (n=233), functional end-to-end (n=71), and the triangulating stapling method (n=346). Demographic data and clinical characteristics of the three groups were similar. Anastomotic leakage was significantly more common in the hand-sewn group than the triangular stapling group (hand-sewn; 3.0%, functional end-to-end; 2.8%, triangulating, 0.6%) (P < 0.05). No patient developed bleeding or stenosis at the anastomosis, and the incidence of wound infection was equivalent among the three groups. One death due to anastomotic failure occurred in each of the functional end-to-end and triangulating stapling groups. The cost of triangulating stapling was approximately Yen 36,000 lower than the cost of the functional end-to-end anastomosis. The triangulating stapling technique is an attractive alternative to other methods for creating a colocolonic anastomosis.
Uav Photogrammetry: Block Triangulation Comparisons
NASA Astrophysics Data System (ADS)
Gini, R.; Pagliari, D.; Passoni, D.; Pinto, L.; Sona, G.; Dosso, P.
2013-08-01
UAVs systems represent a flexible technology able to collect a big amount of high resolution information, both for metric and interpretation uses. In the frame of experimental tests carried out at Dept. ICA of Politecnico di Milano to validate vector-sensor systems and to assess metric accuracies of images acquired by UAVs, a block of photos taken by a fixed wing system is triangulated with several software. The test field is a rural area included in an Italian Park ("Parco Adda Nord"), useful to study flight and imagery performances on buildings, roads, cultivated and uncultivated vegetation. The UAV SenseFly, equipped with a camera Canon Ixus 220HS, flew autonomously over the area at a height of 130 m yielding a block of 49 images divided in 5 strips. Sixteen pre-signalized Ground Control Points, surveyed in the area through GPS (NRTK survey), allowed the referencing of the block and accuracy analyses. Approximate values for exterior orientation parameters (positions and attitudes) were recorded by the flight control system. The block was processed with several software: Erdas-LPS, EyeDEA (Univ. of Parma), Agisoft Photoscan, Pix4UAV, in assisted or automatic way. Results comparisons are given in terms of differences among digital surface models, differences in orientation parameters and accuracies, when available. Moreover, image and ground point coordinates obtained by the various software were independently used as initial values in a comparative adjustment made by scientific in-house software, which can apply constraints to evaluate the effectiveness of different methods of point extraction and accuracies on ground check points.
NASA Astrophysics Data System (ADS)
Crawford, David F.
Curvature Cosmology proposes a new cosmological model very different from, and more elegant than, the Big-Bang Theory. Curvature Cosmology is based on two major hypotheses that Hubble redshift is due to an interaction of photons with curved spacetime and that there is a pressure that acts to stabilise expansion and provides a static, stable universe. The main focus of this book is to describe these two hypotheses in detail and to examine all relevant cosmological data in the context of this new model of the universe. This model proposes that, though evolution of stars and galaxies is evident, the statistical properties of the universe are the same at all places and at all times. In short, the universe is ageless, has no defined beginning (unlike the Big-Bang model), and carries no evidence of expansion, despite the changeability of its components. Curvature Cosmology calls for a paradigm shift in current cosmology and requires at least basic (if not more complex) knowledge of past and current cosmological models and equations.
Unitary evolution for a quantum Kantowski-Sachs cosmology
NASA Astrophysics Data System (ADS)
Pal, Sridip; Banerjee, Narayan
2015-10-01
It is shown that like the Bianchi I, V and IX models, a Kantowski-Sachs cosmological model also allows unitary evolution on quantization. It has also been shown that this unitarity is not at the expense of anisotropy. Non-unitarity, if there is any, cannot escape notice here, as the evolution is studied against a properly oriented time parameter fixed by the evolution of the fluid. Furthermore, we have constructed a wave packet by superposing different energy eigenstates, thereby establishing unitarity in a non-trivial way, which is a stronger result than an energy eigenstate trivially giving a time independent probability density. For α \
Bianchi's Bäcklund transformation for higher dimensional quadrics
NASA Astrophysics Data System (ADS)
Dincă, Ion I.
2016-12-01
We provide a generalization of Bianchi's Bäcklund transformation from 2-dimensional quadrics to higher dimensional quadrics (which is also a generalization of Tenenblat-Terng's Bäcklund transformation of isometric deformations of Hn(R) in R 2 n - 1 to general quadrics). Our investigation is the higher dimensional version of Bianchi's main three theorems on the theory of isometric deformations of quadrics and Bianchi's treatment of the Bäcklund transformation for diagonal paraboloids via conjugate systems. It became the driving force which led to the flourishing of the classical differential geometry in the second half of the XIX th century and its profound study by illustrious geometers led to interesting results. Today it is still an open problem in its full generality, but basic familiar results like the Gauß-Bonnet fundamental theorem of surfaces and the Codazzi-Mainardi equations (independently discovered also by Peterson) were first communicated to the French Academy of Sciences. A list (most likely incomplete) of the winners of the prize includes Bianchi, Bonnet, Guichard, Weingarten.Up to 1899 isometric deformations of the (pseudo-)sphere and isotropic quadrics without center (from a metric point of view they can be considered as metrically degenerate quadrics without center) together with their Bäcklund transformation and the complementary transformation of isometric deformations of surfaces of revolution were investigated by geometers such as Bäcklund, Bianchi, Bonnet, Darboux, Goursat, Hazzidakis, Lie, Weingarten, etc.In 1899 Guichard discovered that when quadrics with(out) center and of revolution around the focal axis roll on their isometric deformations their foci describe constant mean curvature (minimal) surfaces (and Bianchi proved the converse: all constant mean curvature (minimal) surfaces can be realized in this way).With Guichard's result the race to find the isometric
Stochastic eternal inflation in a Bianchi type I universe
NASA Astrophysics Data System (ADS)
Kohli, Ikjyot Singh; Haslam, Michael C.
2016-01-01
The phenomenon of stochastic eternal inflation is studied for a chaotic inflation potential in a Bianchi type I spacetime background. After deriving the appropriate stochastic Klein-Gordon equation, we give details on the conditions for eternal inflation. It is shown that for eternal inflation to occur, the amount of anisotropy must be small. In fact, it is shown that eternal inflation will only take place if the shear anisotropy variables take on values within a small region of the interior of the Kasner circle. We then calculate the probability of eternal inflation occurring based on techniques from stochastic calculus.
Generalized Kasner Cosmologies with Induced Matter
NASA Astrophysics Data System (ADS)
Halpern, Paul
2000-04-01
We extend Paul Wesson's five dimensional induced matter model, which has previously been applied to a variety of isotropic cases, to a generalization of Kasner's anisotropic (Bianchi-type-I) cosmology. Wesson's model is a Kaluza-Klein approach in which assumptions of compactness are relaxed for the fifth coordinate, leading to extra "induced matter" terms in the stress-energy tensor. In similar spirit, we construct a five dimensional metric in which the spatial slices possess Bianchi-type-I geometry. We supplement the fourth time coordinate, t, with a fifth coordinate, ψ. We assume that each of the scale factors are dependent on both t and ψ. (This extends the work of Soccorro, Villanueva, and Pimental, who solved a related problem with only time dependence.) We find a set of solutions for the five dimensional Einstein equations, and determine the pressure and density of induced matter. We show that the assumption of positive density leads to the contraction over time of the fifth scale factor. Finally, employing our model, we speculate about a possible mechanism for the isotropization of the early universe.
NASA Astrophysics Data System (ADS)
Krauss, L. M.
1999-01-01
The long-derided cosmological constant - a contrivance of Albert Einstein's that represents a bizarre form of energy inherent in space itself - is one of two contenders for explaining changes in the expansion rate of the Universe.
NASA Astrophysics Data System (ADS)
Chen, P.
2014-05-01
Recent years have witnessed tremendous progress in our understanding of the cosmos, which in turn points to even deeper questions to be further addressed. Concurrently the laser technology has undergone dramatic revolutions, providing exciting opportunity for science applications. History has shown that the symbiosis between direct observations and laboratory investigation is instrumental in the progress of astrophysics. We believe that this remains true in cosmology. Current frontier phenomena related to particle astrophysics and cosmology typically involve one or more of the following conditions: (1) extremely high energy events;(2) very high density, high temperature processes; (3) super strong field environments. Laboratory experiments using high intensity lasers can calibrate astrophysical observations, investigate underlying dynamics of astrophysical phenomena, and probe fundamental physics in extreme limits. In this article we give an overview of the exciting prospect of laser cosmology. In particular, we showcase its unique capability of investigating frontier cosmology issues such as cosmic accelerator and quantum gravity.
NASA Astrophysics Data System (ADS)
Blau, S. K.; Guth, A. H.
Contents: 1. Introduction. 2. Summary of the standard cosmological model. 3. Problems of the standard cosmological model. 4. The original inflationary universe. 5. Successes of the original inflationary model. 6. Problems of the original inflationary model. 7. The new inflationary universe. 8. Density perturbations in the new inflationary universe. 9. Quantum theory of the new inflationary universe phase transition. 10. Inflation in the minimal SU(5) grand unified theory. 11. False vacuum bubbles and child universes. 12. Conclusion.
The Raychaudhuri equation in homogeneous cosmologies
Albareti, F.D.; Cembranos, J.A.R.; Cruz-Dombriz, A. de la; Dobado, A. E-mail: cembra@fis.ucm.es E-mail: dobado@fis.ucm.es
2014-03-01
In this work we address the issue of studying the conditions required to guarantee the Focusing Theorem for both null and timelike geodesic congruences by using the Raychaudhuri equation. In particular we study the case of Friedmann-Robertson-Walker as well as more general Bianchi Type I spacetimes. The fulfillment of the Focusing Theorem is mandatory in small scales since it accounts for the attractive character of gravity. However, the Focusing Theorem is not satisfied at cosmological scales due to the measured negative deceleration parameter. The study of the conditions needed for congruences convergence is not only relevant at the fundamental level but also to derive the viability conditions to be imposed on extended theories of gravity describing the different expansion regimes of the universe. We illustrate this idea for f(R) gravity theories.
Spectral Properties of Unimodular Lattice Triangulations
NASA Astrophysics Data System (ADS)
Krüger, Benedikt; Schmidt, Ella M.; Mecke, Klaus
2016-05-01
Random unimodular lattice triangulations have been recently used as an embedded random graph model, which exhibit a crossover behavior between an ordered, large-world and a disordered, small-world behavior. Using the ergodic Pachner flips that transform such triangulations into another and an energy functional that corresponds to the degree distribution variance, Markov chain Monte Carlo simulations can be applied to study these graphs. Here, we consider the spectra of the adjacency and the Laplacian matrix as well as the algebraic connectivity and the spectral radius. Power law dependencies on the system size can clearly be identified and compared to analytical solutions for periodic ground states. For random triangulations we find a qualitative agreement of the spectral properties with well-known random graph models. In the microcanonical ensemble analytical approximations agree with numerical simulations. In the canonical ensemble a crossover behavior can be found for the algebraic connectivity and the spectral radius, thus combining large-world and small-world behavior in one model. The considered spectral properties can be applied to transport problems on triangulation graphs and the crossover behavior allows a tuning of important transport quantities.
Flip to Regular Triangulation and Convex Hull.
Gao, Mingcen; Cao, Thanh-Tung; Tan, Tiow-Seng
2017-02-01
Flip is a simple and local operation to transform one triangulation to another. It makes changes only to some neighboring simplices, without considering any attribute or configuration global in nature to the triangulation. Thanks to this characteristic, several flips can be independently applied to different small, non-overlapping regions of one triangulation. Such operation is favored when designing algorithms for data-parallel, massively multithreaded hardware, such as the GPU. However, most existing flip algorithms are designed to be executed sequentially, and usually need some restrictions on the execution order of flips, making them hard to be adapted to parallel computation. In this paper, we present an in depth study of flip algorithms in low dimensions, with the emphasis on the flexibility of their execution order. In particular, we propose a series of provably correct flip algorithms for regular triangulation and convex hull in 2D and 3D, with implementations for both CPUs and GPUs. Our experiment shows that our GPU implementation for constructing these structures from a given point set achieves up to two orders of magnitude of speedup over other popular single-threaded CPU implementation of existing algorithms.
Representing Solar Active Regions with Triangulations
NASA Technical Reports Server (NTRS)
Turmon, M. J.; Mukhtar, S.
1998-01-01
The solar chromosphere consists of three classes which contribute differently to ultraviolet radiation reaching the earth. We describe a data set of solar images, means of segmenting the images into the constituent classes, and novel high-level representation for compact objects based on a triangulation spatial 'membership function'.
Advancing-Front Algorithm For Delaunay Triangulation
NASA Technical Reports Server (NTRS)
Merriam, Marshal L.
1993-01-01
Efficient algorithm performs Delaunay triangulation to generate unstructured grids for use in computing two-dimensional flows. Once grid generated, one can optionally call upon additional subalgorithm that removes diagonal lines from quadrilateral cells nearly rectangular. Resulting approximately rectangular grid reduces cost per iteration of flow-computing algorithm.
NASA Astrophysics Data System (ADS)
Lattanzi, M. G.
The accurate measurement of the motions of stars in our Galaxy can provide access to the cosmological signatures in the disk and halo, while astrometric experiments from within our Solar System can uniquely probe possible deviations from General Relativity. This article will introduce to the fact that astrometry has the potential, thanks also to impressive technological advancements, to become a key player in the field of local cosmology. For example, accurate absolute kinematics at the scale of the Milky Way can, for the first time in situ, account for the predictions made by the cold dark matter model for the Galactic halo, and eventually map out the distribution of dark matter, or other formation mechanisms, required to explain the signatures recently identified in the old component of the thick disk. Final notes dwell on to what extent Gaia can fulfill the expectations of astrometric cosmology and on what must instead be left to future, specifically designed, astrometric experiments.
NASA Astrophysics Data System (ADS)
Harvey, Alex
1993-10-01
Two of the most common terms employed in discussing cosmological models are open and closed. They are occasionally misused either by not recognizing or by not making it clear that each term may be used to characterize, independently and simultaneously, both the dynamic behavior and spatial geometric structure of the model under discussion. In addition, the spatial geometric structure implied by the terms open and closed is itself often either misunderstood or misused. Lastly, the role played by the cosmological constant is often improperly slighted. This paper is intended to give several examples of the abuse of terminology and clarify the distinction by means of a brief, elementary overview of Friedmann-Robertson-Walker cosmological models.
NASA Astrophysics Data System (ADS)
Narimani, Ali; Moss, Adam; Scott, Douglas
2012-10-01
Although it is well known that any consideration of the variations of fundamental constants should be restricted to their dimensionless combinations, the literature on variations of the gravitational constant G is entirely dimensionfull. To illustrate applications of this to cosmology, we explicitly give a dimensionless version of the parameters of the standard cosmological model, and describe the physics of both Big Bang Nucleosynthesis and recombination in a dimensionless manner. Rigorously determining how to talk about the model in a way which avoids physical dimensions is a requirement for proceeding with a calculation to constrain time-varying fundamental constants. The issue that appears to have been missed in many studies is that in cosmology the strength of gravity is bound up in the cosmological equations, and the epoch at which we live is a crucial part of the model. We argue that it is useful to consider the hypothetical situation of communicating with another civilization (with entirely different units), comparing only dimensionless constants, in order to decide if we live in a Universe governed by precisely the same physical laws. In this thought experiment, we would also have to compare epochs, which can be defined by giving the value of any one of the evolving cosmological parameters. By setting things up carefully in this way one can avoid inconsistent results when considering variable constants, caused by effectively fixing more than one parameter today. We show examples of this effect by considering microwave background anisotropies, being careful to maintain dimensionlessness throughout. We present Fisher matrix calculations to estimate how well the fine structure constants for electromagnetism and gravity can be determined with future microwave background experiments. We highlight how one can be misled by simply adding G to the usual cosmological parameter set.
On the asserted clash between the Freud and the Bianchi identities
NASA Astrophysics Data System (ADS)
Antoci, S.
1995-09-01
Through a constructive method it is shown that the claim advanced in recent times about a clash that should occur between the Freud and the Bianchi identities in Einstein's general theory of relativity is based on a faulty argument.
A global conformal extension theorem for perfect fluid Bianchi space-times
Luebbe, Christian Tod, Paul
2008-12-15
A global extension theorem is established for isotropic singularities in polytropic perfect fluid Bianchi space-times. When an extension is possible, the limiting behaviour of the physical space-time near the singularity is analysed.
Triangulation using synthetic aperture radar images
NASA Technical Reports Server (NTRS)
Wu, Sherman S. C.; Howington-Kraus, Annie E.
1991-01-01
For the extraction of topographic information about Venus from stereoradar images obtained from the Magellan Mission, a Synthetic Aperture Radar (SAR) compilation system was developed on analytical stereoplotters. The system software was extensively tested by using stereoradar images from various spacecraft and airborne radar systems, including Seasat, SIR-B, ERIM XCL, and STAR-1. Stereomodeling from radar images was proven feasible, and development is on a correct approach. During testing, the software was enhanced and modified to obtain more flexibility and better precision. Triangulation software for establishing control points by using SAR images was also developed through a joint effort with the Defense Mapping Agency. The SAR triangulation system comprises four main programs, TRIDATA, MODDATA, TRISAR, and SHEAR. The first two programs are used to sort and update the data; the third program, the main one, performs iterative statistical adjustment; and the fourth program analyzes the results. Also, input are flight data and data from the Global Positioning System and Inertial System (navigation information). The SAR triangulation system was tested with six strips of STAR-1 radar images on a VAX-750 computer. Each strip contains images of 10 minutes flight time (equivalent to a ground distance of 73.5 km); the images cover a ground width of 22.5 km. All images were collected from the same side. With an input of 44 primary control points, 441 ground control points were produced. The adjustment process converged after eight iterations. With a 6-m/pixel resolution of the radar images, the triangulation adjustment has an average standard elevation error of 81 m. Development of Magellan radargrammetry will be continued to convert both SAR compilation and triangulation systems into digital form.
Conformal Ricci collineations in LRS Bianchi type V spacetimes with perfect fluid matter
NASA Astrophysics Data System (ADS)
Khan, Fawad; Hussain, Tahir; Akhtar, Sumaira Saleem
2017-08-01
Considering the perfect fluid as a source of energy-momentum tensor, we have classified locally rotationally symmetric (LRS) Bianchi type V spacetimes according to their conformal Ricci collineations (CRCs). It is shown that the LRS Bianchi type V spacetimes with perfect fluid matter admit 9- or 15-dimensional Lie algebra of CRCs when the Ricci tensor is non-degenerate, while the group of CRCs is infinite for degenerate Ricci tensor.
Paal, Eugen; Virkepu, Jueri
2009-05-15
Operadic Lax representations for the harmonic oscillator are used to construct the dynamical deformations of three-dimensional (3D) real Lie algebras in the Bianchi classification. It is shown that the energy conservation of the harmonic oscillator is related to the Jacobi identities of the dynamically deformed algebras. Based on this observation, it is proved that the dynamical deformations of 3D real Lie algebras in the Bianchi classification over the harmonic oscillator are Lie algebras.
Observations on interfacing loop quantum gravity with cosmology
NASA Astrophysics Data System (ADS)
Pawłowski, Tomasz
2015-12-01
A simple idea of relating the loop quantum gravity (LQG) and loop quantum cosmology (LQC) degrees of freedom is introduced and used to define a relatively robust interface between these theories in context of toroidal Bianchi I model. The idea is an expansion of the construction originally introduced by Ashtekar and Wilson-Ewing and relies on explicit averaging of a certain subclass of spin networks over the subgroup of the diffeomorphisms remaining after the gauge fixing used in homogeneous LQC. It is based on the set of clearly defined principles and thus is a convenient tool to control the emergence and behavior of the cosmological degrees of freedom in studies of dynamics in canonical LQG. The constructed interface is further adapted to isotropic spacetimes. Relating the proposed LQG-LQC interface with some results on black hole entropy suggests a modification to the area gap value currently used in LQC.
Nonlinear stability of cosmological solutions in massive gravity
Felice, Antonio De; Gümrükçüoğlu, A. Emir; Lin, Chunshan; Mukohyama, Shinji E-mail: emir.gumrukcuoglu@ipmu.jp E-mail: shinji.mukohyama@ipmu.jp
2013-05-01
We investigate nonlinear stability of two classes of cosmological solutions in massive gravity: isotropic Friedmann-Lemaître-Robertson-Walker (FLRW) solutions and anisotropic FLRW solutions. For this purpose we construct the linear cosmological perturbation theory around axisymmetric Bianchi type-I backgrounds. We then expand the background around the two classes of solutions, which are fixed points of the background evolution equation, and analyze linear perturbations on top of it. This provides a consistent truncation of nonlinear perturbations around these fixed point solutions and allows us to analyze nonlinear stability in a simple way. In particular, it is shown that isotropic FLRW solutions exhibit nonlinear ghost instability. On the other hand, anisotropic FLRW solutions are shown to be ghost-free for a range of parameters and initial conditions.
Dark-energy cosmological models in f(G) gravity
Shamir, M. F.
2016-10-15
We discuss dark-energy cosmological models in f(G) gravity. For this purpose, a locally rotationally symmetric Bianchi type I cosmological model is considered. First, exact solutions with a well-known form of the f(G) model are explored. One general solution is discussed using a power-law f(G) gravity model and physical quantities are calculated. In particular, Kasner’s universe is recovered and the corresponding f(G) gravity models are reported. Second, the energy conditions for the model under consideration are discussed using graphical analysis. It is concluded that solutions with f(G) = G{sup 5/6} support expansion of universe while those with f(G) = G{sup 1/2} do not favor the current expansion.
Dark-energy cosmological models in f( G) gravity
NASA Astrophysics Data System (ADS)
Shamir, M. F.
2016-10-01
We discuss dark-energy cosmological models in f( G) gravity. For this purpose, a locally rotationally symmetric Bianchi type I cosmological model is considered. First, exact solutions with a well-known form of the f( G) model are explored. One general solution is discussed using a power-law f( G) gravity model and physical quantities are calculated. In particular, Kasner's universe is recovered and the corresponding f( G) gravity models are reported. Second, the energy conditions for the model under consideration are discussed using graphical analysis. It is concluded that solutions with f( G) = G 5/6 support expansion of universe while those with f( G) = G 1/2 do not favor the current expansion.
Towards generic resolution of strong singularities in loop quantum cosmology
NASA Astrophysics Data System (ADS)
Singh, Parampreet
2010-10-01
Singularities are the boundaries of classical spacetime in General Relativity. It has been always hoped that quantum gravitational effects may resolve these singularities. In recent years, progress in loop quantum cosmology has provided insights on the resolution of big bang, big crunch and other spacelike singularities. In this talk we will give an update on the recent status of the generic resolution of strong spacelike singularities in loop quantum cosmology. We will show that for flat and curved Roberston-Walker backgrounds and also for Bianchi-I models, loop quantum gravity effects resolve all strong curvature singularities. However, weak curvature singularities, that is those beyond which geodesics can be continued, may not be resolved.
Inhomogeneous cosmology. III - Primordial gravitational waves and dust
NASA Technical Reports Server (NTRS)
Adams, P. J.; Hellings, R. W.; Zimmerman, R. L.
1987-01-01
In this paper, the properties of a special class of inhomogeneous cosmological models and the interaction of the inhomogeneities with the evolution of the background geometry and matter are studied. The cosmological model is chosen so that the initial inhomogeneities evolve into 'plane' gravitational waves propagating through a smooth Bianchi I dust background. It is shown how the inhomogeneities interact with matter, 3 K radiation, and the background geometry, causing the expansion to slow down in some regions and speed up in others. It is also shown how the gravitational waves can produce a 'dragging of the inertial frame' which will affect the observed distribution of matter and 3 K radiation. In particular, this frame-dragging effect can account for a major fraction of the obsserved dipole component between the 3 K background radiation and the rest frame of global matter, an effect usually assumed to have been produced by large-scale local motion.
Evolution of perturbations in anisotropic loop quantum cosmology
NASA Astrophysics Data System (ADS)
Vijayakumar, Sreenath; Agullo, Ivan; Olmedo, Javier
2017-01-01
In loop quantum cosmology the big bang singularity is replaced by a quantum bounce. The evolution of primordial perturbations through such a bounce in a Friedmann-Lemaître-Robertson-Walker universe has been studied in great detail. However, it is well known that any tiny anisotropy will grow (up to an upper bound) as the universe contracts and undergoes a bounce. Anisotropies will then decrease and eventually dilute in the expanding branch, but quantum perturbations may retain memory of the anisotropic bounce. In this talk, we present our efforts in understanding the effect of anisotropies (of Bianchi-I type) on the evolution of primordial perturbations in loop quantum cosmology, and in exploring its phenomenological implications. This work is supported by the NSF Grant No. PHY-1403943.
Behaviour of the cosmological model with variable deceleration parameter
NASA Astrophysics Data System (ADS)
Tiwari, R. K.; Beesham, A.; Shukla, B. K.
2016-12-01
We consider the Bianchi type-VI0 massive string universe with decaying cosmological constant Λ. To solve Einstein's field equations, we assume that the shear scalar is proportional to the expansion scalar and that the deceleration parameter q is a linear function of the Hubble parameter H, i.e., q=α +β H, which yields the scale factor a = e^{1/β√{2β t+k1}}. The model expands exponentially with cosmic time t. The value of the cosmological constant Λ is small and positive. Also, we discuss physical parameters as well as the jerk parameter j, which predict that the universe in this model originates as in the Λ CDM model.
Numerical Bianchi type I solutions in semiclassical gravitation
Vitenti, Sandro D. P.; Mueller, Daniel
2006-09-15
It is believed that soon after the Planck era, spacetime should have a semiclassical nature. In this context we consider quantum fields propagating in a classical gravitational field and study the backreaction of these fields, using the expected value of the energy-momentum tensor as source of the gravitational field. According to this theory, the escape from general relativity theory is unavoidable. Two geometric counter-term are needed to regularize the divergences which come from the expected value. There is a parameter associated to each counter-term and in this work we found numerical solutions of this theory to particular initial conditions, for general Bianchi Type I spaces. We show that even though there are spurious solutions some of them can be considered physical. These physical solutions include de Sitter and Minkowski that are obtained asymptotically.
Nonlinear spinor fields in Bianchi type-VI0 spacetime
NASA Astrophysics Data System (ADS)
Saha, Bijan
2015-10-01
Within the scope of Bianchi type- V I 0 spacetime we study the role of spinor field on the evolution of the Universe. It is found that the presence of the non-trivial non-diagonal components of the energy-momentum tensor of the spinor field plays a vital role on the evolution of the Universe. As a result of their mutual influence, there occur two different scenarios. In one case the invariants constructed from the bilinear forms of the spinor field become trivial, thus giving rise to a massless and linear spinor field Lagrangian. According to the second scenario massive and nonlinear terms do not vanish and depending on the sign of the coupling constants we have either an expanding mode of expansion or the one that, after obtaining some maximum value, contracts and ends in a big crunch generating spacetime singularity. This result shows that the spinor field is highly sensitive to the gravitational one.
NASA Astrophysics Data System (ADS)
Maurya, Dinesh Chandra; Zia, Rashid; Pradhan, Anirudh
Before 1998, it was usually expected that the universe was expanding with a constant rate or the expansion was slowing down. In 1998, the surprising discovery based on type Ia supernovae, that the rate of expansion of the universe is increasing, forced the researchers to reconsider the various cosmological models proposed so far. The current study is also an effort to revisit the LRS Bianchi type-II, dark energy (DE) model by taking time-dependent deceleration parameter (DP) instead of constant DP. We have assumed the variable scale factor a(t) = [sinh(αt)] 1 n, which gives the variable DP as q(t) = nsech2(αt) - 1, with these considerations, the solutions of field equations are calculated. Various parameters of DE models are also calculated, and it is found that these are consistent with the recent observations.
NASA Astrophysics Data System (ADS)
Plionis, M.
2004-07-01
The recent scientific efforts in Astrophysics & Cosmology have brought a revolution to our understanding of the Cosmos. Amazing results is the outcome of amazing experiments! The huge scientific, technological & financial effort that has gone into building the 10-m class telescopes as well as many space and balloon observatories, essential to observe the multitude of cosmic phenomena in their manifestations at different wavelengths, from gamma-rays to the millimetre and the radio, has given and is still giving its fruits of knowledge. These recent scientific achievements in Observational and Theoretical Cosmology were presented in the "Multiwavelength Cosmology" conference that took place on beautiful Mykonos island in the Aegean between 17 and 20 June 2003. More than 180 Cosmologists from all over the world gathered for a four-day intense meeting in which recent results from large ground based surveys (AAT/2-df, SLOAN) and space missions (WMAP, Chandra, XMM, ISO, HST) were presented and debated, providing a huge impetus to our knowledge of the Cosmos. The future of the subject (experiments, and directions of research) was also discussed. The conference was devoted mostly on the constraints on Cosmological models and galaxy formation theories that arise from the study of the high redshift Universe, from clusters of galaxies, and their evolution, from the cosmic microwave background, the large-scale structure and star-formation history. Link: Multidimensional cosmology
NASA Astrophysics Data System (ADS)
Alvarez, Enrique
This paper briefly reports on some recent attempts to construct a cosmology consistent with present ideas about the fundamental theories of nature, which generally involve extra dimensions. The decoupling of the extra dimensions from the usual ones is analyzed, as well as the possiblity of phase transitions in a "superstring universe".
A first look at transition amplitudes in (2 + 1)-dimensional causal dynamical triangulations
NASA Astrophysics Data System (ADS)
Cooperman, Joshua H.; Miller, Jonah M.
2014-02-01
We study a lattice regularization of the gravitational path integral—causal dynamical triangulations—for (2 + 1)-dimensional Einstein gravity with positive cosmological constant in the presence of past and future spacelike boundaries of fixed intrinsic geometries. For spatial topology of a 2-sphere, we determine the form of the Einstein-Hilbert action supplemented by the Gibbons-Hawking-York boundary terms within the Regge calculus of causal triangulations. Employing this action we numerically simulate a variety of transition amplitudes from the past boundary to the future boundary. To the extent that we have so far investigated them, these transition amplitudes appear consistent with the gravitational effective action previously found to characterize the ground state of quantum spacetime geometry within the Euclidean de Sitter-like phase. Certain of these transition amplitudes convincingly demonstrate that the so-called stalks present in this phase are numerical artifacts of the lattice regularization, seemingly indicate that the quantization technique of causal dynamical triangulations differs in detail from that of the no-boundary proposal of Hartle and Hawking, and possibly represent the first numerical simulations of portions of temporally unbounded quantum spacetime geometry within the causal dynamical triangulations approach. We also uncover tantalizing evidence suggesting that Lorentzian not Euclidean de Sitter spacetime dominates the ground state on sufficiently large scales.
NASA Astrophysics Data System (ADS)
Bothun, Greg
2011-10-01
Ever since Aristotle placed us, with certainty, in the Center of the Cosmos, Cosmological models have more or less operated from a position of known truths for some time. As early as 1963, for instance, it was ``known'' that the Universe had to be 15-17 billion years old due to the suspected ages of globular clusters. For many years, attempts to determine the expansion age of the Universe (the inverse of the Hubble constant) were done against this preconceived and biased notion. Not surprisingly when more precise observations indicated a Hubble expansion age of 11-13 billion years, stellar models suddenly changed to produce a new age for globular cluster stars, consistent with 11-13 billion years. Then in 1980, to solve a variety of standard big bang problems, inflation was introduced in a fairly ad hoc manner. Inflation makes the simple prediction that the net curvature of spacetime is zero (i.e. spacetime is flat). The consequence of introducing inflation is now the necessary existence of a dark matter dominated Universe since the known baryonic material could comprise no more than 1% of the necessary energy density to make spacetime flat. As a result of this new cosmological ``truth'' a significant world wide effort was launched to detect the dark matter (which obviously also has particle physics implications). To date, no such cosmological component has been detected. Moreover, all available dynamical inferences of the mass density of the Universe showed in to be about 20% of that required for closure. This again was inconsistent with the truth that the real density of the Universe was the closure density (e.g. Omega = 1), that the observations were biased, and that 99% of the mass density had to be in the form of dark matter. That is, we know the universe is two component -- baryons and dark matter. Another prevailing cosmological truth during this time was that all the baryonic matter was known to be in galaxies that populated our galaxy catalogs. Subsequent
Laser triangulation: fundamental uncertainty in distance measurement.
Dorsch, R G; Häusler, G; Herrmann, J M
1994-03-01
We discuss the uncertainty limit in distance sensing by laser triangulation. The uncertainty in distance measurement of laser triangulation sensors and other coherent sensors is limited by speckle noise. Speckle arises because of the coherent illumination in combination with rough surfaces. A minimum limit on the distance uncertainty is derived through speckle statistics. This uncertainty is a function of wavelength, observation aperture, and speckle contrast in the spot image. Surprisingly, it is the same distance uncertainty that we obtained from a single-photon experiment and from Heisenberg's uncertainty principle. Experiments confirm the theory. An uncertainty principle connecting lateral resolution and distance uncertainty is introduced. Design criteria for a sensor with minimum distanc uncertainty are determined: small temporal coherence, small spatial coherence, a large observation aperture.
Personal authentication using hand vein triangulation
NASA Astrophysics Data System (ADS)
Kumar, Ajay; Prathyusha, K. Venkata
2008-03-01
This paper presents a new approach to authenticate individuals using triangulation of hand vein images. The proposed method is fully automated and employs palm dorsal hand vein images acquired from the low-cost, near infrared, contactless imaging. The knuckle tips are used as key points for image normalization and the extraction of region of interest. The matching scores are generated in two parallel stages; (i) hierarchical matching score from the four topologies of triangulation in binarized vein structures and (ii) from the geometrical features consisting of knuckle point perimeter distances in the acquired images. The weighted score level combination from these two matching scores are used to authenticate the individuals. The achieved experimental results from the proposed system using contactless, palm dorsal hand vein images are promising and suggest more user friendly alternative for user identification.
Causal Dynamical Triangulations in Four Dimensions
NASA Astrophysics Data System (ADS)
Görlich, Andrzej
2011-11-01
Recent results obtained within a non-perturbative approach to quantum gravity based on the method of four-dimensional Causal Dynamical Triangulations are described. The phase diagram of the model consists of three phases. In the physically most interesting phase, the time-translational symmetry is spontaneously broken. Calculations of expectation values required introducing procedures taking into account the inhomogeneity of configurations. It was shown that the dynamically emerged four-dimensional background geometry corresponds to a Euclidean de Sitter space and reveals no fractality at large distances. Measurements of the covariance matrix of scale factor fluctuations allowed to reconstruct the effective action, which remained in agreement with the discrete minisuperspace action. Values of the Hausdorff dimension and spectral dimension of three-dimensional spatial slices suggest their fractal nature, which was confirmed by a direct analysis of triangulation structure. The Monte Carlo algorithm used to obtain presented results is described.
Extending particle tracking capability with Delaunay triangulation.
Chen, Kejia; Anthony, Stephen M; Granick, Steve
2014-04-29
Particle tracking, the analysis of individual moving elements in time series of microscopic images, enables burgeoning new applications, but there is need to better resolve conformation and dynamics. Here we describe the advantages of Delaunay triangulation to extend the capabilities of particle tracking in three areas: (1) discriminating irregularly shaped objects, which allows one to track items other than point features; (2) combining time and space to better connect missing frames in trajectories; and (3) identifying shape backbone. To demonstrate the method, specific examples are given, involving analyzing the time-dependent molecular conformations of actin filaments and λ-DNA. The main limitation of this method, shared by all other clustering techniques, is the difficulty to separate objects when they are very close. This can be mitigated by inspecting locally to remove edges that are longer than their neighbors and also edges that link two objects, using methods described here, so that the combination of Delaunay triangulation with edge removal can be robustly applied to processing large data sets. As common software packages, both commercial and open source, can construct Delaunay triangulation on command, the methods described in this paper are both computationally efficient and easy to implement.
Coefficient adaptive triangulation for strongly anisotropic problems
D`Azevedo, E.F.; Romine, C.H.; Donato, J.M.
1996-01-01
Second order elliptic partial differential equations arise in many important applications, including flow through porous media, heat conduction, the distribution of electrical or magnetic potential. The prototype is the Laplace problem, which in discrete form produces a coefficient matrix that is relatively easy to solve in a regular domain. However, the presence of anisotropy produces a matrix whose condition number is increased, making the resulting linear system more difficult to solve. In this work, we take the anisotropy into account in the discretization by mapping each anisotropic region into a ``stretched`` coordinate space in which the anisotropy is removed. The region is then uniformly triangulated, and the resulting triangulation mapped back to the original space. The effect is to generate long slender triangles that are oriented in the direction of ``preferred flow.`` Slender triangles are generally regarded as numerically undesirable since they tend to cause poor conditioning; however, our triangulation has the effect of producing effective isotropy, thus improving the condition number of the resulting coefficient matrix.
NASA Astrophysics Data System (ADS)
Alvarez, Enrique
1985-01-01
Some cosmological consequences of the assumption that superstrings are more fundamental objects than ordinary local quantum fields are examined. We study, in particular, the dependence of both the string tension and the temperature of the primordial string soup on cosmic time. A particular scenario is proposed in which the universe undergoes a contracting ``string phase'' before the ordinary ``big bang,'' which according to this picture is nothing but the outcome of the transition from nonlocal to local fundamental physics.
NASA Astrophysics Data System (ADS)
Grant, E.; Murdin, P.
2000-11-01
During the early Middle Ages (ca 500 to ca 1130) scholars with an interest in cosmology had little useful and dependable literature. They relied heavily on a partial Latin translation of PLATO's Timaeus by Chalcidius (4th century AD), and on a series of encyclopedic treatises associated with the names of Pliny the Elder (ca AD 23-79), Seneca (4 BC-AD 65), Macrobius (fl 5th century AD), Martianus ...
NASA Astrophysics Data System (ADS)
Kirillov, A. A.; Savelova, E. P.
2016-05-01
We describe in details the procedure how the Lobachevsky space can be factorized to a space of the constant negative curvature filled with a gas of wormholes. We show that such wormholes have throat sections in the form of tori and are traversable and stable in the cosmological context. The relation of such wormholes to the dark matter phenomenon is briefly described. We also discuss the possibility of the existence of analogous factorizations for all types of homogeneous spaces.
A new class of LRS Bianchi type-II dark energy models with variable EoS parameter
NASA Astrophysics Data System (ADS)
Pradhan, Anirudh; Amirhashchi, Hassan; Jaiswal, Rekha
2011-08-01
A new class of dark energy models in a Locally Rotationally Symmetric Bianchi type-II (LRS B-II) space-time with variable equation of state (EoS) parameter and constant deceleration parameter have been investigated in the present paper. The Einstein's field equations have been solved by applying a variation law for generalized Hubble's parameter given by Berman: Nuovo Cimento 74:182 (1983) which generates two types of solutions for the average scale factor, one is of power-law type and other is of the exponential-law form. Using these two forms, Einstein's field equations are solved separately that correspond to expanding singular and non-singular models of the universe respectively. The dark energy EoS parameter ω is found to be time dependent and its existing range for both models is in good agreement with the three recent observations of (i) SNe Ia data (Knop et al.: Astrophys. J. 598:102 (2003)), (ii) SNe Ia data collaborated with CMBR anisotropy and galaxy clustering statistics (Tegmark et al.: Astrophys. J. 606:702 (2004)) and latest (iii) a combination of cosmological datasets coming from CMB anisotropies, luminosity distances of high redshift type Ia supernovae and galaxy clustering (Hinshaw et al.: Astrophys. J. Suppl. 180:225 (2009); Komatsu et al. Astrophys. J. Suppl. 180:330 (2009)). The cosmological constant Λ is found to be a positive decreasing function of time and it approaches a small positive value at late time (i.e. the present epoch) which is corroborated by results from recent supernovae Ia observations. The physical and geometric behaviour of the universe have also been discussed in detail.
Homogeneous noncommutative quantum cosmology
Maceda, Marco; Macias, Alfredo; Pimentel, Luis O.
2008-09-15
Using the Groenewold-Moyal product, the noncommutative Bianchi IX model is constructed by imposing commutation relations on the minisuperspace variables ({omega},{beta}{sub +},{beta}{sub -}). A noncommutative 'wormhole' solution to the corresponding Wheeler-DeWitt equation is constructed and its behavior at fixed {omega} is analyzed.
Implementing a triangulation protocol in bereavement research: a methodological discussion.
Briller, Sherylyn H; Meert, Kathleen L; Schim, Stephanie Myers; Thurston, Celia S; Kabel, Allison
2008-01-01
Triangulation is a comparative strategy for examining data that strengthens qualitative and multi-method research. Despite the benefits of triangulation noted in the research methods literature, few concrete models for operationalization of protocols exist. Lack of documentation of explicit triangulation procedures is especially true in the area of bereavement research. This article describes how an interdisciplinary research team implemented a triangulation protocol in a study of the needs of bereaved parents. Triangulation enabled the integration of diverse data sources, methods, and disciplinary perspectives. These processes yielded a more meaningful typology of bereaved parents' needs than would have otherwise been possible. Extending the use of triangulation will enhance multi-faceted understandings of bereavement.
Numerical simulations of loop quantum Bianchi-I spacetimes
NASA Astrophysics Data System (ADS)
Diener, Peter; Joe, Anton; Megevand, Miguel; Singh, Parampreet
2017-05-01
Due to the numerical complexities of studying evolution in an anisotropic quantum spacetime, in comparison to the isotropic models, the physics of loop quantized anisotropic models has remained largely unexplored. In particular, robustness of bounce and the validity of effective dynamics have so far not been established. Our analysis fills these gaps for the case of vacuum Bianchi-I spacetime. To efficiently solve the quantum Hamiltonian constraint we perform an implementation of the Cactus framework which is conventionally used for applications in numerical relativity. Using high performance computing, numerical simulations for a large number of initial states with a wide variety of fluctuations are performed. Big bang singularity is found to be replaced by anisotropic bounces for all the cases. We find that for initial states which are sharply peaked at the late times in the classical regime and bounce at a mean volume much greater than the Planck volume, effective dynamics is an excellent approximation to the underlying quantum dynamics. Departures of the effective dynamics from the quantum evolution appear for the states probing deep Planck volumes. A detailed analysis of the behavior of this departure reveals a non-monotonic and subtle dependence on fluctuations of the initial states. We find that effective dynamics in almost all of the cases underestimates the volume and hence overestimates the curvature at the bounce, a result in synergy with earlier findings in the isotropic case. The expansion and shear scalars are found to be bounded throughout the evolution.
Anisotropic, nonsingular early universe model leading to a realistic cosmology
Dechant, Pierre-Philippe; Lasenby, Anthony N.; Hobson, Michael P.
2009-02-15
We present a novel cosmological model in which scalar field matter in a biaxial Bianchi IX geometry leads to a nonsingular 'pancaking' solution: the hypersurface volume goes to zero instantaneously at the 'big bang', but all physical quantities, such as curvature invariants and the matter energy density remain finite, and continue smoothly through the big bang. We demonstrate that there exist geodesics extending through the big bang, but that there are also incomplete geodesics that spiral infinitely around a topologically closed spatial dimension at the big bang, rendering it, at worst, a quasiregular singularity. The model is thus reminiscent of the Taub-NUT vacuum solution in that it has biaxial Bianchi IX geometry and its evolution exhibits a dimensionality reduction at a quasiregular singularity; the two models are, however, rather different, as we will show in a future work. Here we concentrate on the cosmological implications of our model and show how the scalar field drives both isotropization and inflation, thus raising the question of whether structure on the largest scales was laid down at a time when the universe was still oblate (as also suggested by [T. S. Pereira, C. Pitrou, and J.-P. Uzan, J. Cosmol. Astropart. Phys. 9 (2007) 6.][C. Pitrou, T. S. Pereira, and J.-P. Uzan, J. Cosmol. Astropart. Phys. 4 (2008) 4.][A. Guemruekcueoglu, C. Contaldi, and M. Peloso, J. Cosmol. Astropart. Phys. 11 (2007) 005.]). We also discuss the stability of our model to small perturbations around biaxiality and draw an analogy with cosmological perturbations. We conclude by presenting a separate, bouncing solution, which generalizes the known bouncing solution in closed FRW universes.
The Cosmological Constant in Quantum Cosmology
Wu Zhongchao
2008-10-10
Hawking proposed that the cosmological constant is probably zero in quantum cosmology in 1984. By using the right configuration for the wave function of the universe, a complete proof is found very recently.
Algorithms for high aspect ratio oriented triangulations
NASA Technical Reports Server (NTRS)
Posenau, Mary-Anne K.
1995-01-01
Grid generation plays an integral part in the solution of computational fluid dynamics problems for aerodynamics applications. A major difficulty with standard structured grid generation, which produces quadrilateral (or hexahedral) elements with implicit connectivity, has been the requirement for a great deal of human intervention in developing grids around complex configurations. This has led to investigations into unstructured grids with explicit connectivities, which are primarily composed of triangular (or tetrahedral) elements, although other subdivisions of convex cells may be used. The existence of large gradients in the solution of aerodynamic problems may be exploited to reduce the computational effort by using high aspect ratio elements in high gradient regions. However, the heuristic approaches currently in use do not adequately address this need for high aspect ratio unstructured grids. High aspect ratio triangulations very often produce the large angles that are to be avoided. Point generation techniques based on contour or front generation are judged to be the most promising in terms of being able to handle complicated multiple body objects, with this technique lending itself well to adaptivity. The eventual goal encompasses several phases: first, a partitioning phase, in which the Voronoi diagram of a set of points and line segments (the input set) will be generated to partition the input domain; second, a contour generation phase in which body-conforming contours are used to subdivide the partition further as well as introduce the foundation for aspect ratio control, and; third, a Steiner triangulation phase in which points are added to the partition to enable triangulation while controlling angle bounds and aspect ratio. This provides a combination of the advancing front/contour techniques and refinement. By using a front, aspect ratio can be better controlled. By using refinement, bounds on angles can be maintained, while attempting to minimize
Strategies for nonobtuse boundary Delaunay triangulations
Murphy, M. |; Gable, C.W.
1998-12-31
Delaunay Triangulations with nonobtuse triangles at the boundaries satisfy a minimal requirement for Control Volume meshes. They motivate this quality requirement, discuss it in context with others that have been proposed, and give point placement strategies that generate the fewest or close to the fewest number of Steiner points needed to satisfy it for a particular problem instance. The advantage is that this strategy places a number of Steiner points proportional to the combinatorial size of the input rather than the local feature size, resulting in far fewer points in many cases.
NASA Astrophysics Data System (ADS)
Khan, Suhail; Hussain, Tahir; Khan, Gulzar Ali
The aim of this paper is to explore teleparallel conformal Killing vector fields (CKVFs) of locally rotationally symmetric (LRS) Bianchi type V spacetimes in the context of teleparallel gravity and compare the obtained results with those of general relativity (GR). The general solution of teleparallel conformal Killing's equations is found in terms of some unknown functions of t and x, along with a set of integrability conditions. The integrability conditions are solved in some particular cases to get the final form of teleparallel CKVFs. It is observed that the LRS Bianchi type V spacetimes admit proper teleparallel CKVF in only one case, while in remaining cases the teleparallel CKVFs reduce to teleparallel Killing vector fields (KVFs). Moreover, it is shown that the LRS Bianchi type V spacetimes do not admit any proper teleparallel homothetic vector field (HVF).
Energy distributions of Bianchi type-VI h Universe in general relativity and teleparallel gravity
NASA Astrophysics Data System (ADS)
Özkurt, Şeref; Aygün, Sezg&idot; n.
2017-04-01
In this paper, we have investigated the energy and momentum density distributions for the inhomogeneous generalizations of homogeneous Bianchi type-VI h metric with Einstein, Bergmann-Thomson, Landau-Lifshitz, Papapetrou, Tolman and Møller prescriptions in general relativity (GR) and teleparallel gravity (TG). We have found exactly the same results for Einstein, Bergmann-Thomson and Landau-Lifshitz energy-momentum distributions in Bianchi type-VI h metric for different gravitation theories. The energy-momentum distributions of the Bianchi type- VI h metric are found to be zero for h = -1 in GR and TG. However, our results agree with Tripathy et al, Tryon, Rosen and Aygün et al.
Behavior of the Universe anisotropy in a big-bounce cosmology
NASA Astrophysics Data System (ADS)
Moriconi, Riccardo; Montani, Giovanni
2017-06-01
We investigate the classical and quantum behavior of a Bianchi I model in the presence of a stiff matter contribution when the Vilenkin interpretation of the wave function of the Universe is taken into account. We study its evolution in the so-called polymer representation of quantum mechanics, in order to characterize the modifications that a discrete nature in the isotropic variable of the Universe induces on the morphology of the cosmological singularity. We demonstrate that in such a model the big-bang singularity is removed at a semiclassical level in favor of a big bounce when a lattice on the isotropic variable is considered. Furthermore, the analysis of the mean values on the quantum degrees of freedom, i.e., the variables β+,β- in the Misner picture, and the investigation on the evolution of the wave packets show how the typical diverging behavior associated to the anisotropies of the Universe in proximity of the initial singularity disappears in our polymer modified scheme. Indeed, the anisotropies remain finite across the big bounce and they assume a value that depends on the initial conditions fixed far from the turning point. Finally, we demonstrate that the proposed scenario can be extended, with a suitable choice of the configuration parameters, to the Bianchi IX cosmology and therefore it can be regarded as a paradigm for the generic cosmological model.
Surface roughness measurement with laser triangulation
NASA Astrophysics Data System (ADS)
Bai, Fuzhong; Zhang, Xiaoyan; Tian, Chaoping
2016-09-01
A surface roughness measurement method is introduced in the paper, which is based on laser triangulation and digital image processing technique. In the measuring system, we use the line-structured light as light source, microscope lens and high-accuracy CCD sensor as displacement sensor as well. In addition, the working angle corresponding to the optimal sensitivity is considered in the optical structure design to improve the measuring accuracy. Through necessary image processing operation for the light strip image, such as center-line extraction with the barycenter algorithm, Gaussian filtering, the value of roughness is calculated. A standard planing surface is measured experimentally with the proposed method and the stylus method (Mitutoyo SJ-410) respectively. The profilograms of surface appearance are greatly similar in the shape and the amplitude to two methods. Also, the roughness statistics values are close. The results indicate that the laser triangulation with the line-structured light can be applied to measure the surface roughness with the advantages of rapid measurement and visualized display of surface roughness profile.
Good Random Multi-Triangulation of Surfaces.
de Medeiros Filho, Esdras; Siqueira, Marcelo
2017-05-12
We introduce the Hierarchical Poisson Disk Sampling Multi-Triangulation (HPDS-MT) of surfaces, a novel structure that combines the power of multi-triangulation (MT) with the benefits of Hierarchical Poisson Disk Sampling (HPDS). MT is a general framework for representing surfaces through variable resolution triangle meshes, while HPDS is a well-spaced random distribution with blue noise characteristics. The distinguishing feature of the HPDS-MT is its ability to extract adaptive meshes whose triangles are guaranteed to have good shape quality. The key idea behind the HPDS-MT is a preprocessed hierarchy of points, which is used in the construction of a MT via incremental simplification. In addition to proving theoretical properties on the shape quality of the triangle meshes extracted by the HPDS-MT, we provide an implementation that computes the HPDS-MT with high accuracy. Our results confirm the theoretical guarantees and outperform similar methods. We also prove that the Hausdorff distance between the original surface and any (extracted) adaptive mesh is bounded by the sampling distribution of the radii of Poisson-disks over the surface. Finally, we illustrate the advantages of the HPDS-MT in some typical problems of geometry processing.
Krioukov, Dmitri; Kitsak, Maksim; Sinkovits, Robert S; Rideout, David; Meyer, David; Boguñá, Marián
2012-01-01
Prediction and control of the dynamics of complex networks is a central problem in network science. Structural and dynamical similarities of different real networks suggest that some universal laws might accurately describe the dynamics of these networks, albeit the nature and common origin of such laws remain elusive. Here we show that the causal network representing the large-scale structure of spacetime in our accelerating universe is a power-law graph with strong clustering, similar to many complex networks such as the Internet, social, or biological networks. We prove that this structural similarity is a consequence of the asymptotic equivalence between the large-scale growth dynamics of complex networks and causal networks. This equivalence suggests that unexpectedly similar laws govern the dynamics of complex networks and spacetime in the universe, with implications to network science and cosmology.
Krioukov, Dmitri; Kitsak, Maksim; Sinkovits, Robert S.; Rideout, David; Meyer, David; Boguñá, Marián
2012-01-01
Prediction and control of the dynamics of complex networks is a central problem in network science. Structural and dynamical similarities of different real networks suggest that some universal laws might accurately describe the dynamics of these networks, albeit the nature and common origin of such laws remain elusive. Here we show that the causal network representing the large-scale structure of spacetime in our accelerating universe is a power-law graph with strong clustering, similar to many complex networks such as the Internet, social, or biological networks. We prove that this structural similarity is a consequence of the asymptotic equivalence between the large-scale growth dynamics of complex networks and causal networks. This equivalence suggests that unexpectedly similar laws govern the dynamics of complex networks and spacetime in the universe, with implications to network science and cosmology. PMID:23162688
Triangulation, Respondent Validation, and Democratic Participation in Mixed Methods Research
ERIC Educational Resources Information Center
Torrance, Harry
2012-01-01
Over the past 10 years or so the "Field" of "Mixed Methods Research" (MMR) has increasingly been exerting itself as something separate, novel, and significant, with some advocates claiming paradigmatic status. Triangulation is an important component of mixed methods designs. Triangulation has its origins in attempts to validate research findings…
Triangulation, Respondent Validation, and Democratic Participation in Mixed Methods Research
ERIC Educational Resources Information Center
Torrance, Harry
2012-01-01
Over the past 10 years or so the "Field" of "Mixed Methods Research" (MMR) has increasingly been exerting itself as something separate, novel, and significant, with some advocates claiming paradigmatic status. Triangulation is an important component of mixed methods designs. Triangulation has its origins in attempts to validate research findings…
Imparting small vorticity to a Bianchi type-VIh empty spacetime
NASA Astrophysics Data System (ADS)
Batakis, Nikos A.
1981-04-01
We present and briefly discuss a Bianchi type-VIh empty spacetime. The field equations have been solved after being linearized with respect to a parameter which imparts vorticity to the model. The limit of zero vorticity is an already known solution.
Inhomogeneous generalizations of Bianchi Type VIh universes with stiff perfect fluid and radiation
NASA Astrophysics Data System (ADS)
Roy, S. R.; Prasad, A.
1995-03-01
Families of inhomogeneous models filled with a stiff perfect fluid and radiation have been derived in which there is no flow of total momentum. The models are generalizations of those of Bianchi Type VIh and are discussed for some particular forms of the arbitrary functions appearing in them.
Einstein-Weyl field equations in a Bianchi type-IX space-time
Kolassis, C.A.; Le Denmat, G.
1984-07-15
It is proved that there exists no solution of the combined gravitational-neutrino field equations in general relativity if the space-time metric admits a group of isometries of Bianchi type IX and the neutrino field has geodesic and shearfree rays.
DIVE in the cosmic web: voids with Delaunay triangulation from discrete matter tracer distributions
NASA Astrophysics Data System (ADS)
Zhao, Cheng; Tao, Charling; Liang, Yu; Kitaura, Francisco-Shu; Chuang, Chia-Hsun
2016-07-01
We present a novel parameter-free cosmological void finder (DIVE, Delaunay TrIangulation Void findEr) based on Delaunay Triangulation (DT), which efficiently computes the empty spheres constrained by a discrete set of tracers. We define the spheres as DT voids, and describe their properties, including a universal density profile together with an intrinsic scatter. We apply this technique on 100 halo catalogues with volumes of 2.5 h-1Gpc side each, with a bias and number density similar to the Baryon Oscillation Spectroscopic Survey CMASS luminous red galaxies, performed with the PATCHY code. Our results show that there are two main species of DT voids, which can be characterized by the radius: they have different responses to halo redshift space distortions, to number density of tracers, and reside in different dark matter environments. Based on dynamical arguments using the tidal field tensor, we demonstrate that large DT voids are hosted in expanding regions, whereas the haloes used to construct them reside in collapsing ones. Our approach is therefore able to efficiently determine the troughs of the density field from galaxy surveys, and can be used to study their clustering. We further study the power spectra of DT voids, and find that the bias of the two populations are different, demonstrating that the small DT voids are essentially tracers of groups of haloes.
Isotropic and anisotropic bouncing cosmologies in Palatini gravity
Barragan, Carlos; Olmo, Gonzalo J.
2010-10-15
We study isotropic and anisotropic (Bianchi I) cosmologies in Palatini f(R) and f(R,R{sub {mu}{nu}R}{sup {mu}{nu}}) theories of gravity with a perfect fluid and consider the existence of nonsingular bouncing solutions in the early universe. We find that all f(R) models with isotropic bouncing solutions develop shear singularities in the anisotropic case. On the contrary, the simple quadratic model R+aR{sup 2}/R{sub P}+R{sub {mu}{nu}R}{sup {mu}{nu}/}R{sub P} exhibits regular bouncing solutions in both isotropic and anisotropic cases for a wide range of equations of state, including dust (for a<0) and radiation (for arbitrary a). It thus represents a purely gravitational solution to the big bang singularity and anisotropy problems of general relativity without the need for exotic (w>1) sources of matter/energy or extra degrees of freedom.
Cosmological coevolution of Yang-Mills fields and perfect fluids
Barrow, John D.; Jin, Yoshida; Maeda, Kei-ichi
2005-11-15
We study the coevolution of Yang-Mills fields and perfect fluids in Bianchi type I universes. We investigate numerically the evolution of the universe and the Yang-Mills fields during the radiation and dust eras of a universe that is almost isotropic. The Yang-Mills field undergoes small amplitude chaotic oscillations, as do the three expansion scale factors which are also displayed by the expansion scale factors of the universe. The results of the numerical simulations are interpreted analytically and compared with past studies of the cosmological evolution of magnetic fields in radiation and dust universes. We find that, whereas magnetic universes are strongly constrained by the microwave background anisotropy, Yang-Mills universes are principally constrained by primordial nucleosynthesis but the bound is comparatively weak with {omega}{sub YM}<0.105{omega}{sub rad}.
An exotic k-essence interpretation of interactive cosmological models
NASA Astrophysics Data System (ADS)
Forte, Mónica
2016-01-01
We define a generalization of scalar fields with non-canonical kinetic term which we call exotic k-essence or, briefly, exotik. These fields are generated by the global description of cosmological models with two interactive fluids in the dark sector and under certain conditions they correspond to usual k-essences. The formalism is applied to the cases of constant potential and of inverse square potential and also we develop the purely exotik version for the modified holographic Ricci type (MHR) of dark energy, where the equations of state are not constant. With the kinetic function F=1+mx and the inverse square potential we recover, through the interaction term, the identification between k-essences and quintessences of an exponential potential, already known for Friedmann-Robertson-Walker and Bianchi type I geometries. Worked examples are shown that include the self-interacting MHR and also models with crossing of the phantom divide line (PDL).
NASA Astrophysics Data System (ADS)
Aref'eva, I. Ya.; Volovich, I. V.
2011-08-01
Classical versions of the Big Bang cosmological models of the universe contain a singularity at the start of time, hence the time variable in the field equations should run over a half-line. Nonlocal string field theory equations with infinite number of derivatives are considered and an important difference between nonlocal operators on the whole real line and on a half-line is pointed out. We use the heat equation method and show that on the half-line in addition to the usual initial data a new arbitrary function (external source) occurs that we call the daemon function. The daemon function governs the evolution of the universe similar to Maxwell's demon in thermodynamics. The universe and multiverse are open systems interacting with the daemon environment. In the simplest case the nonlocal scalar field reduces to the usual local scalar field coupled with an external source which is discussed in the stochastic approach to inflation. The daemon source can help to get the chaotic inflation scenario with a small scalar field.
Weinstein, M
2003-11-19
This paper discusses the problem of inflation in the context of Friedmann-Robertson-Walker Cosmology. We show how, after a simple change of variables, one can quantize the problem in a way which parallels the classical discussion. The result is that two of the Einstein equations arise as exact equations of motion; one of the usual Einstein equations (suitably quantized) survives as a constraint equation to be imposed on the space of physical states. However, the Friedmann equation, which is also a constraint equation and which is the basis of the Wheeler-DeWitt equation, acquires a welcome quantum correction that becomes significant for small scale factors. We then discuss the extension of this result to a full quantum mechanical derivation of the anisotropy ({delta}{rho}/{rho}) in the cosmic microwave background radiation and the possibility that the extra term in the Friedmann equation could have observable consequences. Finally, we suggest interesting ways in which these techniques can be generalized to cast light on the question of chaotic or eternal inflation. In particular, we suggest that one can put an experimental bound on how far away a universe with a scale factor very different from our own must be, by looking at its effects on our CMB radiation.
NASA Astrophysics Data System (ADS)
Tipler, Frank J.
1996-09-01
I show that if Newtonian gravity is formulated in geometrical language, then Newtonian cosmology is as rigorous as relativistic cosmology. In homogeneous and isotropic universes, the geodesic deviation equation in Newtonian cosmology is proven to be exactly the same as the geodesic deviation equation in relativistic Friedmann cosmologies. This equation can be integrated to yield a constraint equation formally identical to the Friedmann equation. However, Newtonian cosmology is more general than Friedmann cosmology: by generalizing the flat-space Newtonian gravity force law to Riemannian metrics, I show that ever-expanding and recollapsing universes are allowed in any homogeneous and isotropic spatial geometry.
Triangulation of communication skills in qualitative research instruments.
Begley, C M
1996-10-01
Triangulation is a credible and useful method of conducting research which can result in an increase in both quality and quantity of data gathered. The five documented types of triangulation (data, investigator, theoretical, methodological, unit of analysis) do not completely answer all the needs of nurse researchers, particularly in the field of qualitative research. Using more than one method of data collection from within the same research tradition (within-method triangulation) is an accepted and effective technique. Extending the concept of triangulation to include the development of research tools leads to the proposal that the conscious use of two or three types of communication within each qualitative research instrument would improve its effectiveness over a tool which used only one type. This application of 'triangulation of communication skills' is considered within each of the major qualitative research tools, and the benefits outlined. The implications for nursing research and nurse researchers of consciously using non-verbal cues to supplement verbal information are described. It is suggested that using triangulation of communication skills in this way may improve the validity of data obtained and, if clearly documented, increase the credibility of the findings. In particular, when conducting qualitative interviews, the expert use of triangulation of communication skills will enhance the quality and quantity of data gathered. To this end, novice researchers need education and practice in using communication skills to best effect, in order to ensure the validity and completeness of their findings.
Incremental triangulation by way of edge swapping and local optimization
NASA Technical Reports Server (NTRS)
Wiltberger, N. Lyn
1994-01-01
This document is intended to serve as an installation, usage, and basic theory guide for the two dimensional triangulation software 'HARLEY' written for the Silicon Graphics IRIS workstation. This code consists of an incremental triangulation algorithm based on point insertion and local edge swapping. Using this basic strategy, several types of triangulations can be produced depending on user selected options. For example, local edge swapping criteria can be chosen which minimizes the maximum interior angle (a MinMax triangulation) or which maximizes the minimum interior angle (a MaxMin or Delaunay triangulation). It should be noted that the MinMax triangulation is generally only locally optical (not globally optimal) in this measure. The MaxMin triangulation, however, is both locally and globally optical. In addition, Steiner triangulations can be constructed by inserting new sites at triangle circumcenters followed by edge swapping based on the MaxMin criteria. Incremental insertion of sites also provides flexibility in choosing cell refinement criteria. A dynamic heap structure has been implemented in the code so that once a refinement measure is specified (i.e., maximum aspect ratio or some measure of a solution gradient for the solution adaptive grid generation) the cell with the largest value of this measure is continually removed from the top of the heap and refined. The heap refinement strategy allows the user to specify either the number of cells desired or refine the mesh until all cell refinement measures satisfy a user specified tolerance level. Since the dynamic heap structure is constantly updated, the algorithm always refines the particular cell in the mesh with the largest refinement criteria value. The code allows the user to: triangulate a cloud of prespecified points (sites), triangulate a set of prespecified interior points constrained by prespecified boundary curve(s), Steiner triangulate the interior/exterior of prespecified boundary curve
Triangulation algorithms for the representation of molecular surface properties
NASA Astrophysics Data System (ADS)
Heiden, Wolfgang; Schlenkrich, Michael; Brickmann, Jürgen
1990-09-01
A triangulation algorithm for a dotted surface (i.e. a surface defined by point coordinates in three dimensions) is given. The individual triangles are generated on the basis of a hierarchy of strategies according to increasing surface complexity. While for small molecules an elementary algorithm is sufficient to triangulate the surface, large molecules-like proteins-generally need all steps of the hierarchy. Although this program has been developed with the aim of triangulating molecular surfaces, it can in principle be applied to any surface defined by 3D point coordinates.
Onomatopoeia characters extraction from comic images using constrained Delaunay triangulation
NASA Astrophysics Data System (ADS)
Liu, Xiangping; Shoji, Kenji; Mori, Hiroshi; Toyama, Fubito
2014-02-01
A method for extracting onomatopoeia characters from comic images was developed based on stroke width feature of characters, since they nearly have a constant stroke width in a number of cases. An image was segmented with a constrained Delaunay triangulation. Connected component grouping was performed based on the triangles generated by the constrained Delaunay triangulation. Stroke width calculation of the connected components was conducted based on the altitude of the triangles generated with the constrained Delaunay triangulation. The experimental results proved the effectiveness of the proposed method.
An advancing front Delaunay triangulation algorithm designed for robustness
NASA Technical Reports Server (NTRS)
Mavriplis, D. J.
1993-01-01
A new algorithm is described for generating an unstructured mesh about an arbitrary two-dimensional configuration. Mesh points are generated automatically by the algorithm in a manner which ensures a smooth variation of elements, and the resulting triangulation constitutes the Delaunay triangulation of these points. The algorithm combines the mathematical elegance and efficiency of Delaunay triangulation algorithms with the desirable point placement features, boundary integrity, and robustness traditionally associated with advancing-front-type mesh generation strategies. The method offers increased robustness over previous algorithms in that it cannot fail regardless of the initial boundary point distribution and the prescribed cell size distribution throughout the flow-field.
An advancing front Delaunay triangulation algorithm designed for robustness
NASA Technical Reports Server (NTRS)
Mavriplis, D. J.
1992-01-01
A new algorithm is described for generating an unstructured mesh about an arbitrary two-dimensional configuration. Mesh points are generated automatically by the algorithm in a manner which ensures a smooth variation of elements, and the resulting triangulation constitutes the Delaunay triangulation of these points. The algorithm combines the mathematical elegance and efficiency of Delaunay triangulation algorithms with the desirable point placement features, boundary integrity, and robustness traditionally associated with advancing-front-type mesh generation strategies. The method offers increased robustness over previous algorithms in that it cannot fail regardless of the initial boundary point distribution and the prescribed cell size distribution throughout the flow-field.
Degravitation, inflation and the cosmological constant as an afterglow
NASA Astrophysics Data System (ADS)
Patil, Subodh P.
2009-01-01
In this report, we adopt the phenomenological approach of taking the degravitation paradigm seriously as a consistent modification of gravity in the IR, and investigate its consequences for various cosmological situations. We motivate degravitation — where Netwon's constant is promoted to a scale dependent filter function — as arising from either a small (resonant) mass for the graviton, or as an effect in semi-classical gravity. After addressing how the Bianchi identities are to be satisfied in such a set up, we turn our attention towards the cosmological consequences of degravitation. By considering the example filter function corresponding to a resonantly massive graviton (with a filter scale larger than the present horizon scale), we show that slow roll inflation, hybrid inflation and old inflation remain quantitatively unchanged. We also find that the degravitation mechanism inherits a memory of past energy densities in the present epoch in such a way that is likely significant for present cosmological evolution. For example, if the universe underwent inflation in the past due to it having tunneled out of some false vacuum, we find that degravitation implies a remnant `afterglow' cosmological constant, whose scale immediately afterwards is parametrically suppressed by the filter scale (L) in Planck units Λ ~ l2pl/L2. We discuss circumstances through which this scenario reasonably yields the presently observed value for Λ ~ O(10-120). We also find that in a universe still currently trapped in some false vacuum state, resonance graviton models of degravitation only degravitate initially Planck or GUT scale energy densities down to the presently observed value over timescales comparable to the filter scale. We argue that different functional forms for the filter function will yield similar conclusions. In this way, we argue that although the degravitation models we study have the potential to explain why the cosmological constant is not large in addition to
Exact solutions of the Bianchi types V and IX via time-dependent quasi-Maxwell equations
NASA Astrophysics Data System (ADS)
Yavari, Morteza
2014-02-01
The exact solutions of the Einstein field equations for the Bianchi types V and IX in presence of a perfect fluid via the time-dependent quasi-Maxwell (TQM) equations are investigated by using the threading formalism.
Matter and dynamics in closed cosmologies
NASA Astrophysics Data System (ADS)
Heinzle, J. Mark; Röhr, Niklas; Uggla, Claes
2005-04-01
To systematically analyze the dynamical implications of the matter content in cosmology, we generalize earlier dynamical systems approaches so that perfect fluids with a general barotropic equation of state can be treated. We focus on locally rotationally symmetric Bianchi type IX and Kantowski-Sachs orthogonal perfect fluid models, since such models exhibit a particularly rich dynamical structure and also illustrate typical features of more general cases. For these models, we recast Einstein’s field equations into a regular system on a compact state space, which is the basis for our analysis. We prove that models expand from a singularity and recollapse to a singularity when the perfect fluid satisfies the strong energy condition. When the matter source admits Einstein’s static model, we present a comprehensive dynamical description, which includes the qualitative asymptotic behavior, of models in the neighborhood of the Einstein model; the results refute earlier claims about “homoclinic phenomena and chaos.” We also discuss aspects of the global dynamics of models; in particular, we give criteria for the collapse to a singularity, and we describe when models expand forever to a state of infinite dilution; possible initial and final states are analyzed. Numerical investigations complement the analytical results.
NASA Astrophysics Data System (ADS)
Gasperini, Maurizio
2011-03-01
Preface; Acknowledgements; Notation, units and conventions; 1. A short review of standard and inflationary cosmology; 2. The basic string cosmology equations; 3. Conformal invariance and string effective action; 4. Duality symmetries and cosmological solutions; 5. Inflationary kinematics; 6. The string phase; 7. The cosmic background of relic gravitational waves; 8. Scalar perturbations and the anisotropy of the CMB radiation; 9. Dilaton phenomenology; 10. Elements of brane cosmology; Index.
NASA Technical Reports Server (NTRS)
Bradas, James C.; Fennelly, Alphonsus J.; Smalley, Larry L.
1987-01-01
It is shown that a generalized (or 'power law') inflationary phase arises naturally and inevitably in a simple (Bianchi type-I) anisotropic cosmological model in the self-consistent Einstein-Cartan gravitation theory with the improved stress-energy-momentum tensor with the spin density of Ray and Smalley (1982, 1983). This is made explicit by an analytical solution of the field equations of motion of the fluid variables. The inflation is caused by the angular kinetic energy density due to spin. The model further elucidates the relationship between fluid vorticity, the angular velocity of the inertially dragged tetrads, and the precession of the principal axes of the shear ellipsoid. Shear is not effective in damping the inflation.
NASA Technical Reports Server (NTRS)
Bradas, James C.; Fennelly, Alphonsus J.; Smalley, Larry L.
1987-01-01
It is shown that a generalized (or 'power law') inflationary phase arises naturally and inevitably in a simple (Bianchi type-I) anisotropic cosmological model in the self-consistent Einstein-Cartan gravitation theory with the improved stress-energy-momentum tensor with the spin density of Ray and Smalley (1982, 1983). This is made explicit by an analytical solution of the field equations of motion of the fluid variables. The inflation is caused by the angular kinetic energy density due to spin. The model further elucidates the relationship between fluid vorticity, the angular velocity of the inertially dragged tetrads, and the precession of the principal axes of the shear ellipsoid. Shear is not effective in damping the inflation.
Surface Triangulation for CSG in Mercury
Engel, Daniel; O'Brien, Matthew J.
2015-08-26
Visualization routines for rendering complicated geometries are very useful for engineers and scientists who are trying to build 3D prototypes of their designs. A common way to rapidly add interesting features to a 3D model is through the use of a concept called Constructive Solid Geometry. CSG uses compositions of the boolean set operations to manipulate basic geometric primitives to form more complicated objects. The most common boolean operations employed are union, intersection, and subtraction. Most computer-aided design software packages contain some sort of ability visualize CSG. The typical workflow for the user is as follows: The user specifies the individual primitive components, the user arbitrarily combines each of these primitives with boolean operations, the software generates a CSG tree structure which normally stores these solids implicitly with their defining equation, the tree is traversed and a general algorithm is applied to render the appropriate geometry onto the screen. Algorithms for visualizing CSG have been extensively developed for over a decade. Points sampled from the implicit solids are typically used as input by variations of algorithms like marching cubes and point-cloud surface reconstruction. Here, we explain a surface triangulation method from the graphics community that is being used for surface visualization in the framework of a Monte-Carlo neutron transport code called Mercury.
Rail profile control using laser triangulation scanners
NASA Astrophysics Data System (ADS)
Boronahin, Ð. ńlexandr M.; Larionov, Daniil Yu.; Podgornaya, Liudmila N.; Shalymov, Roman V.; Filatov, Yuri V.; Bokhman, Evgueny D.
2016-11-01
Rail track geometric parameters measurement requires knowledge of left and right rail head location in each section. First of all displacement in transverse plane of rail head point located at a distance of 14 mm below the running surface, must be controlled [1]. It is carried out by detecting of each rail profile using triangulation laser scanners. Optical image recognition is carried out successfully in the laboratory, approaches used for this purpose are widely known. However, laser scanners operation has several features on railways leading to necessity of traditional approaches adaptation for solving these particular problems. The most significant problem is images noisiness due to the solar flashes and the effect of "Moon path" on the smooth rail surface. Using of optical filters gives inadequate result, because scanner laser diodes radiation frequency varies with temperature changes that forbid the use of narrow-band filters. Consideration of these features requires additional constructive and algorithmic solutions, including involvement of information from other sensors of the system. The specific usage of optical scanners for rail profiles control is the subject of the paper.
Blind guidance system based on laser triangulation
NASA Astrophysics Data System (ADS)
Wu, Jih-Huah; Wang, Jinner-Der; Fang, Wei; Lee, Yun-Parn; Shan, Yi-Chia; Kao, Hai-Ko; Ma, Shih-Hsin; Jiang, Joe-Air
2012-05-01
We propose a new guidance system for the blind. An optical triangulation method is used in the system. The main components of the proposed system comprise of a notebook computer, a camera, and two laser modules. The track image of the light beam on the ground or on the object is captured by the camera and then the image is sent to the notebook computer for further processing and analysis. Using a developed signal-processing algorithm, our system can determine the object width and the distance between the object and the blind person through the calculation of the light line positions on the image. A series of feasibility tests of the developed blind guidance system were conducted. The experimental results show that the distance between the test object and the blind can be measured with a standard deviation of less than 8.5% within the range of 40 and 130 cm, while the test object width can be measured with a standard deviation of less than 4.5% within the range of 40 and 130 cm. The application potential of the designed system to the blind guidance can be expected.
The ising model on the dynamical triangulated random surface
Aleinov, I.D.; Migelal, A.A.; Zmushkow, U.V. )
1990-04-20
The critical properties of Ising model on the dynamical triangulated random surface embedded in D-dimensional Euclidean space are investigated. The strong coupling expansion method is used. The transition to thermodynamical limit is performed by means of continuous fractions.
Examining laser triangulation system performance using a software simulation
NASA Astrophysics Data System (ADS)
Collier, Jeffery S.; Nurre, Joseph H.
1999-03-01
The invention of the laser diode, the microcomputer and the CCD camera have made possible the new technology of triangulation measurement systems. Current applications range from scanning the insides of old pipes, to a vision tool for the blind. As such, it is important that techniques be developed to minimize the error in laser triangulation measurement systems. Due to the nonlinear nature of the problem and the fact that error is dependent on an ever changing and vast number of subjects, a computer simulation was written to examine the trade-off between occlusion and data quality. A computer simulation allows for a large amount of flexibility. The software gives the user the ability to calculate the error for a given triangulation configuration without having to build and test the actual hardware. This paper describes and demonstrates the use of the simulator. Limitless laser triangulation systems can be modeled and most subjects represented in CAD files can be used in the computer simulation.
Position and orientation inference via on-board triangulation.
Advani, Madhu; Weile, Daniel S
2017-01-01
This work proposes a new approach to determine the spatial location and orientation of an object using measurements performed on the object itself. The on-board triangulation algorithm we outline could be implemented in lieu of, or in addition to, well-known alternatives such as Global Positioning System (GPS) or standard triangulation, since both of these correspond to significantly different geometric pictures and necessitate different hardware and algorithms. We motivate the theory by describing situations in which on-board triangulation would be useful and even preferable to standard methods. The on-board triangulation algorithm we outline involves utilizing dumb beacons which broadcast omnidirectional single frequency radio waves, and smart antenna arrays on the object itself to infer the direction of the beacon signals, which may be used for onboard calculation of the position and orientation of the object. Numerical examples demonstrate the utility of the method and its noise tolerance.
Position and orientation inference via on-board triangulation
Advani, Madhu
2017-01-01
This work proposes a new approach to determine the spatial location and orientation of an object using measurements performed on the object itself. The on-board triangulation algorithm we outline could be implemented in lieu of, or in addition to, well-known alternatives such as Global Positioning System (GPS) or standard triangulation, since both of these correspond to significantly different geometric pictures and necessitate different hardware and algorithms. We motivate the theory by describing situations in which on-board triangulation would be useful and even preferable to standard methods. The on-board triangulation algorithm we outline involves utilizing dumb beacons which broadcast omnidirectional single frequency radio waves, and smart antenna arrays on the object itself to infer the direction of the beacon signals, which may be used for onboard calculation of the position and orientation of the object. Numerical examples demonstrate the utility of the method and its noise tolerance. PMID:28644874
On the viability of the truncated Israel-Stewart theory in cosmology
NASA Astrophysics Data System (ADS)
Shogin, Dmitry; Amund Amundsen, Per; Hervik, Sigbjørn
2015-10-01
We apply the causal Israel-Stewart theory of irreversible thermodynamics to model the matter content of the Universe as a dissipative fluid with bulk and shear viscosity. Along with the full transport equations we consider their widely used truncated version. By implementing a dynamical systems approach to Bianchi type IV and V cosmological models with and without cosmological constant, we determine the future asymptotic states of such Universes and show that the truncated Israel-Stewart theory leads to solutions essentially different from the full theory. The solutions of the truncated theory may also manifest unphysical properties. Finally, we find that in the full theory shear viscosity can give a substantial rise to dissipative fluxes, driving the fluid extremely far from equilibrium, where the linear Israel-Stewart theory ceases to be valid.
Simulations of four-dimensional simplicial quantum gravity as dynamical triangulation
Agishtein, M.E.; Migdal, A.A. )
1992-04-20
In this paper, Four-Dimensional Simplicial Quantum Gravity is simulated using the dynamical triangulation approach. The authors studied simplicial manifolds of spherical topology and found the critical line for the cosmological constant as a function of the gravitational one, separating the phases of opened and closed Universe. When the bare cosmological constant approaches this line from above, the four-volume grows: the authors reached about 5 {times} 10{sup 4} simplexes, which proved to be sufficient for the statistical limit of infinite volume. However, for the genuine continuum theory of gravity, the parameters of the lattice model should be further adjusted to reach the second order phase transition point, where the correlation length grows to infinity. The authors varied the gravitational constant, and they found the first order phase transition, similar to the one found in three-dimensional model, except in 4D the fluctuations are rather large at the transition point, so that this is close to the second order phase transition. The average curvature in cutoff units is large and positive in one phase (gravity), and small negative in another (antigravity). The authors studied the fractal geometry of both phases, using the heavy particle propagator to define the geodesic map, as well as with the old approach using the shortest lattice paths.
On triangulations of the plane by pencils of conics. II
Lazareva, V B; Shelekhov, A M
2013-06-30
The present work continues our previous paper in which all possible triangulations of the plane using three pencils of circles were listed. In the present article we find all projectively distinct triangulations of the plane by pencils of conics that are obtained by projecting regular three-webs, cut out on a nondegenerate cubic surface by three pencils of planes, whose axes lie on this surface. Bibliography: 6 titles.
Yet another method for triangulation and contouring for automated cartography
NASA Technical Reports Server (NTRS)
De Floriani, L.; Falcidieno, B.; Nasy, G.; Pienovi, C.
1982-01-01
An algorithm is presented for hierarchical subdivision of a set of three-dimensional surface observations. The data structure used for obtaining the desired triangulation is also singularly appropriate for extracting contours. Some examples are presented, and the results obtained are compared with those given by Delaunay triangulation. The data points selected by the algorithm provide a better approximation to the desired surface than do randomly selected points.
Yet another method for triangulation and contouring for automated cartography
NASA Technical Reports Server (NTRS)
De Floriani, L.; Falcidieno, B.; Nasy, G.; Pienovi, C.
1982-01-01
An algorithm is presented for hierarchical subdivision of a set of three-dimensional surface observations. The data structure used for obtaining the desired triangulation is also singularly appropriate for extracting contours. Some examples are presented, and the results obtained are compared with those given by Delaunay triangulation. The data points selected by the algorithm provide a better approximation to the desired surface than do randomly selected points.
NASA Astrophysics Data System (ADS)
Chamcham, Khalil; Silk, Joseph; Barrow, John D.; Saunders, Simon
2017-04-01
Part I. Issues in the Philosophy of Cosmology: 1. Cosmology, cosmologia and the testing of cosmological theories George F. R. Ellis; 2. Black holes, cosmology and the passage of time: three problems at the limits of science Bernard Carr; 3. Moving boundaries? – comments on the relationship between philosophy and cosmology Claus Beisbart; 4. On the question why there exists something rather than nothing Roderich Tumulka; Part II. Structures in the Universe and the Structure of Modern Cosmology: 5. Some generalities about generality John D. Barrow; 6. Emergent structures of effective field theories Jean-Philippe Uzan; 7. Cosmological structure formation Joel R. Primack; 8. Formation of galaxies Joseph Silk; Part III. Foundations of Cosmology: Gravity and the Quantum: 9. The observer strikes back James Hartle and Thomas Hertog; 10. Testing inflation Chris Smeenk; 11. Why Boltzmann brains do not fluctuate into existence from the de Sitter vacuum Kimberly K. Boddy, Sean M. Carroll and Jason Pollack; 12. Holographic inflation revised Tom Banks; 13. Progress and gravity: overcoming divisions between general relativity and particle physics and between physics and HPS J. Brian Pitts; Part IV. Quantum Foundations and Quantum Gravity: 14. Is time's arrow perspectival? Carlo Rovelli; 15. Relational quantum cosmology Francesca Vidotto; 16. Cosmological ontology and epistemology Don N. Page; 17. Quantum origin of cosmological structure and dynamical reduction theories Daniel Sudarsky; 18. Towards a novel approach to semi-classical gravity Ward Struyve; Part V. Methodological and Philosophical Issues: 19. Limits of time in cosmology Svend E. Rugh and Henrik Zinkernagel; 20. Self-locating priors and cosmological measures Cian Dorr and Frank Arntzenius; 21. On probability and cosmology: inference beyond data? Martin Sahlén; 22. Testing the multiverse: Bayes, fine-tuning and typicality Luke A. Barnes; 23. A new perspective on Einstein's philosophy of cosmology Cormac O
Algebraic Error Based Triangulation and Metric of Lines.
Wu, Fuchao; Zhang, Ming; Wang, Guanghui; Hu, Zhanyi
2015-01-01
Line triangulation, a classical geometric problem in computer vision, is to determine the 3D coordinates of a line based on its 2D image projections from more than two views of cameras with known projection matrices. Compared to point features, line segments are more robust to matching errors, occlusions, and image uncertainties. In addition to line triangulation, a better metric is needed to evaluate 3D errors of line triangulation. In this paper, the line triangulation problem is investigated by using the Lagrange multipliers theory. The main contributions include: (i) Based on the Lagrange multipliers theory, a formula to compute the Plücker correction is provided, and from the formula, a new linear algorithm, LINa, is proposed for line triangulation; (ii) two optimal algorithms, OPTa-I and OPTa-II, are proposed by minimizing the algebraic error; and (iii) two metrics on 3D line space, the orthogonal metric and the quasi-Riemannian metric, are introduced for the evaluation of line triangulations. Extensive experiments on synthetic data and real images are carried out to validate and demonstrate the effectiveness of the proposed algorithms.
Algebraic Error Based Triangulation and Metric of Lines
Wu, Fuchao; Zhang, Ming; Wang, Guanghui; Hu, Zhanyi
2015-01-01
Line triangulation, a classical geometric problem in computer vision, is to determine the 3D coordinates of a line based on its 2D image projections from more than two views of cameras with known projection matrices. Compared to point features, line segments are more robust to matching errors, occlusions, and image uncertainties. In addition to line triangulation, a better metric is needed to evaluate 3D errors of line triangulation. In this paper, the line triangulation problem is investigated by using the Lagrange multipliers theory. The main contributions include: (i) Based on the Lagrange multipliers theory, a formula to compute the Plücker correction is provided, and from the formula, a new linear algorithm, LINa, is proposed for line triangulation; (ii) two optimal algorithms, OPTa-I and OPTa-II, are proposed by minimizing the algebraic error; and (iii) two metrics on 3D line space, the orthogonal metric and the quasi-Riemannian metric, are introduced for the evaluation of line triangulations. Extensive experiments on synthetic data and real images are carried out to validate and demonstrate the effectiveness of the proposed algorithms. PMID:26218615
Philosophical Roots of Cosmology
NASA Astrophysics Data System (ADS)
Ivanovic, M.
2008-10-01
We shall consider the philosophical roots of cosmology in the earlier Greek philosophy. Our goal is to answer the question: Are earlier Greek theories of pure philosophical-mythological character, as often philosophers cited it, or they have scientific character. On the bases of methodological criteria, we shall contend that the latter is the case. In order to answer the question about contemporary situation of the relation philosophy-cosmology, we shall consider the next question: Is contemporary cosmology completely independent of philosophical conjectures? The answer demands consideration of methodological character about scientific status of contemporary cosmology. We also consider some aspects of the relation contemporary philosophy-cosmology.
Analytic self-gravitating Skyrmions, cosmological bounces and AdS wormholes
NASA Astrophysics Data System (ADS)
Ayón-Beato, Eloy; Canfora, Fabrizio; Zanelli, Jorge
2016-01-01
We present a self-gravitating, analytic and globally regular Skyrmion solution of the Einstein-Skyrme system with winding number w = ± 1, in presence of a cosmological constant. The static spacetime metric is the direct product R ×S3 and the Skyrmion is the self-gravitating generalization of the static hedgehog solution of Manton and Ruback with unit topological charge. This solution can be promoted to a dynamical one in which the spacetime is a cosmology of the Bianchi type-IX with time-dependent scale and squashing coefficients. Remarkably, the Skyrme equations are still identically satisfied for all values of these parameters. Thus, the complete set of field equations for the Einstein-Skyrme-Λ system in the topological sector reduces to a pair of coupled, autonomous, nonlinear differential equations for the scale factor and a squashing coefficient. These equations admit analytic bouncing cosmological solutions in which the universe contracts to a minimum non-vanishing size, and then expands. A non-trivial byproduct of this solution is that a minor modification of the construction gives rise to a family of stationary, regular configurations in General Relativity with negative cosmological constant supported by an SU (2) nonlinear sigma model. These solutions represent traversable AdS wormholes with NUT parameter in which the only "exotic matter" required for their construction is a negative cosmological constant.
NASA Astrophysics Data System (ADS)
Tipler, Frank J.
1996-10-01
It is generally believed that it is not possible to rigorously analyze a homogeneous and isotropic cosmological model in Newtonian mechanics. I show on the contrary that if Newtonian gravity theory is rewritten in geometrical language in the manner outlined in 1923-1924 by Élie Cartan [Ann. Ecole Norm. Sup. 40, 325-412 (1923); 41, 1-25 (1924)], then Newtonian cosmology is as rigorous as Friedmann cosmology. In particular, I show that the equation of geodesic deviation in Newtonian cosmology is exactly the same as equation of geodesic deviation in the Friedmann universe, and that this equation can be integrated to yield a constraint equation formally identical to the Friedmann equation. However, Newtonian cosmology is more general than Friedmann cosmology: Ever-expanding and recollapsing universes are allowed in any noncompact homogeneous and isotropic spatial topology. I shall give a brief history of attempts to do cosmology in the framework of Newtonian mechanics.
A note on tilted Bianchi type VIh models: the type III bifurcation
NASA Astrophysics Data System (ADS)
Coley, A. A.; Hervik, S.
2008-10-01
In this note we complete the analysis of Hervik, van den Hoogen, Lim and Coley (2007 Class. Quantum Grav. 24 3859) of the late-time behaviour of tilted perfect fluid Bianchi type III models. We consider models with dust, and perfect fluids stiffer than dust, and eludicate the late-time behaviour by studying the centre manifold which dominates the behaviour of the model at late times. In the dust case, this centre manifold is three-dimensional and can be considered a double bifurcation as the two parameters (h and γ) of the type VIh model are varied. We therefore complete the analysis of the late-time behaviour of tilted ever-expanding Bianchi models of types I VIII.
TRIANGULATION OF THE INTERSTELLAR MAGNETIC FIELD
Schwadron, N. A.; Moebius, E.; Richardson, J. D.; Burlaga, L. F.; McComas, D. J.
2015-11-01
Determining the direction of the local interstellar magnetic field (LISMF) is important for understanding the heliosphere’s global structure, the properties of the interstellar medium, and the propagation of cosmic rays in the local galactic medium. Measurements of interstellar neutral atoms by Ulysses for He and by SOHO/SWAN for H provided some of the first observational insights into the LISMF direction. Because secondary neutral H is partially deflected by the interstellar flow in the outer heliosheath and this deflection is influenced by the LISMF, the relative deflection of H versus He provides a plane—the so-called B–V plane in which the LISMF direction should lie. Interstellar Boundary Explorer (IBEX) subsequently discovered a ribbon, the center of which is conjectured to be the LISMF direction. The most recent He velocity measurements from IBEX and those from Ulysses yield a B–V plane with uncertainty limits that contain the centers of the IBEX ribbon at 0.7–2.7 keV. The possibility that Voyager 1 has moved into the outer heliosheath now suggests that Voyager 1's direct observations provide another independent determination of the LISMF. We show that LISMF direction measured by Voyager 1 is >40° off from the IBEX ribbon center and the B–V plane. Taking into account the temporal gradient of the field direction measured by Voyager 1, we extrapolate to a field direction that passes directly through the IBEX ribbon center (0.7–2.7 keV) and the B–V plane, allowing us to triangulate the LISMF direction and estimate the gradient scale size of the magnetic field.
The Relativistic Boltzmann Equation on Bianchi Type I Space Time for Hard Potentials
NASA Astrophysics Data System (ADS)
Noutchegueme, Norbert; Takou, Etienne; Tchuengue, E. Kamdem
2017-08-01
In this paper, we consider the Cauchy problem for the spatially homogeneous relativistic Boltzmann equation with small initial data. The collision kernel considered here is for a hard potentials case. The background space-time in which the study is done is the Bianchi type I space-time. Under certain conditions made on the scattering kernel and on the metric, a uniqueness global (in time) solution is obtained in a suitable weighted functional space.
NASA Astrophysics Data System (ADS)
Bojowald, Martin
The universe, ultimately, is to be described by quantum theory. Quantum aspects of all there is, including space and time, may not be significant for many purposes, but are crucial for some. And so a quantum description of cosmology is required for a complete and consistent worldview. At any rate, even if we were not directly interested in regimes where quantum cosmology plays a role, a complete physical description could not stop at a stage before the whole universe is reached. Quantum theory is essential in the microphysics of particles, atoms, molecules, solids, white dwarfs and neutron stars. Why should one expect this ladder of scales to end at a certain size? If regimes are sufficiently violent and energetic, quantum effects are non-negligible even on scales of the whole cosmos; this is realized at least once in the history of the universe: at the big bang where the classical theory of general relativity would make energy densities diverge.
Laser triangulation measurements of scoliotic spine curvatures.
Čelan, Dušan; Jesenšek Papež, Breda; Poredoš, Primož; Možina, Janez
2015-01-01
The main purpose of this research was to develop a new method for differentiating between scoliotic and healthy subjects by analysing the curvatures of their spines in the cranio-caudal view. The study included 247 subjects with physiological curvatures of the spine and 28 subjects with clinically confirmed scoliosis. The curvature of the spine was determined by a computer analysis of the surface of the back, measured with a non-invasive, 3D, laser-triangulation system. The determined spinal curve was represented in the transversal plane, which is perpendicular to the line segment that was defined by the initial point and the end point of the spinal curve. This was achieved using a rotation matrix. The distances between the extreme points in the antero-posterior (AP) and left-right (LR) views were calculated in relation to the length of the spine as well as the quotient of these two values LR/AP. All the measured parameters were compared between the scoliotic and control groups using the Student's t-Test in case of normal data and Kruskal-Wallis test in case of non-normal data. Besides, a comprehensive diagram representing the distances between the extreme points in the AP and LR views was introduced, which clearly demonstrated the direction and the size of the thoracic and lumbar spinal curvatures for each individual subject. While the distances between the extreme points of the spine in the AP view were found to differ only slightly between the groups (p = 0.1), the distances between the LR extreme points were found to be significantly greater in the scoliosis group, compared to the control group (p < 0.001). The quotient LR/AP was statistically significantly different in both groups (p < 0.001). The main innovation of the presented method is the ability to differentiate a scoliotic subject from a healthy subject by assessing the curvature of the spine in the cranio-caudal view. Therefore, the proposed method could be useful for human posture
Measurement Uncertainty of Microscopic Laser Triangulation on Technical Surfaces.
Mueller, Thomas; Poesch, Andreas; Reithmeier, Eduard
2015-12-01
Laser triangulation is widely used to measure three-dimensional structure of surfaces. The technique is suitable for macroscopic and microscopic surface measurements. In this paper, the measurement uncertainty of laser triangulation is investigated on technical surfaces for microscopic measurement applications. Properties of technical surfaces are, for example, reflectivity, surface roughness, and the presence of scratches and pores. These properties are more influential in the microscopic laser triangulation than in the macroscopic one. In the Introduction section of this paper, the measurement uncertainty of laser triangulation is experimentally investigated for 13 different specimens. The measurements were carried out with and without a laser speckle reducer. In the Materials and Methods section of this paper, the surfaces of the 13 specimens are characterized in order to be able to find correlations between the surface properties and the measurement uncertainty. The last section of this paper describes simulations of the measurement uncertainty, which allow for the calculation of the measurement uncertainty with only one source of uncertainty present. The considerations in this paper allow for the assessment of the measurement uncertainty of laser triangulation on any technical surface when some surface properties, such as roughness, are known.
Wong, Yvonne Y. Y.
2008-01-24
I give an overview of the effects of neutrinos on cosmology, focussing in particular on the role played by neutrinos in the evolution of cosmological perturbations. I discuss how recent observations of the cosmic microwave background and the large-scale structure of galaxies can probe neutrino masses with greater precision than current laboratory experiments. I describe several new techniques that will be used to probe cosmology in the future.
Two-point correlation functions in inhomogeneous and anisotropic cosmologies
NASA Astrophysics Data System (ADS)
Marcori, Oton H.; Pereira, Thiago S.
2017-02-01
Two-point correlation functions are ubiquitous tools of modern cosmology, appearing in disparate topics ranging from cosmological inflation to late-time astrophysics. When the background spacetime is maximally symmetric, invariance arguments can be used to fix the functional dependence of this function as the invariant distance between any two points. In this paper we introduce a novel formalism which fixes this functional dependence directly from the isometries of the background metric, thus allowing one to quickly assess the overall features of Gaussian correlators without resorting to the full machinery of perturbation theory. As an application we construct the CMB temperature correlation function in one inhomogeneous (namely, an off-center LTB model) and two spatially flat and anisotropic (Bianchi) universes, and derive their covariance matrices in the limit of almost Friedmannian symmetry. We show how the method can be extended to arbitrary N-point correlation functions and illustrate its use by constructing three-point correlation functions in some simple geometries.
NASA Astrophysics Data System (ADS)
López-Corredoira, M.
2009-08-01
Certain results of observational cosmology cast critical doubt on the foundations of standard cosmology but leave most cosmologists untroubled. Alternative cosmological models that differ from the Big Bang have been published and defended by heterodox scientists; however, most cosmologists do not heed these. This may be because standard theory is correct and all other ideas and criticisms are incorrect, but it is also to a great extent due to sociological phenomena such as the ``snowball effect'' or ``groupthink''. We might wonder whether cosmology, the study of the Universe as a whole, is a science like other branches of physics or just a dominant ideology.
Cosmology and neutrino properties
Dolgov, A. D.
2008-12-15
A brief review for particle physicists on the cosmological impact of neutrinos and on restrictions on neutrino properties from cosmology is given. The paper includes a discussion of upper bounds on neutrino mass and possible ways to relax them, methods to observe the cosmic-neutrino background, bounds on the cosmological lepton asymmetry which are strongly improved by neutrino oscillations, cosmological effects of breaking of the spin-statistics theorem for neutrinos, bounds on mixing parameters of active and possible sterile neutrinos with account of active-neutrino oscillations, bounds on right-handed currents and neutrino magnetic moments, and some more.
Inherent weaknesses of cosmology
NASA Technical Reports Server (NTRS)
Chiu, H.-Y.
1986-01-01
Sources of astrophysical evidence necessary to verify a cosmological model are reviewed. Cosmological history of the universe is divided into four epochs, each unique in its physical conditions related to observability at present. The current epoch, started after recombination of hydrogen in the universe, offers the most in observability. In earlier epochs, verifiable astrophysical evidence gradually disappeared. It seems that no astrophysical evidence has been left behind from the singularity epoch of the Universe. The gradual disappearance of astrophysical evidence ascertainable at present is the result of physical conditions structured within the cosmological models, hence indicating certain inherent weaknesses of cosmology as a verifiable physical theory.
Analysis of imaging for laser triangulation sensors under Scheimpflug rule.
Miks, Antonin; Novak, Jiri; Novak, Pavel
2013-07-29
In this work a detailed analysis of the problem of imaging of objects lying in the plane tilted with respect to the optical axis of the rotationally symmetrical optical system is performed by means of geometrical optics theory. It is shown that the fulfillment of the so called Scheimpflug condition (Scheimpflug rule) does not guarantee the sharp image of the object as it is usually declared because of the fact that due to the dependence of aberrations of real optical systems on the object distance the image becomes blurred. The f-number of a given optical system also varies with the object distance. It is shown the influence of above mentioned effects on the accuracy of the laser triangulation sensors measurements. A detailed analysis of laser triangulation sensors, based on geometrical optics theory, is performed and relations for the calculation of measurement errors and construction parameters of laser triangulation sensors are derived.
Development of a diffraction-type optical triangulation sensor.
Liu, Chien-Hung; Jywe, Wen-Yuh; Chen, Chao-Kwai
2004-10-20
We propose a diffraction-type optical triangulation sensor based on the diffraction theorem and the laser triangulation method. The advantage of the proposed sensor is that it obtains not only the linear displacement of a moving object but also its three angular motion errors. The developed sensor is composed mainly of a laser source, two quadrant detectors, and a reflective diffraction grating. The reflective diffraction grating can reflect the incident laser beam into several diffractive rays, and two quadrant detectors were set up for detecting the position of 0- and + 1-order diffraction rays. According to the optical triangulation relationship between the spatial incident angles of a laser beam and the output coordinates of two quadrant detectors, the displacement and the three angular motion errors of a moving object can be obtained simultaneously.
Moving sound source localization based on triangulation method
NASA Astrophysics Data System (ADS)
Miao, Feng; Yang, Diange; Wen, Junjie; Lian, Xiaomin
2016-12-01
This study develops a sound source localization method that extends traditional triangulation to moving sources. First, the possible sound source locating plane is scanned. Secondly, for each hypothetical source location in this possible plane, the Doppler effect is removed through the integration of sound pressure. Taking advantage of the de-Dopplerized signals, the moving time difference of arrival (MTDOA) is calculated, and the sound source is located based on triangulation. Thirdly, the estimated sound source location is compared to the original hypothetical location and the deviations are recorded. Because the real sound source location leads to zero deviation, the sound source can be finally located by minimizing the deviation matrix. Simulations have shown the superiority of MTDOA method over traditional triangulation in case of moving sound sources. The MTDOA method can be used to locate moving sound sources with as high resolution as DAMAS beamforming, as shown in the experiments, offering thus a new method for locating moving sound sources.
Cosmological anisotropy from non-comoving dark matter and dark energy
Harko, Tiberiu; Lobo, Francisco S. N. E-mail: flobo@cii.fc.ul.pt
2013-07-01
We consider a cosmological model in which the two major fluid components of the Universe, dark energy and dark matter, flow with distinct four-velocities. This cosmological configuration is equivalent to a single anisotropic fluid, expanding with a four-velocity that is an appropriate combination of the two fluid four-velocities. The energy density of the single cosmological fluid is larger than the sum of the energy densities of the two perfect fluids, i.e., dark energy and dark matter, respectively, and contains a correction term due to the anisotropy generated by the differences in the four-velocities. Furthermore, the gravitational field equations of the two-fluid anisotropic cosmological model are obtained for a Bianchi type I geometry. By assuming that the non-comoving motion of the dark energy and dark matter induces small perturbations in the homogeneous and isotropic Friedmann-Lemaitre-Robertson-Walker type cosmological background, and that the anisotropy parameter is small, the equations of the cosmological perturbations due to the non-comoving nature of the two major components are obtained. The time evolution of the metric perturbations is explicitly obtained for the cases of the exponential and power law background cosmological expansion. The imprints of a non-comoving dark energy - dark matter on the Cosmic Microwave Background and on the luminosity distance are briefly discussed, and the temperature anisotropies and the quadrupole are explicitly obtained in terms of the metric perturbations of the flat background metric. Therefore, if there is a slight difference between the four-velocities of the dark energy and dark matter, the Universe would acquire some anisotropic characteristics, and its geometry will deviate from the standard FLRW one. In fact, the recent Planck results show that the presence of an intrinsic large scale anisotropy in the Universe cannot be excluded a priori, so that the model presented in this work can be considered as a
Research on pavement roughness based on the laser triangulation
NASA Astrophysics Data System (ADS)
Chen, Wenxue; Ni, Zhibin; Hu, Xinhan; Lu, Xiaofeng
2016-06-01
Pavement roughness is one of the most important factors for appraising highway construction. In this paper, we choose the laser triangulation to measure pavement roughness. The principle and configuration of laser triangulation are introduced. Based on this technology, the pavement roughness of a road surface is measured. The measurement results are given in this paper. The measurement range of this system is 50 μm. The measurement error of this technology is analyzed. This technology has an important significance to appraise the quality of highway after completion of the workload.
Laser triangulation for liquid film thickness measurements through multiple interfaces.
Peterson, Jerrod P; Peterson, Richard B
2006-07-10
Laser triangulation is used to measure the thickness of a liquid film in a test section consisting of a quartz viewing window, a water layer, and a hydrophobic membrane. The triangulation sensor acquires measurements to the bounding surfaces of the film while peering through multiple interfaces. This allows the difference between the two measurements to constitute the local film thickness. A refraction model is developed and applied to the analysis of data collected from the experiment. For verification, an empirical method is also developed and compared to the analytical approach. The measurement technique is intended to assess the stability of liquid films for use as gas-liquid contactors.
An efficient advancing front algorithm for Delaunay triangulation
NASA Technical Reports Server (NTRS)
Merriam, Marshal L.
1991-01-01
There has been some recent interest in fluid dynamics calculations on unstructured meshes. One method of unstructured mesh generation involves Delaunay triangulation. This method has certain advantages but it can be expensive to implement. Furthermore, there can be problems with crossing grid lines near boundaries. A method shown here avoids many of the robustness and efficiency problems previously associated with Delaunay triangulation. As an added feature, a simple algorithm is shown which allows removal of diagonal edges from cells that are nearly rectangular. This can result in significant savings in the cost per iteration of a flow solver using this grid.
McAllister, Liam P.; Silverstein, Eva
2007-10-22
We give an overview of the status of string cosmology. We explain the motivation for the subject, outline the main problems, and assess some of the proposed solutions. Our focus is on those aspects of cosmology that benefit from the structure of an ultraviolet-complete theory.
Cosmological Implications of Geometrothermodynamics
NASA Astrophysics Data System (ADS)
Luongo, O.; Quevedo, H.
2015-01-01
We use the formalism of Geometrothermodynamics to derive a series of fundamental equations for thermodynamic systems. It is shown that all these fundamental equations can be used in the context of relativistic cosmology to derive diverse scenarios which include the standard cosmological model, a unified model for dark energy and dark matter, and an effective inflationary model.
Klebanov, I.; Susskind, L.
1988-10-01
We review Coleman's wormhole mechanism for the vanishing of the cosmological constant. We find a discouraging result that wormholes much bigger than the Planck size are generated. We also consider the implications of the wormhole theory for cosmology. 7 refs., 2 figs.
NASA Astrophysics Data System (ADS)
Lusso, Elisabeta
2016-10-01
I will review previous methods that have tried to employ active galactic nuclei to measure cosmological parameters. I will introduce a novel technique able to test the cosmological model using quasars as “standard candles” by employing the non- linear relation between their intrinsic UV and X-ray emission as an absolute distance indicator.
Exploring bouncing cosmologies with cosmological surveys
NASA Astrophysics Data System (ADS)
Cai, Yi-Fu
2014-08-01
From recent observational data two significant directions have been made in the field of theoretical cosmology recently. First, we are now able to make use of present observations, such as the Planck and BICEP2 data, to examine theoretical predictions from the standard inflationary ΛCDM which were made decades of years ago. Second, we can search for new cosmological signatures as a way to explore physics beyond the standard cosmic paradigm. In particular, a subset of early universe models admit a nonsingular bouncing solution that attempts to address the issue of the big bang singularity. These models have achieved a series of considerable developments in recent years, in particular in their perturbative frameworks, which made brand-new predictions of cosmological signatures that could be visible in current and forthcoming observations. Herein we present two representative paradigms of early universe physics. The first is the reputed new matter (or matter-ekpyrotic) bounce scenario in which the universe starts with a matter-dominated contraction phase and transitions into an ekpyrotic phase. In the setting of this paradigm, we have proposed some possible mechanisms of generating a red tilt for primordial curvature perturbations and confront the general predictions with recent cosmological observations. The second is the matter-bounce inflation scenario which can be viewed as an extension of inflationary cosmology with a matter contraction before inflation. We present a class of possible model constructions and review the implications on the current CMB experiments. Lastly a review of significant achievements of these paradigms beyond the inflationary ΛCDM model is made, which is expected to shed new light on the future direction of observational cosmology.
NASA Astrophysics Data System (ADS)
Tseytlin, A. A.; Vafa, C.
1992-03-01
Aspects of string cosmology for critical and non-critical strings are discussed emphasizing the necessity to account for the dilaton dynamics for a proper incorporation of ``large-small'' duality. This drastically modifies the intuition one has with Einstein's gravity. For example winding modes, even though contributing to the energy density, oppose expansion and if not annihilated will stop the expansion. Moreover we find that the radiation dominated era of the standard cosmology emerges quite naturally in string cosmology. Our analysis of non-critical string cosmology provides a reinterpretation of the (universal cover of the) recently studied two-dimensional black hole solution as a conformal realization of cosmological solutions found previously by Mueller. Supported in part by Packard Foundation and NSF grants PHY-89-57162 and PHY-87-14654.
Cosmology and particle physics
NASA Technical Reports Server (NTRS)
Turner, Michael S.
1988-01-01
The interplay between cosmology and elementary particle physics is discussed. The standard cosmology is reviewed, concentrating on primordial nucleosynthesis and discussing how the standard cosmology has been used to place constraints on the properties of various particles. Baryogenesis is discussed, showing how a scenario in which the B-, C-, and CP-violating interactions in GUTs provide a dynamical explanation for the predominance of matter over antimatter and for the present baryon-to-photon ratio. It is shown how the very early dynamical evolution of a very weakly coupled scalar field which is initially displaced from the minimum of its potential may explain a handful of very fundamental cosmological facts which are not explained by the standard cosmology.
Cosmology and particle physics
NASA Technical Reports Server (NTRS)
Turner, Michael S.
1988-01-01
The interplay between cosmology and elementary particle physics is discussed. The standard cosmology is reviewed, concentrating on primordial nucleosynthesis and discussing how the standard cosmology has been used to place constraints on the properties of various particles. Baryogenesis is discussed, showing how a scenario in which the B-, C-, and CP-violating interactions in GUTs provide a dynamical explanation for the predominance of matter over antimatter and for the present baryon-to-photon ratio. It is shown how the very early dynamical evolution of a very weakly coupled scalar field which is initially displaced from the minimum of its potential may explain a handful of very fundamental cosmological facts which are not explained by the standard cosmology.
Testing loop quantum cosmology
NASA Astrophysics Data System (ADS)
Wilson-Ewing, Edward
2017-03-01
Loop quantum cosmology predicts that quantum gravity effects resolve the big-bang singularity and replace it by a cosmic bounce. Furthermore, loop quantum cosmology can also modify the form of primordial cosmological perturbations, for example by reducing power at large scales in inflationary models or by suppressing the tensor-to-scalar ratio in the matter bounce scenario; these two effects are potential observational tests for loop quantum cosmology. In this article, I review these predictions and others, and also briefly discuss three open problems in loop quantum cosmology: its relation to loop quantum gravity, the trans-Planckian problem, and a possible transition from a Lorentzian to a Euclidean space-time around the bounce point.
Revisiting the two formulations of Bianchi identities and their implications on moduli stabilization
NASA Astrophysics Data System (ADS)
Shukla, Pramod
2016-08-01
In the context of non-geometric type II orientifold compactifications, there have been two formulations for representing the various NS-NS Bianchi-identities. In the first formulation, the standard three-form flux ( H 3), the geometric flux ( ω) and the non-geometric fluxes ( Q and R) are expressed by using the real six-dimensional indices (e.g. {H}_{ijk}, {ω_{ij}}^k, {Q_i}{_{jk}} and R ijk ), and this formulation has been heavily utilized for simplifying the scalar potentials in toroidal-orientifolds. On the other hand, relevant for the studies beyond toroidal backgrounds, a second formulation is utilized in which all flux components are written in terms of various involutively even/odd (2 , 1)- and (1 , 1)-cohomologies of the complex threefold. In the lights of recent model building interests and some observations made in [1, 2], in this article, we revisit two most commonly studied toroidal examples in detail to illustrate that the present forms of these two formulations are not completely equivalent. To demonstrate the same, we translate all the identities of the first formulation into cohomology ingredients, and after a tedious reshuffling of the subsequent constraints, interestingly we find that all the identities of the second formulation are embedded into the first formulation which has some additional constraints. In addition, we look for the possible solutions of these Bianchi identities in a detailed analysis, and we find that some solutions can reduce the size of scalar potential very significantly, and in some cases are too strong to break the no-scale structure completely. Finally, we also comment on the influence of imposing some of the solutions of Bianchi identities in studying moduli stabilization.
A Triangulation Method for Identifying Hydrostratigraphic Locations of Well Screens
Whiteside, T. S.
2015-01-31
A method to identify the hydrostratigraphic location of well screens was developed using triangulation with known locations. This method was applied to all of the monitor wells being used to develop the new GSA groundwater model. Results from this method are closely aligned with those from an alternate method which uses a mesh surface.
Surface reconstruction using Delaunay triangulation for applications in life sciences
NASA Astrophysics Data System (ADS)
Grise, Graziela; Meyer-Hermann, Michael
2011-04-01
The Delaunay triangulation is an established method to define neighborhood relations in multi-particle systems. In particular, this method was employed for interacting multi-cellular systems in Biology. The extension of this method to a sub-cellular level that considers the membrane and the inner structure of cells is not straight forward and subject of this article. It is the objective to use a three-dimensional Delaunay-triangulation as a basis for the definition of a triangulation of a subset of particles that form a surface. An essential problem of this objective is the conservation of the number of particles belonging to the surface. This excludes established surface reconstruction algorithms. The presented algorithm allows the definition of a triangulation within a subset of particles attributed to a surface without the deletion of particles. A particular challenge is the deletion of connection that infer three-dimensional structures in the surface. The presented method is suitable for many configurations. Its performance and its limitations are analyzed and discussed. The developed algorithm for the reconstruction of connections in a surface is suitable to be used for simulations of biological cells because of the inherent conservation of the number of particles attributed to the membrane.
Multi-Sensor Triangulation of Multi-Source Spatial Data
NASA Technical Reports Server (NTRS)
Habib, Ayman; Kim, Chang-Jae; Bang, Ki-In
2007-01-01
The introduced methodologies are successful in: a) Ising LIDAR features for photogrammetric geo-refererncing; b) Delivering a geo-referenced imagery of the same quality as point-based geo-referencing procedures; c) Taking advantage of the synergistic characteristics of spatial data acquisition systems. The triangulation output can be used for the generation of 3-D perspective views.
The Use of Triangulation Methods in Qualitative Educational Research
ERIC Educational Resources Information Center
Oliver-Hoyo, Maria; Allen, DeeDee
2006-01-01
Triangulation involves the careful reviewing of data collected through different methods in order to achieve a more accurate and valid estimate of qualitative results for a particular construct. This paper describes how we used three qualitative methods of data collection to study attitudes of students toward graphing, hands-on activities, and…
A Simple Quality Triangulation Algorithm for Complex Geometries
USDA-ARS?s Scientific Manuscript database
This paper presents a new and simple algorithm for quality triangulation in complex geometries. The proposed algorithm is based on an initial equilateral triangle mesh covering the whole domain. The mesh nodes close to the boundary edges satisfy the so-called non-encroaching criterion: the distance ...
The Momentum 4-Vector Imparted by Gravitational Waves in Bianchi-Type Metrics
NASA Astrophysics Data System (ADS)
Havare, Ali; Korunur, Murat; Salti, Mustafa
2006-01-01
Considering the Møller, Weinberg and Qadir-Sharif's definitions in general relativity, we find the momentum 4-vector of the closed universe based on the Bianchi-type metrics. The momentum 4-vector (due to matter plus fields) is found to be zero. This result supports the viewpoints of Albrow and Tryon and extends the previous works by Cooperstock Israelit, Rosen, Johri et al., Banerjee Sen and Vargas who investigated the problem of the energy in Friedmann Robertson Walker universe and Saltı-Havare who studied the problem of the energy-momentum of the viscous Kasner-type space-times.
Bianchi type-II universe with wet dark fluid in general theory of relativity
NASA Astrophysics Data System (ADS)
Mahanta, Chandra Rekha; Sheikh, Azizur Rahman
2017-09-01
In this paper, dark energy models of the universe filled with wet dark fluid are constructed in the frame work of LRS Bianchi type-II space-time in General Theory of Relativity. A new equation of state modeled on the equation of state p = γ ( ρ - ρ_{*} ), which can describe liquid including water, is used. The exact solutions of Einstein's field equations are obtained in quadrature form and the models corresponding to the cases γ = 0 and γ = 1 are discussed in details.
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)
Abdulwahhab, Muhammad Alim; Jhangeer, Adil
Conservation laws of various systems have been studied for decades due to their unparalleled importance in unraveling systems’ intricacies without having to go into microscopic details of the physical process involved. Their association with symmetries has not only had a stupendous impact in the formulation of the fundamental laws of physics, but also open doors to further explorations and unifications of others. In this study, we present the Lie symmetries and nonlinearly self-adjoint classifications of the wave equation on Bianchi I spacetime. For different forms of the metric potentials, generalized higher order non-trivial conserved vectors are constructed. Some exact invariant solutions are also exhibited.
Comparison of three-dimensional retinal imaging methods: the method of scanning laser triangulation.
Milbocker, M T; Reznichenko, Y M
1991-10-01
Three methods of three-dimensional imaging of the vitreous and the fundus of the human eye are compared. Equations are derived for the theoretical depth resolution of stereophotogrammetry, scanning laser tomography, and scanning laser triangulation. Scanning laser triangulation provides superior depth resolution without requiring axial scanning. A description of a prototype scanning laser triangulator is given.
ERIC Educational Resources Information Center
Fosco, Gregory M.; Grych, John H.
2010-01-01
Although triangulation into parental conflict is a risk factor for child and adolescent maladjustment, little is known about how triangulation affects adolescents' functioning or the factors that lead children to be drawn into parental disagreements. This prospective study examined the relations between triangulation, appraisals of conflict, and…
Cosmological perturbations in teleparallel Loop Quantum Cosmology
NASA Astrophysics Data System (ADS)
Haro, Jaime
2013-11-01
Cosmological perturbations in Loop Quantum Cosmology (LQC) are usually studied incorporating either holonomy corrections, where the Ashtekar connection is replaced by a suitable sinus function in order to have a well-defined quantum analogue, or inverse-volume corrections coming from the eigenvalues of the inverse-volume operator. In this paper we will develop an alternative approach to calculate cosmological perturbations in LQC based on the fact that, holonomy corrected LQC in the flat Friedmann-Lemaître-Robertson-Walker (FLRW) geometry could be also obtained as a particular case of teleparallel F(T) gravity (teleparallel LQC). The main idea of our approach is to mix the simple bounce provided by holonomy corrections in LQC with the non-singular perturbation equations given by F(T) gravity, in order to obtain a matter bounce scenario as a viable alternative to slow-roll inflation. In our study, we have obtained an scale invariant power spectrum of cosmological perturbations. However, the ratio of tensor to scalar perturbations is of order 1, which does not agree with the current observations. For this reason, we suggest a model where a transition from the matter domination to a quasi de Sitter phase is produced in order to enhance the scalar power spectrum.
Newtonian and Relativistic Cosmologies
NASA Astrophysics Data System (ADS)
Green, Stephen; Wald, Robert
2012-03-01
Cosmological N-body simulations are now being performed using Newtonian gravity on scales larger than the Hubble radius. It is known that a uniformly expanding, homogeneous ball of dust in Newtonian gravity satisfies the Friedmann equations, and also that a correspondence between Newtonian and relativistic dust cosmologies holds in linearized perturbation theory. Nevertheless, it is not obvious that Newtonian gravity can provide a good global description of an inhomogeneous cosmology with significant nonlinear dynamical behavior at small scales. We investigate this issue in light of a perturbative framework that we have recently developed. We propose a straightforward dictionary---exact at the linearized level---that maps Newtonian dust cosmologies into GR dust cosmologies, and we use our ordering scheme to determine the degree to which the resulting metric and matter distribution solve Einstein's equation. We then find additional corrections needed to satisfy Einstein's equation to ``order 1'' at small scales and to ``order ɛ'' at large scales. We expect that, in realistic Newtonian cosmologies, these additional corrections will be very small; if so, this should provide strong justification for the use of Newtonian simulations to describe GR cosmologies.
Kehagias, A.; Riotto, A.
2016-05-25
Symmetries play an interesting role in cosmology. They are useful in characterizing the cosmological perturbations generated during inflation and lead to consistency relations involving the soft limit of the statistical correlators of large-scale structure dark matter and galaxies overdensities. On the other hand, in observational cosmology the carriers of the information about these large-scale statistical distributions are light rays traveling on null geodesics. Motivated by this simple consideration, we study the structure of null infinity and the associated BMS symmetry in a cosmological setting. For decelerating Friedmann-Robertson-Walker backgrounds, for which future null infinity exists, we find that the BMS transformations which leaves the asymptotic metric invariant to leading order. Contrary to the asymptotic flat case, the BMS transformations in cosmology generate Goldstone modes corresponding to scalar, vector and tensor degrees of freedom which may exist at null infinity and perturb the asymptotic data. Therefore, BMS transformations generate physically inequivalent vacua as they populate the universe at null infinity with these physical degrees of freedom. We also discuss the gravitational memory effect when cosmological expansion is taken into account. In this case, there are extra contribution to the gravitational memory due to the tail of the retarded Green functions which are supported not only on the light-cone, but also in its interior. The gravitational memory effect can be understood also from an asymptotic point of view as a transition among cosmological BMS-related vacua.
NASA Astrophysics Data System (ADS)
Kehagias, A.; Riotto, A.
2016-05-01
Symmetries play an interesting role in cosmology. They are useful in characterizing the cosmological perturbations generated during inflation and lead to consistency relations involving the soft limit of the statistical correlators of large-scale structure dark matter and galaxies overdensities. On the other hand, in observational cosmology the carriers of the information about these large-scale statistical distributions are light rays traveling on null geodesics. Motivated by this simple consideration, we study the structure of null infinity and the associated BMS symmetry in a cosmological setting. For decelerating Friedmann-Robertson-Walker backgrounds, for which future null infinity exists, we find that the BMS transformations which leaves the asymptotic metric invariant to leading order. Contrary to the asymptotic flat case, the BMS transformations in cosmology generate Goldstone modes corresponding to scalar, vector and tensor degrees of freedom which may exist at null infinity and perturb the asymptotic data. Therefore, BMS transformations generate physically inequivalent vacua as they populate the universe at null infinity with these physical degrees of freedom. We also discuss the gravitational memory effect when cosmological expansion is taken into account. In this case, there are extra contribution to the gravitational memory due to the tail of the retarded Green functions which are supported not only on the light-cone, but also in its interior. The gravitational memory effect can be understood also from an asymptotic point of view as a transition among cosmological BMS-related vacua.
Bouncing Cosmologies: Progress and Problems
NASA Astrophysics Data System (ADS)
Brandenberger, Robert; Peter, Patrick
2017-02-01
We review the status of bouncing cosmologies as alternatives to cosmological inflation for providing a description of the very early universe, and a source for the cosmological perturbations which are observed today. We focus on the motivation for considering bouncing cosmologies, the origin of fluctuations in these models, and the challenges which various implementations face.
Cosmological models in higher-order gravity
NASA Astrophysics Data System (ADS)
Cotsakis, Spiros
This thesis is divided into two parts. The first part deals with the conformal structure, inflationary regimes, and singularity theorems in the context of higher-order gravity theories. The second part focuses on the question of the nature of cosmological singularities and in particular on the occurrence of chaotic behavior in the framework of these theories. We begin part one by formulating and proving what we call the conformal equivalence theorem which states that higher order gravity theories which are derived from a lagrangian density that is an analytic function of the scalar curvature are conformally equivalent to general relativity plus a scalar field matter source with a particular self-interaction potential. The solution space of higher-order gravity theories is examined and the weak field limit of these theories is calculated. The role of conformal non-invariance and the associated particle production in these theories is discussed. Several interpretative issues concerning the physical equivalence of these theories to general relativity with scalar field matter source are given and the physical reality of the conformally related metric tensors is examined in detail. The existence and stability conditions of the de Sitter space in the context of these theories are established and several examples which lead to successful inflation are presented. Effective potentials are drawn for certain classes of these theories. Singularity theorems are proved in the context of higher-order gravity theories and the status of the cosmic no-hair conjectures in these theories is critically presented. In the second part we start by reviewing certain useful and powerful methods for the study of chaotic behavior near cosmological singularities in general relativity. Recent numerical evidence that concerns the genericity of such oscillatory solutions is critically presented and commented upon. A new method based on the analytic theory of ordinary differential equations is
Loop quantum cosmology of the k=1 FRW: A tale of two bounces
NASA Astrophysics Data System (ADS)
Corichi, Alejandro; Karami, Asieh
2011-08-01
We consider the k=1 Friedman-Robertson-Walker (FRW) model within loop quantum cosmology, paying special attention to the existence of an ambiguity in the quantization process. In spatially nonflat anisotropic models such as Bianchi II and IX, the standard method of defining the curvature through closed holonomies is not admissible. Instead, one has to implement the quantum constraints by approximating the connection via open holonomies. In the case of flat k=0 FRW and Bianchi I models, these two quantization methods coincide, but in the case of the closed k=1 FRW model they might yield different quantum theories. In this manuscript we explore these two quantizations and the different effective descriptions they provide of the bouncing cyclic universe. In particular, as we show in detail, the most dramatic difference is that in the theory defined by the new quantization method, there is not one, but two different bounces through which the cyclic universe alternates. We show that for a “large” universe, these two bounces are very similar and, therefore, practically indistinguishable, approaching the dynamics of the “curvature-based” quantum theory.
Geometric perspective on singularity resolution and uniqueness in loop quantum cosmology
NASA Astrophysics Data System (ADS)
Corichi, Alejandro; Singh, Parampreet
2009-08-01
We reexamine the issue of singularity resolution in homogeneous loop quantum cosmology from the perspective of geometrical entities such as expansion rate and the shear scalar. These quantities are very reliable measures of the properties of spacetime and can be defined not only at the classical and effective level, but also at an operator level in the quantum theory. From their behavior in the effective constraint surface and in the effective loop quantum spacetime, we show that one can severely restrict the ambiguities in regularization of the quantum constraint and rule out unphysical choices. We analyze this in the flat isotropic model and the Bianchi-I spacetimes. In the former case we show that the expansion rate is absolutely bounded only for the so-called improved quantization, a result which synergizes with uniqueness of this quantization as proved earlier. Surprisingly, for the Bianchi-I spacetime, we show that out of the available choices, the expansion rate and shear are bounded for only one regularization of the quantum constraint. It turns out that only for this choice, the theory exhibits quantum gravity corrections at a unique scale, and is physically viable.
Geometric perspective on singularity resolution and uniqueness in loop quantum cosmology
Corichi, Alejandro; Singh, Parampreet
2009-08-15
We reexamine the issue of singularity resolution in homogeneous loop quantum cosmology from the perspective of geometrical entities such as expansion rate and the shear scalar. These quantities are very reliable measures of the properties of spacetime and can be defined not only at the classical and effective level, but also at an operator level in the quantum theory. From their behavior in the effective constraint surface and in the effective loop quantum spacetime, we show that one can severely restrict the ambiguities in regularization of the quantum constraint and rule out unphysical choices. We analyze this in the flat isotropic model and the Bianchi-I spacetimes. In the former case we show that the expansion rate is absolutely bounded only for the so-called improved quantization, a result which synergizes with uniqueness of this quantization as proved earlier. Surprisingly, for the Bianchi-I spacetime, we show that out of the available choices, the expansion rate and shear are bounded for only one regularization of the quantum constraint. It turns out that only for this choice, the theory exhibits quantum gravity corrections at a unique scale, and is physically viable.
Mesoamerican Cosmology: Recent Finds
NASA Astrophysics Data System (ADS)
Trejo, J. G.
2009-08-01
The archaeological and ethnological research carried out in the last decades in Mesoamerica has allowed to know better diverse topics of the cosmology in regions little studied till now. Though one can distinguish a common substratum from the Mesoamerican living together throughout many centuries, the cultural local peculiarities frequently seem to dominate the message expressed in the Prehispanic art. In this work we present cosmological ideas from Olmec and Huaxtec regions which show distinctive features but at the same time suggest an obvious unity concerning calendrical concepts. The previous thing demonstrates clearly the richness of alternatives that followed the Mesoamerican cosmological thought.
Hamiltonian cosmology of bigravity
NASA Astrophysics Data System (ADS)
Soloviev, V. O.
2017-03-01
This article is written as a review of the Hamiltonian formalism for the bigravity with de Rham-Gabadadze-Tolley (dRGT) potential, and also of applications of this formalism to the derivation of the background cosmological equations. It is demonstrated that the cosmological scenarios are close to the standard ΛCDM model, but they also uncover the dynamical behavior of the cosmological term. This term arises in bigravity regardless on the choice of the dRGT potential parameters, and its scale is given by the graviton mass. Various matter couplings are considered.
NASA Astrophysics Data System (ADS)
Li, En-Kun; Zhang, Yu; Geng, Jin-Ling; Duan, Peng-Fei
2015-11-01
Generalized second law of thermodynamics in the Bianchi Type I universe with the generalized holographic Ricci dark energy model is studied in this paper. The behavior of dark energy's equation of state parameter indicates that it is matter-like in the early time of the universe but phantom-like in the future. By analysing the evolution of the deviations of state parameter and the total pressure of the universe, we find that for an anisotropic Bianchi Type I universe, it transits from a high anisotropy stage to a more homogeneous stage in the near past. Using the normal entropy given by Gibbs' law of thermodynamics, it is proved that the generalized second law of thermodynamics does not always satisfied throughout the history of the universe when we assume the universe is enclosed by the generalized Ricci scalar radius R_{gr}. It becomes invalid in the near past to the future, and the formation of the galaxies will be helpful in explaining such phenomenon, for that the galaxies's formation is an entropy increase process. The negative change rate of the horizon entropy and internal entropy occur in different period indicates that the influences of galaxies formation is wiped from internal to the universe's horizon.
Energy Density Associated with the Bianchi Type-II Space-Time
NASA Astrophysics Data System (ADS)
Aydogdu, O.; Salti, M.
2006-01-01
To calculate the total energy distribution (due to both matter and fields including gravitation) associated with locally rotationally symmetric (LRS) Bianchi type-II space-times. We use the Bergmann-Thomson energy-momentum complex in both general relativity and teleparallel gravity. We find that the energy density in these different gravitation theories is vanishing at all times. This result is the same as that obtained by one of the present authors who solved the problem of finding the energy-momentum in LRS Bianchi type-II by using the energy-momentum complexes of Einstein and Landau and Lifshitz. The results of this paper also are consistent with those given in the previous works of Cooperstock and Israelit, Rosen, Johri et al., Banerjee-Sen, Vargas, and Salti et al. In this paper, we perform the calculations for a non-diagonal expanding space-time to determine whether the Bergmann-Thomson energy momentum prescription is consistent with the other formulations. (We previously considered diagonal and expanding space-time models.) Our result supports the viewpoints of Albrow and Tryon.
NASA Astrophysics Data System (ADS)
Ellis, George F. R.
2003-01-01
This article gives a brief survey of cosmology to the present day, and then explores a positive but critical approach, looking in turn at issues arising in observations, geometry, and physics, and at the foundational (philosophical) issues that necessarily arise.
Baryogenesis and cosmological antimatter
Dolgov, Alexander D.
2009-04-20
Possible mechanisms of baryogenesis are reviewed. Special attention is payed to those which allow for creation of astronomically significant domains or objects consisting of antimatter. Observational manifestations of cosmological antimatter are discussed.
The cosmological constant problem
Dolgov, A.D.
1989-05-01
A review of the cosmological term problem is presented. Baby universe model and the compensating field model are discussed. The importance of more accurate data on the Hubble constant and the Universe age is stressed. 18 refs.
NASA Astrophysics Data System (ADS)
Nelson, William
2014-03-01
I will discuss my transition from Quantum Gravity and Cosmology to the world of consulting and describe the differences and similarities between academia and industry. I will give some dos and don'ts for industry interviews and jobs searches.
Testing fractional action cosmology
NASA Astrophysics Data System (ADS)
Shchigolev, V. K.
2016-08-01
The present work deals with a combined test of the so-called Fractional Action Cosmology (FAC) on the example of a specific model obtained by the author earlier. In this model, the effective cosmological term is proportional to the Hubble parameter squared through the so-called kinematic induction. The reason of studying this cosmological model could be explained by its ability to describe two periods of accelerated expansion, that is in agreement with the recent observations and the cosmological inflation paradigm. First of all, we put our model through the theoretical tests, which gives a general conception of the influence of the model parameters on its behavior. Then, we obtain some restrictions on the principal parameters of the model, including the fractional index, by means of the observational data. Finally, the cosmography parameters and the observational data compared to the theoretical predictions are presented both analytically and graphically.
NASA Astrophysics Data System (ADS)
Turner, Michael S.
1999-03-01
For two decades the hot big-bang model as been referred to as the standard cosmology - and for good reason. For just as long cosmologists have known that there are fundamental questions that are not answered by the standard cosmology and point to a grander theory. The best candidate for that grander theory is inflation + cold dark matter. It holds that the Universe is flat, that slowly moving elementary particles left over from the earliest moments provide the cosmic infrastructure, and that the primeval density inhomogeneities that seed all the structure arose from quantum fluctuations. There is now prima facie evidence that supports two basic tenets of this paradigm. An avalanche of high-quality cosmological observations will soon make this case stronger or will break it. Key questions remain to be answered; foremost among them are: identification and detection of the cold dark matter particles and elucidation of the dark-energy component. These are exciting times in cosmology!
Cosmology: A research briefing
NASA Technical Reports Server (NTRS)
1995-01-01
As part of its effort to update topics dealt with in the 1986 decadal physics survey, the Board on Physics and Astronomy of the National Research Council (NRC) formed a Panel on Cosmology. The Panel produced this report, intended to be accessible to science policymakers and nonscientists. The chapters include an overview ('What Is Cosmology?'), a discussion of cosmic microwave background radiation, the large-scale structure of the universe, the distant universe, and physics of the early universe.
Fernandez-Jambrina, L.
2010-12-15
In this paper we characterize barotropic index singularities of homogeneous isotropic cosmological models [M. P. Dabrowski and T. Denkiewicz, Phys. Rev. D 79, 063521 (2009).]. They are shown to appear in cosmologies for which the scale factor is analytical with a Taylor series in which the linear and quadratic terms are absent. Though the barotropic index of the perfect fluid is singular, the singularities are weak, as it happens for other models for which the density and the pressure are regular.
Classification of cosmological milestones
Fernandez-Jambrina, L.; Lazkoz, Ruth
2006-09-15
In this paper causal geodesic completeness of Friedmann-Lemaitre-Robertson-Walker (FLRW) cosmological models is analyzed in terms of generalized power expansions of the scale factor in coordinate time. The strength of the found singularities is discussed following the usual definitions due to Tipler and Krolak. It is shown that while classical cosmological models are both timelike and lightlike geodesically incomplete, certain observationally allowed models which have been proposed recently are lightlike geodesically complete.
Foundations of modern cosmology
NASA Astrophysics Data System (ADS)
Hawley, John F.; Holcomb, Katherine A.
2005-07-01
Recent discoveries in astronomy, especially those made with data collected by satellites such as the Hubble Space Telescope and the Wilkinson Microwave Anisotropy Probe, have revolutionized the science of cosmology. These new observations offer the possibility that some long-standing mysteries in cosmology might be answered, including such fundamental questions as the ultimate fate of the universe. Foundations of modern cosmology provides an accessible, thorough and descriptive introduction to the physical basis for modern cosmological theory, from the big bang to a distant future dominated by dark energy. This second edition includes the latest observational results and provides the detailed background material necessary to understand their implications, with a focus on the specific model supported by these observations, the concordance model. Consistent with the book's title, emphasis is given to the scientific framework for cosmology, particularly the basics concepts of physics that underlie modern theories of relativity and cosmology; the importance of data and observations is stressed throughout. The book sketches the historical background of cosmology, and provides a review of the relevant basic physics and astronomy. After this introduction, both special and general relativity are treated, before proceeding to an in-depth discussion of the big bang theory and physics of the early universe. The book includes current research areas, including dark matter and structure formation, dark energy, the inflationary universe, and quantum cosmology. The authors' website (http://www.astro.virginia.edu/~jh8h/Foundations) offers a wealth of supplemental information, including questions and answers, references to other sources, and updates on the latest discoveries.
Cosmological phase transitions
Kolb, E.W. |
1993-10-01
If modern ideas about the role of spontaneous symmetry breaking in fundamental physics are correct, then the Universe should have undergone a series of phase transitions early in its history. The study of cosmological phase transitions has become an important aspect of early-Universe cosmology. In this lecture I review some very recent work on three aspects of phase transitions: the electroweak transition, texture, and axions.
Cosmological Models and Stability
NASA Astrophysics Data System (ADS)
Andersson, Lars
Principles in the form of heuristic guidelines or generally accepted dogma play an important role in the development of physical theories. In particular, philosophical considerations and principles figure prominently in the work of Albert Einstein. As mentioned in the talk by Jiří Bičák at this conference, Einstein formulated the equivalence principle, an essential step on the road to general relativity, during his time in Prague 1911-1912. In this talk, I would like to discuss some aspects of cosmological models. As cosmology is an area of physics where "principles" such as the "cosmological principle" or the "Copernican principle" play a prominent role in motivating the class of models which form part of the current standard model, I will start by comparing the role of the equivalence principle to that of the principles used in cosmology. I will then briefly describe the standard model of cosmology to give a perspective on some mathematical problems and conjectures on cosmological models, which are discussed in the later part of this paper.
Bag, Satadru; Sahni, Varun; Shtanov, Yuri; Unnikrishnan, Sanil E-mail: varun@iucaa.ernet.in E-mail: sanil@lnmiit.ac.in
2014-07-01
We explore the possibility of emergent cosmology using the effective potential formalism. We discover new models of emergent cosmology which satisfy the constraints posed by the cosmic microwave background (CMB). We demonstrate that, within the framework of modified gravity, the emergent scenario can arise in a universe which is spatially open/closed. By contrast, in general relativity (GR) emergent cosmology arises from a spatially closed past-eternal Einstein Static Universe (ESU). In GR the ESU is unstable, which creates fine tuning problems for emergent cosmology. However, modified gravity models including Braneworld models, Loop Quantum Cosmology (LQC) and Asymptotically Free Gravity result in a stable ESU. Consequently, in these models emergent cosmology arises from a larger class of initial conditions including those in which the universe eternally oscillates about the ESU fixed point. We demonstrate that such an oscillating universe is necessarily accompanied by graviton production. For a large region in parameter space graviton production is enhanced through a parametric resonance, casting serious doubts as to whether this emergent scenario can be past-eternal.
Building cosmological frozen stars
NASA Astrophysics Data System (ADS)
Kastor, David; Traschen, Jennie
2017-02-01
Janis-Newman-Winicour (JNW) solutions generalize Schwarzschild to include a massless scalar field. While they share the familiar infinite redshift feature of Schwarzschild, they suffer from the presence of naked singularities. Cosmological versions of JNW spacetimes were discovered some years ago, in the most general case, by Fonarev. Fonarev solutions are also plagued by naked singularities, but have the virtue, unlike e.g. Schwarzschild-deSitter, of being dynamical. Given that exact dynamical cosmological black hole solutions are scarce, Fonarev solutions merit further study. We show how Fonarev solutions can be obtained via generalized dimensional reduction from simpler static vacuum solutions. These results may lead towards constructions of actual dynamical cosmological black holes. In particular, we note that cosmological versions of extremal charged dilaton black holes are known. JNW spacetimes represent a different limiting case of the family of charged dilaton black holes, which have been important in the context of string theory, and better understanding their cosmological versions of JNW spacetimes thus provides a second data point towards finding cosmological versions of the entire family.
Refining a triangulation of a planar straight-line graph to eliminate large angles
Mitchell, S.A.
1993-05-13
Triangulations without large angles have a number of applications in numerical analysis and computer graphics. In particular, the convergence of a finite element calculation depends on the largest angle of the triangulation. Also, the running time of a finite element calculation is dependent on the triangulation size, so having a triangulation with few Steiner points is also important. Bern, Dobkin and Eppstein pose as an open problem the existence of an algorithm to triangulate a planar straight-line graph (PSLG) without large angles using a polynomial number of Steiner points. We solve this problem by showing that any PSLG with {upsilon} vertices can be triangulated with no angle larger than 7{pi}/8 by adding O({upsilon}{sup 2}log {upsilon}) Steiner points in O({upsilon}{sup 2} log{sup 2} {upsilon}) time. We first triangulate the PSLG with an arbitrary constrained triangulation and then refine that triangulation by adding additional vertices and edges. Some PSLGs require {Omega}({upsilon}{sup 2}) Steiner points in any triangulation achieving any largest angle bound less than {pi}. Hence the number of Steiner points added by our algorithm is within a log {upsilon} factor of worst case optimal. We note that our refinement algorithm works on arbitrary triangulations: Given any triangulation, we show how to refine it so that no angle is larger than 7{pi}/8. Our construction adds O(nm+nplog m) vertices and runs in time O(nm+nplog m) log(m+ p)), where n is the number of edges, m is one plus the number of obtuse angles, and p is one plus the number of holes and interior vertices in the original triangulation. A previously considered problem is refining a constrained triangulation of a simple polygon, where p = 1. For this problem we add O({upsilon}{sup 2}) Steiner points, which is within a constant factor of worst case optimal.
Evaluating habitat selection with radio-telemetry triangulation error
Samuel, M.D.; Kenow, K.P.
1992-01-01
Radio-telemetry triangulation errors result in the mislocation of animals and misclassification of habitat use. We present analytical methods that provide improved estimates of habitat use when misclassification probabilities can be determined. When misclassification probabilities cannot be determined, we use random subsamples from the error distribution of an estimated animal location to improve habitat use estimates. We conducted Monte Carlo simulations to evaluate the effects of this subsampling method, triangulation error, number of animal locations, habitat availability, and habitat complexity on bias and variation in habitat use estimates. Results for the subsampling method are illustrated using habitat selection by redhead ducks (Aythya americana ). We recommend the subsampling method with a minimum of 50 random points to reduce problems associated with habitat misclassification.
Evaluating habitat selection with radio-telemetry triangulation error
Samuel, M.D.; Kenow, K.P.
1992-01-01
Radio-telemetry triangulation errors result in the mislocation of animals and misclassification of habitat use. We present analytical methods that provide improved estimates of habitat use when misclassification probabilities can be determined. When misclassification probabilities cannot be determined, we use random subsamples from the error distribution of an estimated animal location to improve habitat use estimates. We conducted Monte Carlo simulations to evaluate the effects of this subsampling method, triangulation error, number of animal locations, habitat availability, and habitat complexity on bias and variation in habitat use estimates. Results for the subsampling method are illustrated using habitat selection by redhead ducks (Aythya americana). We recommend the subsampling method with a minimum of 50 random points to reduce problems associated with habitat misclassification.
Detectability of active triangulation range finder: a solar irradiance approach.
Liu, Huizhe; Gao, Jason; Bui, Viet Phuong; Liu, Zhengtong; Lee, Kenneth Eng Kian; Peh, Li-Shiuan; Png, Ching Eng
2016-06-27
Active triangulation range finders are widely used in a variety of applications such as robotics and assistive technologies. The power of the laser source should be carefully selected in order to satisfy detectability and still remain eye-safe. In this paper, we present a systematic approach to assess the detectability of an active triangulation range finder in an outdoor environment. For the first time, we accurately quantify the background noise of a laser system due to solar irradiance by coupling the Perez all-weather sky model and ray tracing techniques. The model is validated with measurements with a modeling error of less than 14.0%. Being highly generic and sufficiently flexible, the proposed model serves as a guide to define a laser system for any geographical location and microclimate.
Critical region for an Ising model coupled to causal triangulations
NASA Astrophysics Data System (ADS)
Cerda-Hernández, J.
2017-02-01
This paper extends the results obtained by Hernández et al for the annealed Ising model coupled to two-dimensional causal dynamical triangulations. We employ the Fortuin‑Kasteleyn (FK) representation in order to determine a region in the quadrant of the parameters β,μ >0 where the critical curve for the annealed model is possibly located. This can be done by outlining a region where the model has a unique infinite-volume Gibbs measure, and a region where the finite-volume Gibbs measure does not have weak limit (in fact, does not exist if the volume is large enough). We also improve the region where the model has a one dimensional geometry with respect to the unique weak limit measure, which implies that the Ising model on causal triangulation does not have phase transition in this region. Furthermore, we provide a better approximation of the free energy for the coupled model.
Personal authentication using hand vein triangulation and knuckle shape.
Kumar, Ajay; Prathyusha, K Venkata
2009-09-01
This paper presents a new approach to authenticate individuals using triangulation of hand vein images and simultaneous extraction of knuckle shape information. The proposed method is fully automated and employs palm dorsal hand vein images acquired from the low-cost, near infrared, contactless imaging. The knuckle tips are used as key points for the image normalization and extraction of region of interest. The matching scores are generated in two parallel stages: (i) hierarchical matching score from the four topologies of triangulation in the binarized vein structures and (ii) from the geometrical features consisting of knuckle point perimeter distances in the acquired images. The weighted score level combination from these two matching scores are used to authenticate the individuals. The achieved experimental results from the proposed system using contactless palm dorsal-hand vein images are promising (equal error rate of 1.14%) and suggest more user friendly alternative for user identification.
Quality Tetrahedral Mesh Smoothing via Boundary-Optimized Delaunay Triangulation.
Gao, Zhanheng; Yu, Zeyun; Holst, Michael
2012-12-01
Despite its great success in improving the quality of a tetrahedral mesh, the original optimal Delaunay triangulation (ODT) is designed to move only inner vertices and thus cannot handle input meshes containing "bad" triangles on boundaries. In the current work, we present an integrated approach called boundary-optimized Delaunay triangulation (B-ODT) to smooth (improve) a tetrahedral mesh. In our method, both inner and boundary vertices are repositioned by analytically minimizing the error between a paraboloid function and its piecewise linear interpolation over the neighborhood of each vertex. In addition to the guaranteed volume-preserving property, the proposed algorithm can be readily adapted to preserve sharp features in the original mesh. A number of experiments are included to demonstrate the performance of our method.
Discovery and problem solving: Triangulation as a weak heuristic
NASA Technical Reports Server (NTRS)
Rochowiak, Daniel
1987-01-01
Recently the artificial intelligence community has turned its attention to the process of discovery and found that the history of science is a fertile source for what Darden has called compiled hindsight. Such hindsight generates weak heuristics for discovery that do not guarantee that discoveries will be made but do have proven worth in leading to discoveries. Triangulation is one such heuristic that is grounded in historical hindsight. This heuristic is explored within the general framework of the BACON, GLAUBER, STAHL, DALTON, and SUTTON programs. In triangulation different bases of information are compared in an effort to identify gaps between the bases. Thus, assuming that the bases of information are relevantly related, the gaps that are identified should be good locations for discovery and robust analysis.
NASA Astrophysics Data System (ADS)
Socorro, J.; Nuñez, Omar E.
2017-04-01
The multi-scalar field cosmology of the anisotropic Bianchi type-I model is used in order to construct a family of potentials that are the best suited to model the inflation phenomenon. We employ the quantum potential approach to quantum mechanics due to Bohm in order to solve the corresponding Wheeler-DeWitt equation; which in turn enables us to restrict sensibly the aforementioned family of potentials. Supersymmetric Quantum Mechanics (SUSYQM) is also employed in order to constrain the superpotential function, at the same time the tools from SUSY Quantum Mechanics are used to test the family of potentials in order to infer which is the most convenient for the inflation epoch. For completeness solutions to the wave function of the universe are also presented.
BOOK REVIEW: Observational Cosmology Observational Cosmology
NASA Astrophysics Data System (ADS)
Howell, Dale Andrew
2013-04-01
Observational Cosmology by Stephen Serjeant fills a niche that was underserved in the textbook market: an up-to-date, thorough cosmology textbook focused on observations, aimed at advanced undergraduates. Not everything about the book is perfect - some subjects get short shrift, in some cases jargon dominates, and there are too few exercises. Still, on the whole, the book is a welcome addition. For decades, the classic textbooks of cosmology have focused on theory. But for every Sunyaev-Zel'dovich effect there is a Butcher-Oemler effect; there are as many cosmological phenomena established by observations, and only explained later by theory, as there were predicted by theory and confirmed by observations. In fact, in the last decade, there has been an explosion of new cosmological findings driven by observations. Some are so new that you won't find them mentioned in books just a few years old. So it is not just refreshing to see a book that reflects the new realities of cosmology, it is vital, if students are to truly stay up on a field that has widened in scope considerably. Observational Cosmology is filled with full-color images, and graphs from the latest experiments. How exciting it is that we live in an era where satellites and large experiments have gathered so much data to reveal astounding details about the origin of the universe and its evolution. To have all the latest data gathered together and explained in one book will be a revelation to students. In fact, at times it was to me. I've picked up modern cosmological knowledge through a patchwork of reading papers, going to colloquia, and serving on grant and telescope allocation panels. To go back and see them explained from square one, and summarized succinctly, filled in quite a few gaps in my own knowledge and corrected a few misconceptions I'd acquired along the way. To make room for all these graphs and observational details, a few things had to be left out. For one, there are few derivations
Mesh Generation via Local Bisection Refinement of Triangulated Grids
2015-06-01
bucketing techniques in computational geometry, in Computational Geometry, Vol. 2 of Machine Intelligence and Pattern Recognition , Elsevier, North Holland...UNCLASSIFIED Mesh Generation via Local Bisection Refinement of Triangulated Grids Jason R. Looker Joint and Operations Analysis Division Defence...triangles. The mesh refinement algorithm is tested and shown to achieve the anticipated linear running time with respect to the number of triangles in the
Triangulation: a three-dimensional model for continuing education.
Shaffer, M K; Pfeiffer, I L
1981-01-01
A variety of cultural phenomena have recently converged to create a demand for specialized adult education programs. One approach that can provide insights in adjusting traditional educational strategies is triangulation, a procedure that can help delineate both content and teaching approaches by assembling the perceptions of administrators, adult learners, and educators. This procedure can be especially helpful to educators in health care settings who must continually provide meaningful programs for adults.
Calibration of high-speed imaging by laser triangulation.
Larsson, Hans; Hertegård, Stellan
2004-01-01
A method was developed for absolute calibration of endoscopic vocal fold images using laser triangulation. The laser is attached to a rigid endoscope with 8-degrees angle in relation to the optical axis of the endoscope. A special software is used for calibration and measurements from high-speed images. The equipment can provide measurements both in horizontal and vertical planes, and can be used for calibrated measurements of vocal fold length, amplitude of vocal fold vibrations and vertical movements.
Algorithm for Triangulating Visual Landmarks and Determining Their Covariance
2012-01-01
gyroscopes ........................................ 22 1 1. INTRODUCTION The work described in this report has to do with the problem of vision ...the image must be known. The camera calibration matrix is used when modeling the projection of a scene onto an image sensor . This projection can be...is much larger than the gyro noise from tactical- grade inertial measurement units. For example, if triangulation for a visual landmark is performed
Grounded theory, feminist theory, critical theory: toward theoretical triangulation.
Kushner, Kaysi Eastlick; Morrow, Raymond
2003-01-01
Nursing and social science scholars have examined the compatibility between feminist and grounded theory traditions in scientific knowledge generation, concluding that they are complementary, yet not without certain tensions. This line of inquiry is extended to propose a critical feminist grounded theory methodology. The construction of symbolic interactionist, feminist, and critical feminist variants of grounded theory methodology is examined in terms of the presuppositions of each tradition and their interplay as a process of theoretical triangulation.
Parallel implementation of an algorithm for Delaunay triangulation
NASA Technical Reports Server (NTRS)
Merriam, Marshal L.
1992-01-01
The theory and practice of implementing Tanemura's algorithm for 3D Delaunay triangulation on Intel's Gamma prototype, a 128 processor MIMD computer, is described. Efficient implementation of Tanemura's algorithm on a conventional, vector processing supercomputer is problematic. It does not vectorize to any significant degree and requires indirect addressing. Efficient implementation on a parallel architecture is possible, however. Speeds in excess of 20 times a single processor Cray Y-MP are realized on 128 processors of the Intel Gamma prototype.
Parallel implementation of an algorithm for Delaunay triangulation
NASA Technical Reports Server (NTRS)
Merriam, Marshall L.
1992-01-01
This work concerns the theory and practice of implementing Tanemura's algorithm for 3D Delaunay triangulation on Intel's Gamma prototype, a 128 processor MIMD computer. Tanemura's algorithm does not vectorize to any significant degree and requires indirect addressing. Efficient implementation on a conventional, vector processing, supercomputer is problematic. Efficient implementation on a parallel architecture is possible, however. In this work, speeds in excess of 8 times a single processor Cray Y-mp are realized on 128 processors of the Intel Gamma prototype.
Adaptive mesh generation for viscous flows using Delaunay triangulation
NASA Technical Reports Server (NTRS)
Mavriplis, Dimitri J.
1990-01-01
A method for generating an unstructured triangular mesh in two dimensions, suitable for computing high Reynolds number flows over arbitrary configurations is presented. The method is based on a Delaunay triangulation, which is performed in a locally stretched space, in order to obtain very high aspect ratio triangles in the boundary layer and the wake regions. It is shown how the method can be coupled with an unstructured Navier-Stokes solver to produce a solution adaptive mesh generation procedure for viscous flows.
Three dimensional mesh generation by triangulation of arbitrary point sets
NASA Technical Reports Server (NTRS)
Baker, Timothy J.
1987-01-01
A method for generating an unstructured mesh is described. The approach is quite general and joins an arbitrary set of points to produce a covering of three dimensional space by tetrahedra. After removing the tetrahedra that connect surface points, a mesh suitable for a finite element based flow solver is obtained. Details of the triangulation algorithm are provided together with an analysis of the algorithm efficiency and validity.
Adaptive mesh generation for viscous flows using Delaunay triangulation
NASA Technical Reports Server (NTRS)
Mavriplis, Dimitri J.
1988-01-01
A method for generating an unstructured triangular mesh in two dimensions, suitable for computing high Reynolds number flows over arbitrary configurations is presented. The method is based on a Delaunay triangulation, which is performed in a locally stretched space, in order to obtain very high aspect ratio triangles in the boundary layer and the wake regions. It is shown how the method can be coupled with an unstructured Navier-Stokes solver to produce a solution adaptive mesh generation procedure for viscous flows.
Optical triangulation-based microtopographic inspection of surfaces.
Costa, Manuel F M
2012-01-01
The non-invasive inspection of surfaces is a major issue in a wide variety of industries and research laboratories. The vast and increasing range of surface types, tolerance requirements and measurement constraints demanded during the last decades represents a major research effort in the development of new methods, systems and metrological strategies. The discreet dimensional evaluation the rugometric characterization and the profilometric inspection seem to be insufficient in many instances. The full microtopographic inspection has became a common requirement. Among the different systems developed, optical methods have the most important role and among those triangulation-based ones have gained a major status thanks to their flexibility, reliability and robustness. In this communication we will provide a brief historical review on the development of optical triangulation application to the dimensional inspection of objects and surfaces and on the work done at the Microtopography Laboratory of the Physics Department of the University of Minho, Portugal, in the development of methods and systems of optical triangulation-based microtopographic inspection of surfaces.
Optical Triangulation-Based Microtopographic Inspection of Surfaces
Costa, Manuel F. M.
2012-01-01
The non-invasive inspection of surfaces is a major issue in a wide variety of industries and research laboratories. The vast and increasing range of surface types, tolerance requirements and measurement constraints demanded during the last decades represents a major research effort in the development of new methods, systems and metrological strategies. The discreet dimensional evaluation the rugometric characterization and the profilometric inspection seem to be insufficient in many instances. The full microtopographic inspection has became a common requirement. Among the different systems developed, optical methods have the most important role and among those triangulation-based ones have gained a major status thanks to their flexibility, reliability and robustness. In this communication we will provide a brief historical review on the development of optical triangulation application to the dimensional inspection of objects and surfaces and on the work done at the Microtopography Laboratory of the Physics Department of the University of Minho, Portugal, in the development of methods and systems of optical triangulation-based microtopographic inspection of surfaces. PMID:22666036
Anisotropic cosmologies with ghost dark energy models in f (R, T) gravity
NASA Astrophysics Data System (ADS)
Fayaz, V.; Hossienkhani, H.; Zarei, Z.; Azimi, N.
2016-02-01
In this work, the generalized Quantum Chromodynamics (QCD) ghost model of dark energy in the framework of Einstein gravity is investigated. For this purpose, we use the squared sound speed vs2 whose sign determines the stability of the model. At first, the non-interacting ghost dark energy in a Bianchi type-I (BI) background is discussed. Then the equation-of-state parameter, ω_D=pD/ρD, the deceleration parameter, and the evolution equation of the generalized ghost dark energy are obtained. It is shown that the equation-of-state parameter of the ghost dark energy can cross the phantom line ( ω=-1 in some range of the parameter spaces. Then, this investigation was extended to the general scheme for modified f(R,T) gravity reconstruction from a realistic case in an anisotropic Bianchi type-I cosmology, using the dark matter and ghost dark energy. Special attention is taken into account for the case in which the function f is given by f(R,T)=f1(R) +f2(T). We consider a specific model which permits the standard continuity equation in this modified theory. Besides Ω_{Λ} and Ω in standard Einstein cosmology, another density parameter, Ω_{σ}, is expected by the anisotropy. This theory implies that if Ω_{σ} is zero then it yields the FRW universe model. Interestingly enough, we find that the corresponding f ( R, T) gravity of the ghost DE model can behave like phantom or quintessence of the selected models which describe the accelerated expansion of the universe.
NASA Astrophysics Data System (ADS)
Terzis, Petros A.; Christodoulakis, T.
2012-12-01
Lie-group symmetry analysis for systems of coupled, nonlinear ordinary differential equations is performed in order to obtain the entire solution space to Einstein’s field equations for vacuum Bianchi spacetime geometries. The symmetries used are the automorphisms of the Lie algebra of the corresponding three-dimensional isometry group acting on the hyper-surfaces of simultaneity for each Bianchi type, as well as the scaling and the time reparametrization symmetry. A detailed application of the method is presented for Bianchi type IV. The result is the acquisition of the general solution of type IV in terms of sixth Painlevé transcendent PVI, along with the known pp-wave solution. For Bianchi types I, II, V the known entire solution space is attained and very briefly listed, along with two new type V solutions of Euclidean and neutral signature and a type I pp-wave metric.
NASA Astrophysics Data System (ADS)
Silk, Joseph
2008-11-01
The field of cosmology has been transformed since the glorious decades of the 1920's and 1930's when theory and observation converged to develop the current model of the expanding universe. It was a triumph of the theory of general relativity and astronomy. The first revolution came when the nuclear physicists entered the fray. This marked the debut of the hot big bang, in which the light elements were synthesized in the first three minutes. It was soon realised that elements like carbon and iron were synthesized in exploding stars. However helium, as well as deuterium and lithium, remain as George Gamow envisaged, the detritus of the big bang. The climax arrived with one of the most remarkable discoveries of the twentieth century, the cosmic microwave background radiation, in 1964. The fossil glow turned out to have the spectrum of an ideal black body. One could not imagine a stronger confirmation of the hot and dense origin of the universe. This discovery set the scene for the next major advance. It was now the turn of the particle physicists, who realized that the energies attained near the beginning of the universe, and unachievable in any conceivable terrestrial accelerator, provided a unique testing ground for theories of grand unification of the fundamental forces. This led Alan Guth and Andrei Linde in 1980 to propose the theory of inflation, which solved outstanding puzzles of the big bang. One could now understand why the universe is so large and homogeneous, and the origin of the seed fluctuations that gave rise to large-scale structure. A key prediction was that the universe should have Euclidean geometry, now verified to a precision of a few percent. Modern cosmology is firmly embedded in particle physics. It merits a text written by a particle physicist who can however appreciate the contributions of astronomy that provide the foundation and infrastructure for the theory of the expanding universe. There are now several such texts available. The most
Cosmology and Particle Physics
NASA Astrophysics Data System (ADS)
Steigman, G.
1982-01-01
The cosmic connections between physics on the very largest and very smallest scales are reviewed with an emphasis on the symbiotic relation between elementary particle physics and cosmology. After a review of the early Universe as a cosmic accelerator, various cosmological and astrophysical constraints on models of particle physics are outlined. To illustrate this approach to particle physics via cosmology, reference is made to several areas of current research: baryon non-conservation and baryon asymmetry; free quarks, heavy hadrons and other exotic relics; primordial nucleosynthesis and neutrino masses. In the last few years we have witnessed the birth and growth to healthy adolescence of a new collaboration between astrophysicists and particle physicists. The most notable success of this cooperative effort has been to provide the framework for understanding, within the context of GUTs and the hot big-bang cosmology, the universal baryon asymmetry. The most exciting new predictions this effort has spawned are that exotic relics may exist in detectable abundances. In particular, we may live in a neutrino-dominated Universe. In the next few years, accummulating laboratory data (for example proton decay, neutrino masses and oscillations) coupled with theoritical work in particle physics and cosmology will ensure the growth to maturity of this joint effort.
Thermal tachyacoustic cosmology
NASA Astrophysics Data System (ADS)
Agarwal, Abhineet; Afshordi, Niayesh
2014-08-01
An intriguing possibility that can address pathologies in both early Universe cosmology (i.e. the horizon problem) and quantum gravity (i.e. nonrenormalizability), is that particles at very high energies and/or temperatures could propagate arbitrarily fast. A concrete realization of this possibility for the early Universe is the tachyacoustic (or speedy sound) cosmology, which could also produce a scale-invariant spectrum for scalar cosmological perturbations. Here, we study thermal tachyacoustic cosmology (TTC), i.e. this scenario with thermal initial conditions. We find that a phase transition in the early Universe, around the scale of the grand unified theory (GUT scale; T ˜1015 GeV), during which the speed of sound drops by 25 orders of magnitude within a Hubble time, can fit current CMB observations. We further discuss how production of primordial black holes constrains the cosmological acoustic history, while coupling TTC to Horava-Lifshitz gravity leads to a lower limit on the amplitude of tensor modes (r≳10-3), that are detectable by CMBpol (and might have already been seen by the BICEP-Keck Collaboration).
Physical Foundations of Cosmology
NASA Astrophysics Data System (ADS)
Mukhanov, Viatcheslav
2005-11-01
Inflationary cosmology has been developed over the last twenty years to remedy serious shortcomings in the standard hot big bang model of the universe. Taking an original approach, this textbook explains the basis of modern cosmology and shows where the theoretical results come from. The book is divided into two parts; the first deals with the homogeneous and isotropic model of the Universe, the second part discusses how inhomogeneities can explain its structure. Established material such as the inflation and quantum cosmological perturbation are presented in great detail, however the reader is brought to the frontiers of current cosmological research by the discussion of more speculative ideas. An ideal textbook for both advanced students of physics and astrophysics, all of the necessary background material is included in every chapter and no prior knowledge of general relativity and quantum field theory is assumed. Presents detailed derivations of all basic results needed in cosmology, including robust predictions of inflation Contains an analytical treatment of nucleosynthesis, recombination and CMB fluctuations Provides elementary introductions to more advanced topics
Cosmology Solved? Quite Possibly!
NASA Astrophysics Data System (ADS)
Turner, Michael S.
1999-03-01
The discovery of the cosmic microwave background (CMB) in 1964 by Penzias and Wilson led to the establishment of the hot big bang cosmological model some 10 years later. Discoveries made in 1998 may ultimately have as profound an effect on our understanding of the origin and evolution of the universe. Taken at face value, they confirm the basic tenets of inflation + cold dark matter, a bold and expansive theory that addresses all the fundamental questions left unanswered by the hot big bang model and holds that the universe is flat, slowly moving elementary particles provide the cosmic infrastructure, and quantum fluctuations seeded all the structure seen in the universe today. Just as it took a decade to establish the hot big bang model after the discovery of the CMB, it will likely take another 10 years to establish the latest addition to the standard cosmology and make the answer to ``Cosmology solved?'' ``YES!'' Whether or not 1998 proves to be a cosmic milestone, the coming avalanche of high-quality cosmological data promises to make the next 20 years an extremely exciting period for cosmology.
Big Bang, Blowup, and Modular Curves: Algebraic Geometry in Cosmology
NASA Astrophysics Data System (ADS)
Manin, Yuri I.; Marcolli, Matilde
2014-07-01
We introduce some algebraic geometric models in cosmology related to the ''boundaries'' of space-time: Big Bang, Mixmaster Universe, Penrose's crossovers between aeons. We suggest to model the kinematics of Big Bang using the algebraic geometric (or analytic) blow up of a point x. This creates a boundary which consists of the projective space of tangent directions to x and possibly of the light cone of x. We argue that time on the boundary undergoes the Wick rotation and becomes purely imaginary. The Mixmaster (Bianchi IX) model of the early history of the universe is neatly explained in this picture by postulating that the reverse Wick rotation follows a hyperbolic geodesic connecting imaginary time axis to the real one. Penrose's idea to see the Big Bang as a sign of crossover from ''the end of previous aeon'' of the expanding and cooling Universe to the ''beginning of the next aeon'' is interpreted as an identification of a natural boundary of Minkowski space at infinity with the Big Bang boundary.
On the origins of organology: Franz Joseph Gall and a girl named Bianchi.
Eling, Paul; Finger, Stanley; Whitaker, Harry
2017-01-01
Franz Joseph Gall (1758-1828) introduced a new theory of mind and brain at the end of the eighteenth century, which he referred to as organology, dealing with mental functions and their cortical localizations. Gall wrote that observations regarding the verbal learning capacities of his schoolmates brought about his new way of thinking. This widely accepted view, however, requires qualification. Although Gall's experiences and observations as a schoolboy were relevant, especially for his craniology, these childhood memories might have been recalled and reinterpreted after he had started to think about the faculties of mind-specifically after he had met Bianchi, a 5-year-old girl with a special talent for music.
Interacting Dark matter and Holographic dark energy in Bianchi type-V universe
NASA Astrophysics Data System (ADS)
Adhav, K. S.; Munde, S. L.; Tayade, G. B.; Bokey, V. D.
2015-09-01
The spatially homogeneous and anisotropic Bianchi type-V universe filled with interacting Dark matter and Holographic dark energy has been studied. The exact solutions of Einstein's field equations are obtained by (i) applying the special law of variation of Hubble parameter that yields constant values of the deceleration parameter and (ii) using a special form of deceleration parameter. It has been observed that for suitable choice of interaction between dark matter and holographic dark energy there is no coincidence problem (unlike CDM). Also, in all the resulting models the anisotropy of expansion dies out very quickly and attains isotropy after some finite time. The physical and geometrical aspects of the models are also discussed.
Similarity dark energy models in Bianchi type-I space-time
NASA Astrophysics Data System (ADS)
Ali, Ahmad T.; Kumar Yadav, Anil; Alzahrani, Abdulah K.
2016-11-01
We investigate some new similarity inhomogeneous solutions of anisotropic dark energy and perfect fluid in Bianchi type-I space-time. Three different equation-of-state (EoS) parameters along the spatial directions are introduced to quantify the deviation of pressure from isotropy. We consider the case when the dark energy is minimally coupled to the perfect fluid as well as the direct interaction with it. The Lie symmetry generators that leave the equation invariant are identified and we generate an optimal system of one-dimensional sub-algebras. Each element of the optimal system is used to reduce the partial differential equation to an ordinary differential equation which is further analyzed. We solve the Einstein field equations, described by a system of non-linear partial differential equations (NLPDEs), by using the Lie point symmetry analysis method. The geometrical and kinematic features of the models and the behavior of the anisotropy of dark energy are examined in detail.
Particle Accelerators Test Cosmological Theory.
ERIC Educational Resources Information Center
Schramm, David N.; Steigman, Gary
1988-01-01
Discusses the symbiotic relationship of cosmology and elementary-particle physics. Presents a brief overview of particle physics. Explains how cosmological considerations set limits on the number of types of elementary particles. (RT)
Particle Accelerators Test Cosmological Theory.
ERIC Educational Resources Information Center
Schramm, David N.; Steigman, Gary
1988-01-01
Discusses the symbiotic relationship of cosmology and elementary-particle physics. Presents a brief overview of particle physics. Explains how cosmological considerations set limits on the number of types of elementary particles. (RT)
Crack in the cosmological paradigm
NASA Astrophysics Data System (ADS)
Di Valentino, Eleonora
2017-09-01
A time-dependent dark energy component of the Universe may be able to explain tensions between local and primordial measurements of cosmological parameters, shaking current confidence in the concept of a cosmological constant.
NASA Astrophysics Data System (ADS)
Grujic, P. V.
2008-10-01
Cosmos poses unique problems to its investigations, both from the epistemological and ontological aspects. We analyze modern cosmology as science of the totality of the material reality, with emphasis on the physical content of the principal entities involved in describing the Universe as we perceive. In particular we examine the concept of creation and anihilation and argue that these notions, if relevant, are devoid of meaningful content. If applicable, the notion of evolution refers to transition from physical field entities towards inert matter components. We discuss the meaning of the existentional quantificator and show that the cosmology is essentially a historical science. Finally, we consider an interplay between the epistemological and phenomenological aspects, arguing that in cosmology it is the former one may rely on.
General relativity and cosmology
NASA Astrophysics Data System (ADS)
Bucher, Martin; Ni, Wei-Tou
2015-10-01
This year marks the 100th anniversary of Einstein’s 1915 landmark paper “Die Feldgleichungen der Gravitation” in which the field equations of general relativity were correctly formulated for the first time, thus rendering general relativity a complete theory. Over the subsequent hundred years, physicists and astronomers have struggled with uncovering the consequences and applications of these equations. This paper, which was written as an introduction to six chapters dealing with the connection between general relativity and cosmology that will appear in the two-volume book One Hundred Years of General Relativity: From Genesis and Empirical Foundations to Gravitational Waves, Cosmology and Quantum Gravity, endeavors to provide a historical overview of the connection between general relativity and cosmology, two areas whose development has been closely intertwined.
Elementary particles and cosmology
NASA Astrophysics Data System (ADS)
Dobrolyubov, M. I.; Ignatev, A. Yu.; Shaposhnikov, M. E.
1988-12-01
A series of lectures is devoted to actual problems which arise at the junction of elementary particle physics and cosmology. A brief review is given to the standard theory of hot universe and scenario of inflationary universe, modern state of the problem of baryon universe asymmetry and possible new mechanisms of this asymmetry formation. The possibility of construction of cosmological models on the basis of supersymmetric theories is considered: qualitative evaluation of the modern density of relic particles, cosmological restrictions for the mass of the lightest particle, astrophysical restrictions for the coupling constant of weakly interacting particles and matter are given. A perspective direction of search for light particles in light hadron decays is mentioned.
Closed inhomogeneous string cosmologies
Feinstein, A.; Lazkoz, R.; Vazquez-Mozo, M.A.
1997-10-01
We present a general algorithm which permits us to construct solutions in string cosmology for heterotic and type-IIB superstrings in four dimensions. Using a chain of transformations applied in sequence{emdash}conformal, T duality, and SL(2,{bold R}) rotations, along with the usual generating techniques associated with Geroch transformations in Einstein frame{emdash}we obtain solutions with all relevant low-energy remnants of the string theory. To exemplify our algorithm we present an inhomogeneous string cosmology with S{sup 3} topology of spatial sections, discuss some properties of the solution, and point out some subtleties involved in the concept of homogeneity and isotropy in string cosmology. {copyright} {ital 1997} {ital The American Physical Society}
Newtonian and relativistic cosmologies
NASA Astrophysics Data System (ADS)
Green, Stephen R.; Wald, Robert M.
2012-03-01
Cosmological N-body simulations are now being performed using Newtonian gravity on scales larger than the Hubble radius. It is well known that a uniformly expanding, homogeneous ball of dust in Newtonian gravity satisfies the same equations as arise in relativistic Friedmann-Lemaître-Robinson-Walker cosmology, and it also is known that a correspondence between Newtonian and relativistic dust cosmologies continues to hold in linearized perturbation theory in the marginally bound/spatially flat case. Nevertheless, it is far from obvious that Newtonian gravity can provide a good global description of an inhomogeneous cosmology when there is significant nonlinear dynamical behavior at small scales. We investigate this issue in the light of a perturbative framework that we have recently developed [S. R. Green and R. M. Wald, Phys. Rev. DPRVDAQ1550-7998 83, 084020 (2011).10.1103/PhysRevD.83.084020], which allows for such nonlinearity at small scales. We propose a relatively straightforward dictionary—which is exact at the linearized level—that maps Newtonian dust cosmologies into general relativistic dust cosmologies, and we use our “ordering scheme” to determine the degree to which the resulting metric and matter distribution solve Einstein’s equation. We find that, within our ordering scheme, Einstein’s equation fails to hold at “order 1” at small scales and at “order ɛ” at large scales. We then find the additional corrections to the metric and matter distribution needed to satisfy Einstein’s equation to these orders. While these corrections are of some interest in their own right, our main purpose in calculating them is that their smallness should provide a criterion for the validity of the original dictionary (as well as simplified versions of this dictionary). We expect that, in realistic Newtonian cosmologies, these additional corrections will be very small; if so, this should provide strong justification for the use of Newtonian simulations
Nonlinear backreaction in cosmology
NASA Astrophysics Data System (ADS)
Green, Stephen Roland
This thesis, based on two papers by Green and Wald, investigates the problem of nonlinear backreaction in cosmology. We first analyze the problem in a general context by developing a new, mathematically precise framework for treating the effects of nonlinear phenomena occurring on small scales in general relativity. Our framework requires the metric to be close to a background metric (not necessarily a cosmological metric), but allows arbitrarily large stress-energy fluctuations on small scales. We prove that, within our framework, if the matter stress-energy tensor satisfies the weak energy condition (i.e., positivity of energy density in all frames), then the only effect that small-scale inhomogeneities can have on the background metric is to provide an effective stress-energy tensor that is traceless and satisfies the weak energy condition itself—corresponding to the presence of gravitational radiation. In particular, nonlinear effects produced by small-scale inhomogeneities cannot mimic the effects of dark energy. We also develop perturbation theory off of the background metric. We derive an equation for the long-wavelength part of the leading order deviation of the metric from the background metric, which contains the usual terms occurring in linearized perturbation theory plus additional contributions from the small-scale inhomogeneities. Next, we apply our framework to the cosmological context, specializing our background metric to be of the Friedmann-Lemaitre-Robertson-Walker form. We demonstrate that, in the case of dust matter, a cosmological constant, and vanishing spatial curvature (i.e., our universe today), Newtonian gravity alone provides a good
Planck 2015 Cosmological results
NASA Astrophysics Data System (ADS)
Tristram, Matthieu
2015-08-01
On behalf of the Planck collaboration, I will present the cosmological results from the 2015 release. The new release now include polarization data from both the LFI and the HFI.I will focus on the impact of the polarization on both the standard LCDM model and its basic extensions. I will compare these constraints with other cosmological probes such as BAO, gravitational lensing and redshift space distortions.LCDM is still a very good fit of the Planck CMB data. The scalar fluctuations are consistent with adiabatic modes.
Midisuperspace supersymmetric quantum cosmology
Macias, Alfredo; Camacho, Abel; Kunz, Jutta; Laemmerzahl, Claus
2008-03-15
We investigate the canonical quantization in the framework of N=1 simple supergravity for the case of a very simple gravitational midisuperspace described by Gowdy T{sup 3} cosmological models. We consider supersymmetric quantum cosmology in the mentioned midisuperspace, where a matrix representation for the gravitino covector-spinor is used. The full Lorentz constraint and its implications for the wave function of the Universe are analyzed in detail. We found that there are indeed physical states in the midisuperspace sector of the theory in contrast to the case of minisuperspace where there exist no physical states.
Information entropy in cosmology.
Hosoya, Akio; Buchert, Thomas; Morita, Masaaki
2004-04-09
The effective evolution of an inhomogeneous cosmological model may be described in terms of spatially averaged variables. We point out that in this context, quite naturally, a measure arises which is identical to a fluid model of the Kullback-Leibler relative information entropy, expressing the distinguishability of the local inhomogeneous mass density field from its spatial average on arbitrary compact domains. We discuss the time evolution of "effective information" and explore some implications. We conjecture that the information content of the Universe-measured by relative information entropy of a cosmological model containing dust matter-is increasing.
Cosmology with varying constants.
Martins, Carlos J A P
2002-12-15
The idea of possible time or space variations of the 'fundamental' constants of nature, although not new, is only now beginning to be actively considered by large numbers of researchers in the particle physics, cosmology and astrophysics communities. This revival is mostly due to the claims of possible detection of such variations, in various different contexts and by several groups. I present the current theoretical motivations and expectations for such variations, review the current observational status and discuss the impact of a possible confirmation of these results in our views of cosmology and physics as a whole.
Laniakea in a Cosmological Context
NASA Astrophysics Data System (ADS)
Hernandez-Charpak, S. D.; Forero-Romero, J. E.
2017-07-01
Laniakea, our local supercluster, was defined by recent observationa of the local cosmic flow. In this work we present a study on large cosmological N-body simulations aimed at establishing the significance of Laniakea in a cosmological context. We find that superclusters similar in size and structure to Laniakea are relatively uncommon on a broader cosmological context.
Jackson, M.A.
1990-01-01
Two separate studies are contained. The first study is concerned with approximations to cosmological spacetimes. The standard model of cosmology is based on the Friedman-Robertson-Walker spacetimes; these spacetimes are the spatially homogeneous and isotropic solutions of Einstein's equation. The idea of smoothing provides a framework for the use of Friedman-Robertson-Walker spacetimes as approximations to more realistic inhomogeneous spacetimes. An explicit smoothing procedure is examined which is based on smoothing initial data via the Ricci flow equation. The existence and convergence results are proved for the Ricci flows with initial data taken as the spatial three-metrics of certain Bianchi spacetimes and certain Gowdy spacetimes. The results allow consideration of the Bianchi and Gowdy spacetimes as testing grounds for this specific smoothing scheme. The second study pertains to the global existence problem in general relativity. Energy methods are known to be useful in global existence problem; the Bel-Robinson (BR) energy may play the role of an energy norm for general relativity. The evolution of the BR energy was studied in Gowdy T(sup 3) x R spacetimes. A quantity closely related to the BR energy decay monotonically as the spacetime evolves toward the final singularity, except in the special case of Kasner data, for which this quantity is constant.
A Detailed Evaluation of a Laser Triangulation Ranging System for Mobile Robots
1983-08-01
A RPI TECHNICAL REPORT MP-82 A DETAILED EVALUATION OF A LASER - TRIANGULATION RANGING SYSTEM FOR MOBILE ROBOTS by Thomas J. Clement Contract MDA-903...ML/MD VISION SYSTEM THEORY............................... 7 2.1 Laser Triangulation......................................... 7 2.1.1 ML/MD Vision...System Accuracy Factors..................10 2.1.2 Detector "Cone of Vision" Problem ..................... 10 2. 1.3 Laser Triangulation Justification
3D vesicle dynamics simulations with a linearly triangulated surface
NASA Astrophysics Data System (ADS)
Boedec, G.; Leonetti, M.; Jaeger, M.
2011-02-01
Simulations of biomembranes have gained an increasing interest in the past years. Specificities of these membranes propose new challenges for the numerics. In particular, vesicle dynamics are governed by bending forces as well as a surface incompressibility constraint. A method to compute the bending force density resultant onto piecewise linearly triangulated surface meshes is described. This method is coupled with a boundary element method solver for inner and outer fluids, to compute vesicle dynamics under external flows. The surface incompressibility constraint is satisfied by the construction of a projection operator.
On-line metrology with conoscopic holography: beyond triangulation.
Alvarez, Ignacio; Enguita, Jose M; Frade, María; Marina, Jorge; Ojea, Guillermo
2009-01-01
On-line non-contact surface inspection with high precision is still an open problem. Laser triangulation techniques are the most common solution for this kind of systems, but there exist fundamental limitations to their applicability when high precisions, long standoffs or large apertures are needed, and when there are difficult operating conditions. Other methods are, in general, not applicable in hostile environments or inadequate for on-line measurement. In this paper we review the latest research in Conoscopic Holography, an interferometric technique that has been applied successfully in this kind of applications, ranging from submicrometric roughness measurements, to long standoff sensors for surface defect detection in steel at high temperatures.
A hand-held triangulation sensor for small features measurement
NASA Astrophysics Data System (ADS)
Abramovich, Gil; Harding, Kevin
2010-11-01
This paper describes progressive generations of hand held triangulation sensors for measuring small features, from edge breaks to corrosion pits. We describe the design considerations, ergonomics, packaging and interface between the device and part, such as the sensor tip and optional fixtures. We then present a customized design to address different types of surface features and defects. Next, we present the calibration concept, and its execution. The paper closes by summarizing system performance evaluation experiments and their results. It was shown that the system is capable of measuring edges down to a radius of 250 microns at a repeatability of 50 microns.
Hex-dominant mesh generation using 3D constrained triangulation
OWEN,STEVEN J.
2000-05-30
A method for decomposing a volume with a prescribed quadrilateral surface mesh, into a hexahedral-dominated mesh is proposed. With this method, known as Hex-Morphing (H-Morph), an initial tetrahedral mesh is provided. Tetrahedral are transformed and combined starting from the boundary and working towards the interior of the volume. The quadrilateral faces of the hexahedra are treated as internal surfaces, which can be recovered using constrained triangulation techniques. Implementation details of the edge and face recovery process are included. Examples and performance of the H-Morph algorithm are also presented.
Spacetime stereo: a unifying framework for depth from triangulation.
Davis, James; Nehab, Diego; Ramamoorthi, Ravi; Rusinkiewicz, Szymon
2005-02-01
Depth from triangulation has traditionally been investigated in a number of independent threads of research, with methods such as stereo, laser scanning, and coded structured light considered separately. In this paper, we propose a common framework called spacetime stereo that unifies and generalizes many of these previous methods. To show the practical utility of the framework, we develop two new algorithms for depth estimation: depth from unstructured illumination change and depth estimation in dynamic scenes. Based on our analysis, we show that methods derived from the spacetime stereo framework can be used to recover depth in situations in which existing methods perform poorly.
Trees of Nuclei and Bounds on the Number of Triangulations of the 3-Ball
NASA Astrophysics Data System (ADS)
Collet, P.; Eckmann, J.-P.; Younan, M.
2014-01-01
Based on the work of Durhuus-Jónsson and Benedetti-Ziegler, we revisit the question of the number of triangulations of the 3-ball. We introduce a notion of nucleus (a triangulation of the 3-ball without internal nodes, and with each internal face having at most 1 external edge). We show that every triangulation can be built from trees of nuclei. This leads to a new reformulation of this question: We show that if the number of rooted nuclei with t tetrahedra has a bound of the form C t , then the number of rooted triangulations with t tetrahedra is bounded by.
An ancient revisits cosmology.
Greenstein, J L
1993-01-01
In this after-dinner speech, a somewhat light-hearted attempt is made to view the observational side of physical cosmology as a subdiscipline of astrophysics, still in an early stage of sophistication and in need of more theoretical understanding. The theoretical side of cosmology, in contrast, has its deep base in general relativity. A major result of observational cosmology is that an expansion of the Universe arose from a singularity some 15 billion years ago. This has had an enormous impact on the public's view of both astronomy and theology. It places on cosmologists an extra responsibility for clear thinking and interpretation. Recently, gravitational physics caused another crisis from an unexpected observational result that nonbaryonic matter appears to dominate. Will obtaining information about this massive nonbaryonic component require that astronomers cease to rely on measurement of photons? But 40 years ago after radio astronomical techniques uncovered the high-energy universe, we happily introduced new subfields, with techniques from physics and engineering still tied to photon detection. Another historical example shows how a subfield of cosmology, big bang nucleosynthesis, grew in complexity from its spectroscopic astrophysics beginning 40 years ago. Determination of primordial abundances of lighter nuclei does illuminate conditions in the Big Bang, but the observational results faced and overcame many hurdles on the way. PMID:11607403
Coc, Alain
2014-05-09
There are important aspects of Cosmology, the scientific study of the large scale properties of the universe as a whole, for which nuclear physics can provide insights. Here, we will focus on Standard Big-Bang Nucleosynthesis and we refer to the previous edition of the School [1] for the aspects concerning the variations of constants in nuclear cosmo-physics.
Ekpyrotic and cyclic cosmology
NASA Astrophysics Data System (ADS)
Lehners, Jean-Luc
2008-09-01
Ekpyrotic and cyclic cosmologies provide theories of the very early and of the very late universe. In these models, the big bang is described as a collision of branes — and thus the big bang is not the beginning of time. Before the big bang, there is an ekpyrotic phase with equation of state w=Pρ≫1 (where P is the average pressure and ρ the average energy density) during which the universe slowly contracts. This phase resolves the standard cosmological puzzles and generates a nearly scale-invariant spectrum of cosmological perturbations containing a significant non-Gaussian component. At the same time it produces small-amplitude gravitational waves with a blue spectrum. The dark energy dominating the present-day cosmological evolution is reinterpreted as a small attractive force between our brane and a parallel one. This force eventually induces a new ekpyrotic phase and a new brane collision, leading to the idea of a cyclic universe. This review discusses the detailed properties of these models, their embedding in M-theory and their viability, with an emphasis on open issues and observational signatures.
An ancient revisits cosmology.
Greenstein, J L
1993-06-01
In this after-dinner speech, a somewhat light-hearted attempt is made to view the observational side of physical cosmology as a subdiscipline of astrophysics, still in an early stage of sophistication and in need of more theoretical understanding. The theoretical side of cosmology, in contrast, has its deep base in general relativity. A major result of observational cosmology is that an expansion of the Universe arose from a singularity some 15 billion years ago. This has had an enormous impact on the public's view of both astronomy and theology. It places on cosmologists an extra responsibility for clear thinking and interpretation. Recently, gravitational physics caused another crisis from an unexpected observational result that nonbaryonic matter appears to dominate. Will obtaining information about this massive nonbaryonic component require that astronomers cease to rely on measurement of photons? But 40 years ago after radio astronomical techniques uncovered the high-energy universe, we happily introduced new subfields, with techniques from physics and engineering still tied to photon detection. Another historical example shows how a subfield of cosmology, big bang nucleosynthesis, grew in complexity from its spectroscopic astrophysics beginning 40 years ago. Determination of primordial abundances of lighter nuclei does illuminate conditions in the Big Bang, but the observational results faced and overcame many hurdles on the way.
Consistency relation in cosmology
Chiba, Takeshi; Takahashi, Ryuichi
2007-05-15
We provide a consistency relation between cosmological observables in general relativity without relying on the equation of state of dark energy. The consistency relation should be satisfied if general relativity is the correct theory of gravity and dark energy clustering is negligible. As an extension, we also provide the DGP counterpart of the relation.
Sefusatti, Emiliano; Crocce, Martin; Pueblas, Sebastian; Scoccimarro, Roman; /CCPP, New York
2006-04-01
The present spatial distribution of galaxies in the Universe is non-Gaussian, with 40% skewness in 50 h{sup -1} Mpc spheres, and remarkably little is known about the information encoded in it about cosmological parameters beyond the power spectrum. In this work they present an attempt to bridge this gap by studying the bispectrum, paying particular attention to a joint analysis with the power spectrum and their combination with CMB data. They address the covariance properties of the power spectrum and bispectrum including the effects of beat coupling that lead to interesting cross-correlations, and discuss how baryon acoustic oscillations break degeneracies. They show that the bispectrum has significant information on cosmological parameters well beyond its power in constraining galaxy bias, and when combined with the power spectrum is more complementary than combining power spectra of different samples of galaxies, since non-Gaussianity provides a somewhat different direction in parameter space. In the framework of flat cosmological models they show that most of the improvement of adding bispectrum information corresponds to parameters related to the amplitude and effective spectral index of perturbations, which can be improved by almost a factor of two. Moreover, they demonstrate that the expected statistical uncertainties in {sigma}s of a few percent are robust to relaxing the dark energy beyond a cosmological constant.
Quantifying concordance in cosmology
NASA Astrophysics Data System (ADS)
Seehars, Sebastian; Grandis, Sebastian; Amara, Adam; Refregier, Alexandre
2016-05-01
Quantifying the concordance between different cosmological experiments is important for testing the validity of theoretical models and systematics in the observations. In earlier work, we thus proposed the Surprise, a concordance measure derived from the relative entropy between posterior distributions. We revisit the properties of the Surprise and describe how it provides a general, versatile, and robust measure for the agreement between data sets. We also compare it to other measures of concordance that have been proposed for cosmology. As an application, we extend our earlier analysis and use the Surprise to quantify the agreement between WMAP 9, Planck 13, and Planck 15 constraints on the Λ CDM model. Using a principle component analysis in parameter space, we find that the large Surprise between WMAP 9 and Planck 13 (S =17.6 bits, implying a deviation from consistency at 99.8% confidence) is due to a shift along a direction that is dominated by the amplitude of the power spectrum. The Planck 15 constraints deviate from the Planck 13 results (S =56.3 bits), primarily due to a shift in the same direction. The Surprise between WMAP and Planck consequently disappears when moving to Planck 15 (S =-5.1 bits). This means that, unlike Planck 13, Planck 15 is not in tension with WMAP 9. These results illustrate the advantages of the relative entropy and the Surprise for quantifying the disagreement between cosmological experiments and more generally as an information metric for cosmology.
Relativistic cosmology. Proceedings.
NASA Astrophysics Data System (ADS)
Sasaki, M.
The symposium was intended to present in-depth reviews of the problems and prospects of present-day cosmology. The topics covered were the inflationary universe, the large scale structure of the universe, gravitational lenses, black hole physics, numerical relativity, gravitational waves and related subjects.
Culture and Children's Cosmology
ERIC Educational Resources Information Center
Siegal, Michael; Butterworth, George; Newcombe, Peter A.
2004-01-01
In this investigation, we examined children's knowledge of cosmology in relation to the shape of the earth and the day-night cycle. Using explicit questioning involving a choice of alternative answers and 3D models, we carried out a comparison of children aged 4-9 years living in Australia and England. Though Australia and England have a close…
Gravitational lensing in cosmology
NASA Astrophysics Data System (ADS)
Futamase, Toshifumi
2015-02-01
Gravitational lensing is a unique and direct probe of mass in the universe. It depends only on the law of gravity and does not depend on the dynamical state nor the composition of matter. Thus, it is used to study the distribution of the dark matter in the lensing object. Combined with the traditional observations such as optical and X-ray, it gives us useful informations of the structure formation in the universe. The lensing observables depend also on the global geometry as well as large scale structure of the universe. Therefore it is possible to withdraw useful constraints on the cosmological parameters once the distribution of lensing mass is accurately known. Since the first discovery of the lensing event by a galaxy in 1979, various kinds of lensing phenomena caused by star, galaxy, cluster of galaxies and large scale structure have been observed and are used to study mass distribution in various scales and cosmology. Thus, the gravitational lensing is now regarded as an indispensable research field in the observational cosmology. In this paper, we give an instructive introduction to gravitational lensing and its applications to cosmology.
Culture and Children's Cosmology
ERIC Educational Resources Information Center
Siegal, Michael; Butterworth, George; Newcombe, Peter A.
2004-01-01
In this investigation, we examined children's knowledge of cosmology in relation to the shape of the earth and the day-night cycle. Using explicit questioning involving a choice of alternative answers and 3D models, we carried out a comparison of children aged 4-9 years living in Australia and England. Though Australia and England have a close…
Projective relativity, cosmology and gravitation
Arcidiacono, G.
1986-01-01
This book describes the latest applications of projective geometry to cosmology and gravitation. The contents of the book are; the Poincare group and Special Relativity, the thermodynamics and electromagnetism, general relativity, gravitation and cosmology, group theory and models of universe, the special projective relativity, the Fantappie group and Big-Bang cosmology, a new cosmological projective mechanics, the plasma physics and cosmology, the projective magnetohydrodynamics field, projective relativity and waves propagation, the generalizations of the gravitational field, the general projective relativity, the projective gravitational field, the De Sitter Universe and quantum physics, the conformal relativity and Newton gravitation.
Future non-linear stability for solutions of the Einstein-Vlasov system of Bianchi types II and VI0
NASA Astrophysics Data System (ADS)
Nungesser, Ernesto
2012-10-01
In a recent paper [E. Nungesser, "Future non-linear stability for reflection symmetric solutions of the Einstein-Vlasov system of Bianchi types II and VI0," Annales Henri Poincare (2012), 10.1007/s00023-012-0201-0], we have treated the future nonlinear stability for reflection symmetric solutions of the Einstein-Vlasov system of Bianchi types II and VI0. We have been able now to remove the reflection symmetry assumption, thus treating the non-diagonal case. Apart from the increasing complexity, the methods have been essentially the same as in the diagonal case, showing that they are thus quite powerful. Here, the challenge was to put the equations in a form that permits the use of the previous results. We are able to conclude that after a possible basis change, the future of the non-diagonal spacetimes in consideration is asymptotically diagonal.
NASA Astrophysics Data System (ADS)
Katore, S. D.; Kapse, D. V.
2017-02-01
In this paper, we have studied the anisotropic and homogeneous Bianchi type-VI 0 Universe filled with dark matter and holographic dark energy components in the framework of general relativity and Lyra's geometry. The Einstein's field equations have been solved exactly by taking the expansion scalar ( 𝜃) in the model is proportional to the shear scalar ( σ). Some physical and kinematical properties of the models are also discussed.
NASA Astrophysics Data System (ADS)
Lee, Ho; Nungesser, Ernesto
2017-06-01
In this paper we study the Einstein-Boltzmann system with Bianchi I symmetry. We show that for small initial data the corresponding solutions of the Einstein-Boltzmann system are future geodesically complete and that they isotropize and have a dust-like behaviour at late times. Detailed information about the metric and the matter terms is obtained, and the results show that the solutions tend asymptotically to the Einstein-de Sitter solution.
Three-Dimensional Reconstruction Optical System Using Shadows Triangulation
NASA Astrophysics Data System (ADS)
Barba, J. Leiner; Vargas, Q. Lorena; Torres, M. Cesar; Mattos, V. Lorenzo
2008-04-01
In this work is developed a three-dimensional reconstruction system using the Shades3D tool of the Matlab® Programming Language and materials of low cost, such as webcam camera, a stick, a weak structured lighting system composed by a desk lamp, and observation plane in which the object is located. The reconstruction is obtained through a triangulation process that is executed after acquiring a sequence of images of the scene with a shadow projected on the object; additionally an image filtering process is done for obtaining only the part of the scene that will be reconstructed. Previously, it is necessary to develop a calibration process for determining the internal camera geometric and optical characteristics (intrinsic parameters), and the 3D position and orientation of the camera frame relative to a certain world coordinate system (extrinsic parameters). The lamp and the stick are used to produce a shadow which scans the object; in this technique, it is not necessary to know the position of the light source, instead the triangulation is obtained using shadow plane produced by intersection between the stick and the illumination pattern. The webcam camera captures all images with the shadow scanning the object, and Shades3D tool processes all information taking into account captured images and calibration parameters. Likewise, this technique is evaluated in the reconstruction of parts of the human body and its application in the detection of external abnormalities and elaboration of prosthesis or implant.
Computing 2D constrained delaunay triangulation using the GPU.
Qi, Meng; Cao, Thanh-Tung; Tan, Tiow-Seng
2013-05-01
We propose the first graphics processing unit (GPU) solution to compute the 2D constrained Delaunay triangulation (CDT) of a planar straight line graph (PSLG) consisting of points and edges. There are many existing CPU algorithms to solve the CDT problem in computational geometry, yet there has been no prior approach to solve this problem efficiently using the parallel computing power of the GPU. For the special case of the CDT problem where the PSLG consists of just points, which is simply the normal Delaunay triangulation (DT) problem, a hybrid approach using the GPU together with the CPU to partially speed up the computation has already been presented in the literature. Our work, on the other hand, accelerates the entire computation on the GPU. Our implementation using the CUDA programming model on NVIDIA GPUs is numerically robust, and runs up to an order of magnitude faster than the best sequential implementations on the CPU. This result is reflected in our experiment with both randomly generated PSLGs and real-world GIS data having millions of points and edges.
Triangulation of the Gigantic Jets in 20 August 2014
NASA Astrophysics Data System (ADS)
Kang-Ming, P.; Hsu, R. R.; Su, H. T.; Chen, A. B. C.; Chou, J. K.; Chang, S. C.; Wu, Y. J.; Chien-Lun, H.; Yang, I. C.; Tsai, S. H.
2015-12-01
Coordinate optical observation campaigns on TLEs near Taiwan are held since 2011 with the aim to triangulate TLEs. Currently, there are four stations with baseline varying from 100 to 400 km between them. Our optical observation systems recorded 48 various types of TLEs on the night of 20 August 2014, with eight of them being gigantic jets that were recorded by at least two stations. Due to the length of baselines and the TLE occurring locations, the earth curvature needed to be taken into account by means of spherical trigonometry method. The preliminary results shows the gigantic jets occurred over the northern Taiwan and the accuracy of geolocation is less than 1 km and the accuracy of the retrieval height on the key structures is less than 0.5 km. The triangulation results of the eight events indicate most of these gigantic jets terminated at 80-90km, but one of the gigantic jets is likely extend to 100 km. Three of the eight gigantic jets occurred consequently after previous one with time interval of 500ms to more than 100s. The previous gigantic jet is likely to influence the consequent gigantic jet for usually the consequent gigantic jet has more beads structures in high altitude and one of the streamer column of a consequent gigantic jets at 55 -60 km is identified to re-bright, which is more than 100s after the previous gigantic jet.
a Modified Method for Image Triangulation Using Inclined Angles
NASA Astrophysics Data System (ADS)
Alsadik, Bashar
2016-06-01
The ongoing technical improvements in photogrammetry, Geomatics, computer vision (CV), and robotics offer new possibilities for many applications requiring efficient acquisition of three-dimensional data. Image orientation is one of these important techniques in many applications like mapping, precise measurements, 3D modeling and navigation. Image orientation comprises three main techniques of resection, intersection (triangulation) and relative orientation, which are conventionally solved by collinearity equations or by using projection and fundamental matrices. However, different problems still exist in the state - of -the -art of image orientation because of the nonlinearity and the sensitivity to proper initialization and spatial distribution of the points. In this research, a modified method is presented to solve the triangulation problem using inclined angles derived from the measured image coordinates and based on spherical trigonometry rules and vector geometry. The developed procedure shows promising results compared to collinearity approach and to converge to the global minimum even when starting from far approximations. This is based on the strong geometric constraint offered by the inclined angles that are enclosed between the object points and the camera stations. Numerical evaluations with perspective and panoramic images are presented and compared with the conventional solution of collinearity equations. The results show the efficiency of the developed model and the convergence of the solution to global minimum even with improper starting values.
Identification of Novel Autoantigens by a Triangulation Approach
Cottrell, Tricia R.; Hall, John C.; Rosen, Antony; Casciola-Rosen, Livia
2012-01-01
High titer autoantibodies, which are often associated with specific clinical phenotypes, are useful diagnostically and prognostically in systemic autoimmune diseases. In several autoimmune rheumatic diseases (e.g. myositis and Sjogren’s syndrome), 20–40% of patients are autoantibody negative as assessed by conventional assays. The recent discovery of new specificities (e.g., anti-MDA5) in a subset of these autoantibody-negative subjects demonstrates that additional specificities await identification. In this manuscript, we describe a rapid multidimensional method to identify new autoantigens. A central foundation of this rapid approach is the use of an antigen source in which a pathogenic pathway active in the disease is recapitulated. Additionally, the method involves a modified serological proteome analysis strategy which allows confirmation that the correct gel plug has been removed prior to sending for sequencing. Lastly, the approach uses multiple sources of information to enable rapid triangulation and identification of protein candidates. Possible permutations and underlying principles of this triangulation strategy are elaborated to demonstrate the broad utility of this approach for antigen discovery. PMID:22910000
Identification of novel autoantigens by a triangulation approach.
Cottrell, Tricia R; Hall, John C; Rosen, Antony; Casciola-Rosen, Livia
2012-11-30
High titer autoantibodies, which are often associated with specific clinical phenotypes, are useful diagnostically and prognostically in systemic autoimmune diseases. In several autoimmune rheumatic diseases (e.g. myositis and Sjogren's syndrome), 20-40% of patients are autoantibody negative as assessed by conventional assays. The recent discovery of new specificities (e.g., anti-MDA5) in a subset of these autoantibody-negative subjects demonstrates that additional specificities await identification. In this manuscript, we describe a rapid multidimensional method to identify new autoantigens. A central foundation of this rapid approach is the use of an antigen source in which a pathogenic pathway active in the disease is recapitulated. Additionally, the method involves a modified serological proteome analysis strategy which allows confirmation that the correct gel plug has been removed prior to sending for sequencing. Lastly, the approach uses multiple sources of information to enable rapid triangulation and identification of protein candidates. Possible permutations and underlying principles of this triangulation strategy are elaborated to demonstrate the broad utility of this approach for antigen discovery. Copyright © 2012 Elsevier B.V. All rights reserved.
Experiences with systematic triangulation at the Global Environment Facility.
Carugi, Carlo
2016-04-01
Systematic triangulation may address common challenges in evaluation, such as the scarcity or unreliability of data, or the complexities of comparing and cross-checking evidence from diverse disciplines. Used to identify key evaluation findings, its application has proven to be effective in addressing the limitations encountered in country-level evaluation analysis conducted by the Independent Evaluation Office of the Global Environment Facility (GEF). These include the scarcity or unreliability of national statistics on environmental indicators and data series, especially in Least Developed Countries; challenges in evaluating the impacts of GEF projects; and inherent difficulties in defining the GEF portfolio of projects prior to the undertaking of the evaluation. In addition to responding to the need for further developing triangulation protocols, procedures and/or methodologies advocated by some authors, the approach offers a contribution to evaluation practice. This applies particularly to those evaluation units tasked with country-level evaluations in international organizations, facing similar constraints. Copyright © 2015 Elsevier Ltd. All rights reserved.
The finite body triangulation: algorithms, subgraphs, homogeneity estimation and application.
Carson, Cantwell G; Levine, Jonathan S
2016-09-01
The concept of a finite body Dirichlet tessellation has been extended to that of a finite body Delaunay 'triangulation' to provide a more meaningful description of the spatial distribution of nonspherical secondary phase bodies in 2- and 3-dimensional images. A finite body triangulation (FBT) consists of a network of minimum edge-to-edge distances between adjacent objects in a microstructure. From this is also obtained the characteristic object chords formed by the intersection of the object boundary with the finite body tessellation. These two sets of distances form the basis of a parsimonious homogeneity estimation. The characteristics of the spatial distribution are then evaluated with respect to the distances between objects and the distances within them. Quantitative analysis shows that more physically representative distributions can be obtained by selecting subgraphs, such as the relative neighbourhood graph and the minimum spanning tree, from the finite body tessellation. To demonstrate their potential, we apply these methods to 3-dimensional X-ray computed tomographic images of foamed cement and their 2-dimensional cross sections. The Python computer code used to estimate the FBT is made available. Other applications for the algorithm - such as porous media transport and crack-tip propagation - are also discussed. © 2016 The Authors Journal of Microscopy © 2016 Royal Microscopical Society.
Dynamic ray tracing and its application in triangulated media
Rueger, A.
1993-07-01
Hale and Cohen (1991) developed software to generate two-dimensional computer models of complex geology. Their method uses a triangulation technique designed to support efficient and accurate computation of seismic wavefields for models of the earth`s interior. Subsequently, Hale (1991) used this triangulation approach to perform dynamic ray tracing and create synthetic seismograms based on the method of Gaussian beams. Here, I extend this methodology to allow an increased variety of ray-theoretical experiments. Specifically, the developed program GBmod (Gaussian Beam MODeling) can produce arbitrary multiple sequences and incorporate attenuation and density variations. In addition, I have added an option to perform Fresnel-volume ray tracing (Cerveny and Soares, 1992). Corrections for reflection and transmission losses at interfaces, and for two-and-one-half-dimensional (2.5-D) spreading are included. However, despite these enhancements, difficulties remain in attempts to compute accurate synthetic seismograms if strong lateral velocity inhomogeneities are present. Here, these problems are discussed and, to a certain extent, reduced. I provide example computations of high-frequency seismograms based on the method of Gaussian beams to exhibit the advantages and disadvantages of the proposed modeling method and illustrate new features for both surface and vertical seismic profiling (VSP) acquisition geometries.
Solving the horizontal conflation problem with a constrained Delaunay triangulation
NASA Astrophysics Data System (ADS)
Ledoux, Hugo; Ohori, Ken Arroyo
2017-01-01
Datasets produced by different countries or organisations are seldom properly aligned and contain several discrepancies (e.g., gaps and overlaps). This problem has been so far almost exclusively tackled by snapping vertices based on a user-defined threshold. However, as we argue in this paper, this leads to invalid geometries, is error-prone, and leaves several discrepancies along the boundaries. We propose a novel algorithm to align the boundaries of adjacent datasets. It is based on a constrained Delaunay triangulation to identify and eliminate the discrepancies, and the alignment is performed without moving vertices with a snapping operator. This allows us to guarantee that the datasets have been properly conflated and that the polygons are geometrically valid. We present our algorithm, our implementation (based on the stable and fast triangulator in CGAL), and we show how it can be used it practice with different experiments with real-world datasets. Our experiments demonstrate that our approach is highly efficient and that it yields better results than snapping-based methods.
Automated Photogrammetric Image Matching with Sift Algorithm and Delaunay Triangulation
NASA Astrophysics Data System (ADS)
Karagiannis, Georgios; Antón Castro, Francesc; Mioc, Darka
2016-06-01
An algorithm for image matching of multi-sensor and multi-temporal satellite images is developed. The method is based on the SIFT feature detector proposed by Lowe in (Lowe, 1999). First, SIFT feature points are detected independently in two images (reference and sensed image). The features detected are invariant to image rotations, translations, scaling and also to changes in illumination, brightness and 3-dimensional viewpoint. Afterwards, each feature of the reference image is matched with one in the sensed image if, and only if, the distance between them multiplied by a threshold is shorter than the distances between the point and all the other points in the sensed image. Then, the matched features are used to compute the parameters of the homography that transforms the coordinate system of the sensed image to the coordinate system of the reference image. The Delaunay triangulations of each feature set for each image are computed. The isomorphism of the Delaunay triangulations is determined to guarantee the quality of the image matching. The algorithm is implemented in Matlab and tested on World-View 2, SPOT6 and TerraSAR-X image patches.
Tapping Teacher Thinking through Triangulation of Data Sets. R&D Rep. No. 8014.
ERIC Educational Resources Information Center
Morine-Dershimer, Greta
Validity is a central issue in use of self-report data for the investigation of teacher thinking. "Triangulation," or use of several data sets to test, corroborate and elaborate each other, is one method for increasing validity of findings. This paper illustrates a process of triangulation of data obtained by three different data…
An advancing-front Delaunay-triangulation algorithm designed for robustness
NASA Technical Reports Server (NTRS)
Mavriplis, D. J.
1993-01-01
The following topics, which are associated with computational fluid dynamics, are discussed: unstructured mesh generation; the advancing front methodology; failures of the advancing front methodology; Delaunay triangulation; the Tanamua-Merriam algorithm; Yet Another Grid Generator (YAGG); and advancing front-Delaunay triangulation. The discussion is presented in viewgraph form.
The Differential Impact of Parental Warmth on Externalizing Problems among Triangulated Adolescents
Etkin, R. G.; Koss, K. J.; Cummings, E. M.; Davies, P. T.
2013-01-01
Triangulation is a family-wide process in which children are inappropriately involved in interparental conflict, placing them at heightened risk for adjustment problems. A common form of triangulation occurs by parents pressuring their children to take sides, which may result in feelings of being “torn” between parents. Externalizing behaviors in particular may develop as adolescents feel caught in the middle of conflict and forced to choose a side. However, the nature of the triadic process of triangulation may be impacted by dyadic-level relationships within the family. The present study thus explores how positive parenting processes may alter the relations between triangulation and adolescent externalizing problems. Mothers, fathers, and adolescents (n = 301 families) provided assessments of adolescent externalizing problems, triangulation, and maternal and paternal warmth. Analyses revealed a three-way interaction between triangulation and maternal and paternal warmth predicting adolescent externalizing problems; child gender also moderated these relations. Among highly triangulated youth, boys displayed increased externalizing problems when both parents exhibited low or high warmth whereas girls showed increased behavior problems in the context of low maternal but high paternal warmth. These findings indicate the importance of examining the broader family context and gender when considering the impact of triangulation during adolescence. PMID:24796159
Brans-Dicke cosmology with time-dependent cosmological term
NASA Astrophysics Data System (ADS)
Berman, Marcelo Samuel
1990-12-01
Berman and Som's solution for a Brans-Dicke cosmology with time-dependent cosmological term, Robertson-Walker metric, perfect fluid, and perfect gas law of state solves the horizon, homogeneity, and isotropy problems without requiring any unnatural fine tuning in the very early universe, thus being an alternative model to inflation. The model also does not need recourse to quantum cosmology, and solves the flatness and magnetic monopole problems.
Nonlocal teleparallel cosmology.
Bahamonde, Sebastian; Capozziello, Salvatore; Faizal, Mir; Nunes, Rafael C
2017-01-01
Even though it is not possible to differentiate general relativity from teleparallel gravity using classical experiments, it could be possible to discriminate between them by quantum gravitational effects. These effects have motivated the introduction of nonlocal deformations of general relativity, and similar effects are also expected to occur in teleparallel gravity. Here, we study nonlocal deformations of teleparallel gravity along with its cosmological solutions. We observe that nonlocal teleparallel gravity (like nonlocal general relativity) is consistent with the present cosmological data obtained by SNe Ia + BAO + CC + [Formula: see text] observations. Along this track, future experiments probing nonlocal effects could be used to test whether general relativity or teleparallel gravity gives the most consistent picture of gravitational interaction.
Discrete Newtonian cosmology: perturbations
NASA Astrophysics Data System (ADS)
Ellis, George F. R.; Gibbons, Gary W.
2015-03-01
In a previous paper (Gibbons and Ellis 2014 Discrete Newtonian cosmology Class. Quantum Grav. 31 025003), we showed how a finite system of discrete particles interacting with each other via Newtonian gravitational attraction would lead to precisely the same dynamical equations for homothetic motion as in the case of the pressure-free Friedmann-Lemaître-Robertson-Walker cosmological models of general relativity theory, provided the distribution of particles obeys the central configuration equation. In this paper we show that one can obtain perturbed such Newtonian solutions that give the same linearized structure growth equations as in the general relativity case. We also obtain the Dmitriev-Zel’dovich equations for subsystems in this discrete gravitational model, and show how it leads to the conclusion that voids have an apparent negative mass.
NASA Astrophysics Data System (ADS)
Tsamis, N. C.; Woodard, R. P.
2016-08-01
We study a class of nonlocal, action-based, and purely gravitational models. These models seek to describe a cosmology in which inflation is driven by a large, bare cosmological constant that is screened by the self-gravitation between the soft gravitons that inflation rips from the vacuum. Inflation ends with the Universe poised on the verge of gravitational collapse, in an oscillating phase of expansion and contraction that should lead to rapid reheating when matter is included. After the attainment of a hot, dense Universe the nonlocal screening terms become constant as the Universe evolves through a conventional phase of radiation domination. The onset of matter domination triggers a much smaller antiscreening effect that could explain the current phase of acceleration.
NASA Astrophysics Data System (ADS)
Merritt, David
2017-02-01
I argue that some important elements of the current cosmological model are "conventionalist" in the sense defined by Karl Popper. These elements include dark matter and dark energy; both are auxiliary hypotheses that were invoked in response to observations that falsified the standard model as it existed at the time. The use of conventionalist stratagems in response to unexpected observations implies that the field of cosmology is in a state of 'degenerating problemshift' in the language of Imre Lakatos. I show that the 'concordance' argument, often put forward by cosmologists in support of the current paradigm, is weaker than the convergence arguments that were made in the past in support of the atomic theory of matter or the quantization of energy.
Cosmology with hypervelocity stars
Loeb, Abraham
2011-04-01
In the standard cosmological model, the merger remnant of the Milky Way and Andromeda (Milkomeda) will be the only galaxy remaining within our event horizon once the Universe has aged by another factor of ten, ∼ 10{sup 11} years after the Big Bang. After that time, the only extragalactic sources of light in the observable cosmic volume will be hypervelocity stars being ejected continuously from Milkomeda. Spectroscopic detection of the velocity-distance relation or the evolution in the Doppler shifts of these stars will allow a precise measurement of the vacuum mass density as well as the local matter distribution. Already in the near future, the next generation of large telescopes will allow photometric detection of individual stars out to the edge of the Local Group, and may target the ∼ 10{sup 5±1} hypervelocity stars that originated in it as cosmological tracers.
NASA Astrophysics Data System (ADS)
Hobson, Michael P.; Jaffe, Andrew H.; Liddle, Andrew R.; Mukherjee, Pia; Parkinson, David
2009-12-01
Preface; Part I. Methods: 1. Foundations and algorithms John Skilling; 2. Simple applications of Bayesian methods D. S. Sivia and Steve Rawlings; 3. Parameter estimation using Monte Carlo sampling Antony Lewis and Sarah Bridle; 4. Model selection and multi-model interference Andrew R. Liddle, Pia Mukherjee and David Parkinson; 5. Bayesian experimental design and model selection forecasting Roberto Trotta, Martin Kunz, Pia Mukherjee and David Parkinson; 6. Signal separation in cosmology M. P. Hobson, M. A. J. Ashdown and V. Stolyarov; Part II. Applications: 7. Bayesian source extraction M. P. Hobson, Graça Rocha and R. Savage; 8. Flux measurement Daniel Mortlock; 9. Gravitational wave astronomy Neil Cornish; 10. Bayesian analysis of cosmic microwave background data Andrew H. Jaffe; 11. Bayesian multilevel modelling of cosmological populations Thomas J. Loredo and Martin A. Hendry; 12. A Bayesian approach to galaxy evolution studies Stefano Andreon; 13. Photometric redshift estimation: methods and applications Ofer Lahav, Filipe B. Abdalla and Manda Banerji; Index.
Bojowald, Martin
2015-02-01
In quantum cosmology, one applies quantum physics to the whole universe. While no unique version and no completely well-defined theory is available yet, the framework gives rise to interesting conceptual, mathematical and physical questions. This review presents quantum cosmology in a new picture that tries to incorporate the importance of inhomogeneity. De-emphasizing the traditional minisuperspace view, the dynamics is rather formulated in terms of the interplay of many interacting 'microscopic' degrees of freedom that describe the space-time geometry. There is thus a close relationship with more-established systems in condensed-matter and particle physics even while the large set of space-time symmetries (general covariance) requires some adaptations and new developments. These extensions of standard methods are needed both at the fundamental level and at the stage of evaluating the theory by effective descriptions.
The Changing Cosmology Narrative
NASA Astrophysics Data System (ADS)
Eastman, T. E.
2009-12-01
The CBR discovery in 1965 was followed by successive triumphs for the Big Bang approach resulting in the current age of so-called "precision'' cosmology. I propose that the emerging data-rich environment is a game changer because it makes possible a major shift from a focus on theory and confirmation to observations, testing and potential falsification, and a shift from theory-driven claims of "precision'' cosmology to data-driven, multi-level testing of more limited and modest models. Greater flexibility in framing alternative hypotheses, and greater appreciation for rigorous data analysis unencumbered by preferred outcomes, may enable more critical assessments of grand theories that are at present excessively shielded from data-driven scrutiny.
Integrable cosmological potentials
NASA Astrophysics Data System (ADS)
Sokolov, V. V.; Sorin, A. S.
2017-05-01
The problem of classification of the Einstein-Friedman cosmological Hamiltonians H with a single scalar inflaton field φ, which possess an additional integral of motion polynomial in momenta on the shell of the Friedman constraint H=0 , is considered. Necessary and sufficient conditions for the existence of the first-, second- and third-degree integrals are derived. These conditions have the form of ODEs for the cosmological potential V(φ) . In the case of linear and quadratic integrals we find general solutions of the ODEs and construct the corresponding integrals explicitly. A new wide class of Hamiltonians that possess a cubic integral is derived. The corresponding potentials are represented in parametric form in terms of the associated Legendre functions. Six families of special elementary solutions are described, and sporadic superintegrable cases are discussed.
Culture and children's cosmology.
Siegal, Michael; Butterworth, George; Newcombe, Peter A
2004-06-01
In this investigation, we examined children's knowledge of cosmology in relation to the shape of the earth and the day-night cycle. Using explicit questioning involving a choice of alternative answers and 3D models, we carried out a comparison of children aged 4-9 years living in Australia and England Though Australia and England have a close cultural affinity, there are differences in children's early exposure to cosmological concepts. Australian children who have early instruction in this domain were nearly always significantly in advance of their English counterparts. In general, they most often produced responses compatible with a conception of a round earth on which people can live all over without falling off. We consider coherence and fragmentation in children's knowledge in terms of the timing of culturally transmitted information, and in relation to questioning methods used in previous research that may have underestimated children's competence.
NASA Astrophysics Data System (ADS)
Tolish, Alexander; Wald, Robert M.
2016-08-01
The "memory effect" is the permanent change in the relative separation of test particles resulting from the passage of gravitational radiation. We investigate the memory effect for a general, spatially flat Friedmann-Lemaître-Robertson-Walker (FLRW) cosmology by considering the radiation associated with emission events involving particle-like sources. We find that if the resulting perturbation is decomposed into scalar, vector, and tensor parts, only the tensor part contributes to memory. Furthermore, the tensor contribution to memory depends only on the cosmological scale factor at the source and observation events, not on the detailed expansion history of the universe. In particular, for sources at the same luminosity distance, the memory effect in a spatially flat FLRW spacetime is enhanced over the Minkowski case by a factor of (1 +z ).
NASA Astrophysics Data System (ADS)
Bouchet, François R.
2015-08-01
Sketched out in 1992, selected by ESA in 1996, launched in 2009, Planck delivered a "definitive" map of the anisotropies of the Cosmic Microwave Background (CMB) as well as information on their polarisation. The CMB anisotropies, of rms ~100 microK in temperature, reveal the imprint of the primordial fluctuations which initiate the growth of the large scale structures of the Universe, as transformed by their evolution, in particular during the first 370 000 years. This evolution is governed by the Universe content at this early epoch. I will confront what temperature and polarisation anisotropies teach us, both in terms of content of the universe and of characteristics of the primordial fluctuations. I will also discuss the extent of the agreement of Planck cosmology with lower redshift cosmological probes like BAO, Weak Lensing or redshift space distortions. Submitted on behalf of the Planck Collaboration.
NASA Astrophysics Data System (ADS)
Feldbrugge, Job; Lehners, Jean-Luc; Turok, Neil
2017-05-01
We argue that the Lorentzian path integral is a better starting point for quantum cosmology than its Euclidean counterpart. In particular, we revisit the minisuperspace calculation of the Feynman path integral for quantum gravity with a positive cosmological constant. Instead of rotating to Euclidean time, we deform the contour of integration over metrics into the complex plane, exploiting Picard-Lefschetz theory to transform the path integral from a conditionally convergent integral into an absolutely convergent one. We show that this procedure unambiguously determines which semiclassical saddle point solutions are relevant to the quantum mechanical amplitude. Imposing "no-boundary" initial conditions, i.e., restricting attention to regular, complex metrics with no initial boundary, we find that the dominant saddle contributes a semiclassical exponential factor which is precisely the inverse of the famous Hartle-Hawking result.
NASA Astrophysics Data System (ADS)
Hobson, Michael P.; Jaffe, Andrew H.; Liddle, Andrew R.; Mukherjee, Pia; Parkinson, David
2014-02-01
Preface; Part I. Methods: 1. Foundations and algorithms John Skilling; 2. Simple applications of Bayesian methods D. S. Sivia and Steve Rawlings; 3. Parameter estimation using Monte Carlo sampling Antony Lewis and Sarah Bridle; 4. Model selection and multi-model interference Andrew R. Liddle, Pia Mukherjee and David Parkinson; 5. Bayesian experimental design and model selection forecasting Roberto Trotta, Martin Kunz, Pia Mukherjee and David Parkinson; 6. Signal separation in cosmology M. P. Hobson, M. A. J. Ashdown and V. Stolyarov; Part II. Applications: 7. Bayesian source extraction M. P. Hobson, Graça Rocha and R. Savage; 8. Flux measurement Daniel Mortlock; 9. Gravitational wave astronomy Neil Cornish; 10. Bayesian analysis of cosmic microwave background data Andrew H. Jaffe; 11. Bayesian multilevel modelling of cosmological populations Thomas J. Loredo and Martin A. Hendry; 12. A Bayesian approach to galaxy evolution studies Stefano Andreon; 13. Photometric redshift estimation: methods and applications Ofer Lahav, Filipe B. Abdalla and Manda Banerji; Index.
Gravitomagnetic amplification in cosmology
Tsagas, Christos G.
2010-02-15
Magnetic fields interact with gravitational waves in various ways. We consider the coupling between the Weyl and the Maxwell fields in cosmology and study the effects of the former on the latter. The approach is fully analytical and the results are gauge invariant. We show that the nature and the outcome of the gravitomagnetic interaction depends on the electric properties of the cosmic medium. When the conductivity is high, gravitational waves reduce the standard (adiabatic) decay rate of the B field, leading to its superadiabatic amplification. In poorly conductive environments, on the other hand, Weyl-curvature distortions can result into the resonant amplification of large-scale cosmological magnetic fields. Driven by the gravitational waves, these B fields oscillate with an amplitude that is found to diverge when the wavelengths of the two sources coincide. We present technical and physical aspects of the gravitomagnetic interaction and discuss its potential implications.
Cosmological element production.
Wagoner, R V
1967-03-17
Two recent observations appear to have provided critical information about the past history of the universe. The thermal character of the microwave background radiation suggests that the universe has expanded from a state of high temperature and density, and places constraints on such a big-bang cosmology. The observations of very weak helium lines in the spectra of certain stars in the halo of our galaxy are possibly due to a low primeval abundance of this element. However, the simplest model of a big-bang cosmology leads to much higher helium abundances, such as are observed in the solar system and in many stars. The production of helium can be reduced either by altering the early expansion rate or by introducing degenerate electron neutrinos. Observations of interstellar and intergalactic deuterium and He(4), and possibly even He(3) and Li(7), are needed to test the various models.
NASA Astrophysics Data System (ADS)
Kadota, Kenji; Stewart, Ewan D.
2003-07-01
We present a modular cosmology scenario where the difficulties encountered in conventional modular cosmology are solved in a self-consistent manner, with definite predictions to be tested by observation. Notably, the difficulty of the dilaton finding its way to a precarious weak coupling minimum is made irrelevant by having eternal modular inflation at the vacuum supersymmetry breaking scale after the dilaton is stabilised. Neither this eternal inflation nor the subsequent non-slow-roll modular inflation destabilise the dilaton from its precarious minimum due to the low energy scale of the inflation and consequent small back reaction on the dilaton potential. The observed flat CMB spectrum is obtained from fluctuations in the angular component of a modulus near a symmetric point, which are hugely magnified by the roll down of the modulus to Planckian values, allowing them to dominate the final curvature perturbation. We also give precise calculations of the spectral index and its running.
Barrow, J D
1977-05-12
An anisotropic, inhomogeneous cosmological model is proposed in which the inhomogeneity is generated by shear fluctuations. This is a sufficient condition for dissipative heating by collisional neutrinos to explain the present large heat content of the universe, S(b o) approximately 10(8), together with its isotropy and comparative homogeneity on large scales when the photons were last scattered. The model does not require the chaotic motions to be arbitrarily truncated on large scales and isotropises early enough with high entropy to ensure the synthesis of light elements with the observed abundancies. A population of black holes which arises in a natural way can also provide the necessary ingredients for a theory of galaxy formation and morphology. The 10(15)-g black holes, predicted by some authors, are not necessarily expected to be a feature of chaotic cosmologies.
Integrable cosmological potentials
NASA Astrophysics Data System (ADS)
Sokolov, V. V.; Sorin, A. S.
2017-09-01
The problem of classification of the Einstein-Friedman cosmological Hamiltonians H with a single scalar inflaton field φ, which possess an additional integral of motion polynomial in momenta on the shell of the Friedman constraint H=0, is considered. Necessary and sufficient conditions for the existence of the first-, second- and third-degree integrals are derived. These conditions have the form of ODEs for the cosmological potential V(φ). In the case of linear and quadratic integrals we find general solutions of the ODEs and construct the corresponding integrals explicitly. A new wide class of Hamiltonians that possess a cubic integral is derived. The corresponding potentials are represented in parametric form in terms of the associated Legendre functions. Six families of special elementary solutions are described, and sporadic superintegrable cases are discussed.
NASA Astrophysics Data System (ADS)
Merritt, David
2017-02-01
I argue that some important elements of the current cosmological model are 'conventionalist' in the sense defined by Karl Popper. These elements include dark matter and dark energy; both are auxiliary hypotheses that were invoked in response to observations that falsified the standard model as it existed at the time. The use of conventionalist stratagems in response to unexpected observations implies that the field of cosmology is in a state of 'degenerating problemshift' in the language of Imre Lakatos. I show that the 'concordance' argument, often put forward by cosmologists in support of the current paradigm, is weaker than the convergence arguments that were made in the past in support of the atomic theory of matter or the quantization of energy.
Cosmology, Clusters and Calorimeters
NASA Technical Reports Server (NTRS)
Figueroa-Feliciano, Enectali
2005-01-01
I will review the current state of Cosmology with Clusters and discuss the application of microcalorimeter arrays to this field. With the launch of Astro-E2 this summer and a slew of new missions being developed, microcalorimeters are the next big thing in x-ray astronomy. I will cover the basics and not-so-basic concepts of microcalorimeter designs and look at the future to see where this technology will go.
Topics in inflationary cosmologies
Mahajan, S.
1986-04-01
Several aspects of inflationary cosmologies are discussed. An introduction to the standard hot big bang cosmological model is reviewed, and some of the problems associated with it are presented. A short review of the proposals for solving the cosmological conundrums of the big bang model is presented. Old and the new inflationary scenarios are discussed and shown to be unacceptable. Some alternative scenarios especially those using supersymmetry are reviewed briefly. A study is given of inflationary models where the same set of fields that breaks supersymmetry is also responsible for inflation. In these models, the scale of supersymmetry breaking is related to the slope of the potential near the origin and can thus be kept low. It is found that a supersymmetry breaking scale of the order of the weak breaking scale. The cosmology obtained from the simplest of such models is discussed in detail and it is shown that there are no particular problems except a low reheating temperature and a violation of the thermal constraint. A possible solution to the thermal constraint problem is given by introducing a second field, and the role played by this second field in the scenario is discussed. An alternative mechanism for the generation of baryon number within the framework of supergravity inflationary models is studied using the gravitational couplings of the heavy fields with the hidden sector (the sector which breaks supersymmetry). This mechanism is applied to two specific models - one with and one without supersymmetry breaking. The baryon to entropy ratio is found to be dependent on parameters which are model dependent. Finally, the effect of direct coupling between the two sectors on results is related, 88 refs., 6 figs.
NASA Astrophysics Data System (ADS)
Jones, Alexander
The structure, composition, and long-term history of the cosmos were prominent topics in many ancient Greek philosophical systems. Philosophers and philosophically informed astronomers differed over whether the cosmos was finite or infinite, eternal or transient, and composed of discrete particles or continuous, homogeneous elements. The Aristotelian cosmology preferred by astronomers following Ptolemy assumed a finite, spherical shell of eternally unalterable matter enclosing a terrestrial globe composed of earth, water, air, and fire.
Cosmology, Clusters and Calorimeters
NASA Technical Reports Server (NTRS)
Figueroa-Feliciano, Enectali
2005-01-01
I will review the current state of Cosmology with Clusters and discuss the application of microcalorimeter arrays to this field. With the launch of Astro-E2 this summer and a slew of new missions being developed, microcalorimeters are the next big thing in x-ray astronomy. I will cover the basics and not-so-basic concepts of microcalorimeter designs and look at the future to see where this technology will go.
Statistical Methods in Cosmology
NASA Astrophysics Data System (ADS)
Verde, L.
2010-03-01
The advent of large data-set in cosmology has meant that in the past 10 or 20 years our knowledge and understanding of the Universe has changed not only quantitatively but also, and most importantly, qualitatively. Cosmologists rely on data where a host of useful information is enclosed, but is encoded in a non-trivial way. The challenges in extracting this information must be overcome to make the most of a large experimental effort. Even after having converged to a standard cosmological model (the LCDM model) we should keep in mind that this model is described by 10 or more physical parameters and if we want to study deviations from it, the number of parameters is even larger. Dealing with such a high dimensional parameter space and finding parameters constraints is a challenge on itself. Cosmologists want to be able to compare and combine different data sets both for testing for possible disagreements (which could indicate new physics) and for improving parameter determinations. Finally, cosmologists in many cases want to find out, before actually doing the experiment, how much one would be able to learn from it. For all these reasons, sophisiticated statistical techniques are being employed in cosmology, and it has become crucial to know some statistical background to understand recent literature in the field. I will introduce some statistical tools that any cosmologist should know about in order to be able to understand recently published results from the analysis of cosmological data sets. I will not present a complete and rigorous introduction to statistics as there are several good books which are reported in the references. The reader should refer to those.
NASA Astrophysics Data System (ADS)
Ryden, Barbara
2016-11-01
Preface to second edition; Preface to first edition; 1. Introduction; 2. Fundamental observations; 3. Newton versus Einstein; 4. Cosmic dynamics; 5. Model universes; 6. Measuring cosmological parameters; 7. Dark matter; 8. The cosmic microwave background; 9. Nucleosynthesis and the early Universe; 10. Inflation and the very early Universe; 11. Structure formation: gravitational instability; 12. Structure formation: baryons and photons; Epilogue; Bibliography; Table of useful constants; Index.
Cosmological perturbations in antigravity
NASA Astrophysics Data System (ADS)
Oltean, Marius; Brandenberger, Robert
2014-10-01
We compute the evolution of cosmological perturbations in a recently proposed Weyl-symmetric theory of two scalar fields with oppositely signed conformal couplings to Einstein gravity. It is motivated from the minimal conformal extension of the standard model, such that one of these scalar fields is the Higgs while the other is a new particle, the dilaton, introduced to make the Higgs mass conformally symmetric. At the background level, the theory admits novel geodesically complete cyclic cosmological solutions characterized by a brief period of repulsive gravity, or "antigravity," during each successive transition from a big crunch to a big bang. For simplicity, we consider scalar perturbations in the absence of anisotropies, with potential set to zero and without any radiation. We show that despite the necessarily wrong-signed kinetic term of the dilaton in the full action, these perturbations are neither ghostlike nor tachyonic in the limit of strongly repulsive gravity. On this basis, we argue—pending a future analysis of vector and tensor perturbations—that, with respect to perturbative stability, the cosmological solutions of this theory are viable.
Ekpyrotic loop quantum cosmology
Wilson-Ewing, Edward
2013-08-01
We consider the ekpyrotic paradigm in the context of loop quantum cosmology. In loop quantum cosmology the classical big-bang singularity is resolved due to quantum gravity effects, and so the contracting ekpyrotic branch of the universe and its later expanding phase are connected by a smooth bounce. Thus, it is possible to explicitly determine the evolution of scalar perturbations, from the contracting ekpyrotic phase through the bounce and to the post-bounce expanding epoch. The possibilities of having either one or two scalar fields have been suggested for the ekpyrotic universe, and both cases will be considered here. In the case of a single scalar field, the constant mode of the curvature perturbations after the bounce is found to have a blue spectrum. On the other hand, for the two scalar field ekpyrotic model where scale-invariant entropy perturbations source additional terms in the curvature perturbations, the power spectrum in the post-bounce expanding cosmology is shown to be nearly scale-invariant and so agrees with observations.
NASA Astrophysics Data System (ADS)
Hoyle, Fred
The worrying situation at that time in cosmology, as it seemed, turned out to be a relatively minor matter, namely the choice of suitable coordinates. Even the best-known cosmologists - de Sitter, Eddington and Lemaitre - had chosen coordinates appropriate to localities in the universe rather than the whole. This produced a sense of mystery that was more apparent than real as to what happened at the boundary of a locality. It is one of the features of Einstein's general relativity that when you choose coordinate systems with special properties you can mistakenly come to think of the properties as physical instead of as mathematical artefacts. Early workers on gravitational waves thought they were investigating physical waves when in fact the waves were in their coordinate system, and a similar situation existed in cosmology. It was also in 1935-36 that this situation was put right, by H.P. Robertson in the United States and A.E. Walker in Britain and the resulting choice of coordinates later became known as the Robertson-Walker line element. Then in 1937 Robertson published an important article on cosmology in the Reviews of Modern Physics, which unfortunately I didn't read at that time because my research interests were in quantum mechanics and nuclear physics.
The screening Horndeski cosmologies
NASA Astrophysics Data System (ADS)
Starobinsky, Alexei A.; Sushkov, Sergey V.; Volkov, Mikhail S.
2016-06-01
We present a systematic analysis of homogeneous and isotropic cosmologies in a particular Horndeski model with Galileon shift symmetry, containing also a Λ-term and a matter. The model, sometimes called Fab Five, admits a rich spectrum of solutions. Some of them describe the standard late time cosmological dynamic dominated by the Λ-term and matter, while at the early times the universe expands with a constant Hubble rate determined by the value of the scalar kinetic coupling. For other solutions the Λ-term and matter are screened at all times but there are nevertheless the early and late accelerating phases. The model also admits bounces, as well as peculiar solutions describing ``the emergence of time''. Most of these solutions contain ghosts in the scalar and tensor sectors. However, a careful analysis reveals three different branches of ghost-free solutions, all showing a late time acceleration phase. We analyse the dynamical stability of these solutions and find that all of them are stable in the future, since all their perturbations stay bounded at late times. However, they all turn out to be unstable in the past, as their perturbations grow violently when one approaches the initial spacetime singularity. We therefore conclude that the model has no viable solutions describing the whole of the cosmological history, although it may describe the current acceleration phase. We also check that the flat space solution is ghost-free in the model, but it may acquire ghost in more general versions of the Horndeski theory.
NASA Astrophysics Data System (ADS)
Magueijo, João; Zlosnik, T. G.; Kibble, T. W. B.
2013-03-01
Using the chiral representation for spinors we present a particularly transparent way to generate the most general spinor dynamics in a theory where gravity is ruled by the Einstein-Cartan-Holst action. In such theories torsion need not vanish, but it can be reinterpreted as a four-fermion self-interaction within a torsion-free theory. The self-interaction may or may not break parity invariance, and may contribute positively or negatively to the energy density, depending on the couplings considered. We then examine cosmological models ruled by a spinorial field within this theory. We find that while there are cases for which no significant cosmological novelties emerge, the self-interaction can also turn a mass potential into an upside-down Mexican hat potential. Then, as a general rule, the model leads to cosmologies with a bounce, for which there is a maximal energy density, and where the cosmic singularity has been removed. These solutions are stable, and range from the very simple to the very complex.
NASA Astrophysics Data System (ADS)
Benoit-Lévy, Aurélien; Chardin, Gabriel
2014-05-01
We study an unconventional cosmology, in which we investigate the consequences that antigravity would pose to cosmology. We present the main characteristics of the Dirac-Milne Universe, a cosmological model where antimatter has a negative active gravitational mass. In this non-standard Universe, separate domains of matter and antimatter coexist at our epoch without annihilation, separated by a gravitationally induced depletion zone. We show that this cosmology does not require a priori the Dark Matter and Dark Energy components of the standard model of cosmology. Additionally, inflation becomes an unnecessary ingredient. Investigating this model, we show that the classical cosmological tests such as primordial nucleosynthesis, Type Ia supernovæ and Cosmic Microwave Background are surprisingly concordant.
Cosmology for high energy physicists
Albrecht, A.
1987-11-01
The standard big bang model of cosmology is presented. Although not perfect, its many successes make it a good starting point for most discussions of cosmology. Places are indicated where well understood laboratory physics is incorporated into the big bang, leading to successful predictions. Much less established aspects of high energy physics and some of the new ideas they have introduced into the field of cosmology are discussed, such as string theory, inflation and monopoles. 49 refs., 5 figs.
String cosmology and the landscape
NASA Astrophysics Data System (ADS)
Bena, Iosif; Graña, Mariana
2017-03-01
String Theory is believed to have a landscape of 10500 vacua with properties that resemble those of our Universe. The existence of these vacua can be combined with anthropic reasoning to explain some of the hardest problems in cosmology and high-energy physics: the cosmological constant problem, the hierarchy problem, and the un-natural almost-flatness of the inflationary potential. We will explain the construction of these vacua, focusing on the challenges of obtaining vacua with a positive cosmological constant.
Calibration procedure for a laser triangulation scanner with uncertainty evaluation
NASA Astrophysics Data System (ADS)
Genta, Gianfranco; Minetola, Paolo; Barbato, Giulio
2016-11-01
Most of low cost 3D scanning devices that are nowadays available on the market are sold without a user calibration procedure to correct measurement errors related to changes in environmental conditions. In addition, there is no specific international standard defining a procedure to check the performance of a 3D scanner along time. This paper aims at detailing a thorough methodology to calibrate a 3D scanner and assess its measurement uncertainty. The proposed procedure is based on the use of a reference ball plate and applied to a triangulation laser scanner. Experimental results show that the metrological performance of the instrument can be greatly improved by the application of the calibration procedure that corrects systematic errors and reduces the device's measurement uncertainty.
Spatial analysis of the Chania prefecture: Crete triangulation network quality
NASA Astrophysics Data System (ADS)
Achilleos, Georgios
2016-08-01
The network of trigonometric points of a region is the basis upon which any form of cartographic work is attached to the national geodetic coordinate system (data collection, processing, output presentations) and not only. The products of the cartographic work (cartographic representations), provide the background which is used in cases of spatial planning and development strategy. This trigonometric network, except that, provides to a single cartographic work, the ability to exist within a unified official state geodetic reference system, simultaneously determines the quality of the result, since the trigonometric network data that are used, have their own quality. In this paper, we present the research of spatial quality of the trigonometric network of Chania Prefecture in Crete. This analysis examines the triangulation network points, both with respect to their spatial position (distribution in space), and in their accuracy (horizontally and vertically).
A novel spatial clustering algorithm based on Delaunay triangulation
NASA Astrophysics Data System (ADS)
Yang, Xiankun; Cui, Weihong
2008-12-01
Exploratory data analysis is increasingly more necessary as larger spatial data is managed in electro-magnetic media. Spatial clustering is one of the very important spatial data mining techniques. So far, a lot of spatial clustering algorithms have been proposed. In this paper we propose a robust spatial clustering algorithm named SCABDT (Spatial Clustering Algorithm Based on Delaunay Triangulation). SCABDT demonstrates important advantages over the previous works. First, it discovers even arbitrary shape of cluster distribution. Second, in order to execute SCABDT, we do not need to know any priori nature of distribution. Third, like DBSCAN, Experiments show that SCABDT does not require so much CPU processing time. Finally it handles efficiently outliers.
On-Line Metrology with Conoscopic Holography: Beyond Triangulation
Álvarez, Ignacio; Enguita, Jose M.; Frade, María; Marina, Jorge; Ojea, Guillermo
2009-01-01
On-line non-contact surface inspection with high precision is still an open problem. Laser triangulation techniques are the most common solution for this kind of systems, but there exist fundamental limitations to their applicability when high precisions, long standoffs or large apertures are needed, and when there are difficult operating conditions. Other methods are, in general, not applicable in hostile environments or inadequate for on-line measurement. In this paper we review the latest research in Conoscopic Holography, an interferometric technique that has been applied successfully in this kind of applications, ranging from submicrometric roughness measurements, to long standoff sensors for surface defect detection in steel at high temperatures. PMID:22399984
Public Health Triangulation to inform decision-making in Belgium.
Bossuyt, N; Van Casteren, V; Goderis, G; Wens, J; Moreels, S; Vanthomme, K; De Clercq, E
2015-01-01
We assessed the impact of a nation-wide ambulatory care complex intervention (the "care trajectory program") on quality of care in Belgium. We used the three-step public health triangulation method described in this paper and data from four different data sources: a national reimbursement database, an electronic patient record-based general practitioner network, the Belgian general practitioner sentinel network, and a new national registry for care trajectory patients. By applying our method and using the available evidence, we identified key findings that have been accepted by experts and stakeholders. We also produced timely recommendations for the decision-making process, four years after the start of the care trajectory program.
Feature-preserving surface mesh smoothing via suboptimal Delaunay triangulation.
Gao, Zhanheng; Yu, Zeyun; Holst, Michael
2013-01-01
A method of triangular surface mesh smoothing is presented to improve angle quality by extending the original optimal Delaunay triangulation (ODT) to surface meshes. The mesh quality is improved by solving a quadratic optimization problem that minimizes the approximated interpolation error between a parabolic function and its piecewise linear interpolation defined on the mesh. A suboptimal problem is derived to guarantee a unique, analytic solution that is significantly faster with little loss in accuracy as compared to the optimal one. In addition to the quality-improving capability, the proposed method has been adapted to remove noise while faithfully preserving sharp features such as edges and corners of a mesh. Numerous experiments are included to demonstrate the performance of the method.
NASA Astrophysics Data System (ADS)
Shogin, Dmitry; Amund Amundsen, Per
2016-10-01
We test the physical relevance of the full and the truncated versions of the Israel-Stewart (IS) theory of irreversible thermodynamics in a cosmological setting. Using a dynamical systems method, we determine the asymptotic future of plane symmetric Bianchi type I spacetimes with a viscous mathematical fluid, keeping track of the magnitude of the relative dissipative fluxes, which determines the applicability of the IS theory. We consider the situations where the dissipative mechanisms of shear and bulk viscosity are involved separately and simultaneously. It is demonstrated that the only case in the given model when the fluid asymptotically approaches local thermal equilibrium, and the underlying assumptions of the IS theory are therefore not violated, is that of a dissipative fluid with vanishing bulk viscosity. The truncated IS equations for shear viscosity are found to produce solutions which manifest pathological dynamical features and, in addition, to be strongly sensitive to the choice of initial conditions. Since these features are observed already in the case of an oversimplified mathematical fluid model, we have no reason to assume that the truncation of the IS transport equations will produce relevant results for physically more realistic fluids. The possible role of bulk and shear viscosity in cosmological evolution is also discussed.
Cosmological relativity: A special relativity for cosmology
NASA Astrophysics Data System (ADS)
Carmeli, M.
1995-07-01
Under the assumption that Hubble's constant H0 is constant in cosmic time, there is an analogy between the equation of propagation of light and that of expansion of the universe. Using this analogy, and assuming that the laws of physics are the same at all cosmic times, a new special relativity, a cosmological relativity, is developed. As a result, a transformation is obtained that relates physical quantities at different cosmic times. In a one-dimensional motion, the new transformation is given by 10701_2005_Article_BF02059524_TeX2GIFE1.gif x' = {x - Tv}/{(1 - T^2 /T_0^2 )^{{1 / 2}}v' = {v - xT/T_0^2 }/{(1 - T^2 /T_0^2 )^{{1 /2 }} where x and v are the coordinate and velocity, T is the cosmic time measured backward with respect to our present time T=0, tand T0 is Hubble's time. Some consequences of this transformation are given, and its applicability limitation is pointed out.
The Riemann tensor and the Bianchi identity in 5D space-time
NASA Astrophysics Data System (ADS)
Taki, Mehran; Mirjalili, Abolfazl
2017-01-01
The initial assumption of theories with extra dimension is based on the efforts to yield a geometrical interpretation of the gravitation field. In this paper, using an infinitesimal parallel transportation of a vector, we generalize the obtained results in four dimensions to five-dimensional space-time. For this purpose, we first consider the effect of the geometrical structure of 4D space-time on a vector in a round trip of a closed path, which is basically quoted from chapter three of Ref. [5]. If the vector field is a gravitational field, then the required round trip will lead us to an equation which is dynamically governed by the Riemann tensor. We extend this idea to five-dimensional space-time and derive an improved version of Bianchi's identity. By doing tensor contraction on this identity, we obtain field equations in 5D space-time that are compatible with Einstein's field equations in 4D space-time. As an interesting result, we find that when one generalizes the results to 5D space-time, the new field equations imply a constraint on Ricci scalar equations, which might be containing a new physical insight.
VizieR Online Data Catalog: GALEX-GR6/7 data release (Bianchi+ 2014)
NASA Astrophysics Data System (ADS)
Bianchi, L.; Conti, A.; Shiao, B
2014-10-01
The Galaxy Evolution Explorer (GALEX) was a NASA Small Explorer mission which imaged the sky in 2 ultraviolet bands, FUV (far-UV) and NUV (near-UV) and provided the first UV sky surveys. Its characteristics are: -------------------------------------------------------------------- FUV NUV -------------------------------------------------------------------- Bandwidth 1344-1786 1771-2831 (Å) Effective wavelength 1538.6 2315.7 (Å) Astrometry (R<0.6deg) 0.59 0.49 (arcsec) Photometry (1 sigma) 0.05 0.03 (ABmag) Zero point 18.82 20.08 (ABmag) Image resolution 4.2 5.3 (arcsec/pix) Spectral resolution 200 118 (δλ/λ) -------------------------------------------------------------------- GALEX data products include a series of sky imaging surveys with different depth and coverage, UV photometry of over 200 million sources, and about 100,000 slitless grism spectra. The Bianchi et al.2014 catalog includes all the FUV, NUV data at the end of the mission, for the surveys with the widest sky-coverage (AIS and MIS); it gives a unique source list (duplicate measurements are removed) and excludes the artifact-plagued data along the field rim. Details, subcatalogs, and science tools for using this catalog can be found at http://dolomiti.pha.jhu.edu/uvsky (1 data file).
Philosophical aspects of modern cosmology
NASA Astrophysics Data System (ADS)
Zinkernagel, Henrik
2014-05-01
Cosmology is the attempt to understand in scientific terms the structure and evolution of the universe as a whole. This ambition has been with us since the ancient Greeks, even if the developments in modern cosmology have provided a picture of the universe dramatically different from that of Pythagoras, Plato and Aristotle. The cosmological thinking of these figures, e.g. the belief in uniform circular motion of the heavens, was closely related to their philosophical ideas, and it shaped the field of cosmology at least up to the times of Copernicus and Kepler.
Gravitation and modern cosmology - The cosmological constant problem
NASA Astrophysics Data System (ADS)
Zichichi, Antonino; de Sabbata, Venzo; Sanchez, Norma
An updated version of different approaches to the cosmological constant problem discussed at a symposium in honor of Peter Gabriel Bergmann's 75th birthday, that took place in Erice on 17-20 September 1990, is presented. Topics addressed include an effective action model for the cosmological constant revisited; torsion, quantum effects, and the problem of cosmological constant; variations of constants and exact solutions in multidimensional gravity; null surface canonical formalism; qualitative cosmology; and the gravitational field of an arbitrary axisymmetric mass with a magnetic dipole moment. Attention is also given to a simple model of the universe without singularities; string theory and quantization of gravity; and velocity of propagation of gravitational radiation, mass of the gravitation, range of the gravitational force, and the cosmological constant.
Precision cosmological parameter estimation
NASA Astrophysics Data System (ADS)
Fendt, William Ashton, Jr.
2009-09-01
Experimental efforts of the last few decades have brought. a golden age to mankind's endeavor to understand tine physical properties of the Universe throughout its history. Recent measurements of the cosmic microwave background (CMB) provide strong confirmation of the standard big bang paradigm, as well as introducing new mysteries, to unexplained by current physical models. In the following decades. even more ambitious scientific endeavours will begin to shed light on the new physics by looking at the detailed structure of the Universe both at very early and recent times. Modern data has allowed us to begins to test inflationary models of the early Universe, and the near future will bring higher precision data and much stronger tests. Cracking the codes hidden in these cosmological observables is a difficult and computationally intensive problem. The challenges will continue to increase as future experiments bring larger and more precise data sets. Because of the complexity of the problem, we are forced to use approximate techniques and make simplifying assumptions to ease the computational workload. While this has been reasonably sufficient until now, hints of the limitations of our techniques have begun to come to light. For example, the likelihood approximation used for analysis of CMB data from the Wilkinson Microwave Anistropy Probe (WMAP) satellite was shown to have short falls, leading to pre-emptive conclusions drawn about current cosmological theories. Also it can he shown that an approximate method used by all current analysis codes to describe the recombination history of the Universe will not be sufficiently accurate for future experiments. With a new CMB satellite scheduled for launch in the coming months, it is vital that we develop techniques to improve the analysis of cosmological data. This work develops a novel technique of both avoiding the use of approximate computational codes as well as allowing the application of new, more precise analysis
Nonlinear field space cosmology
NASA Astrophysics Data System (ADS)
Mielczarek, Jakub; Trześniewski, Tomasz
2017-08-01
We consider the FRW cosmological model in which the matter content of the Universe (playing the role of an inflaton or quintessence) is given by a novel generalization of the massive scalar field. The latter is a scalar version of the recently introduced nonlinear field space theory, where the physical phase space of a given field is assumed to be compactified at large energies. For our analysis, we choose the simple case of a field with the spherical phase space and endow it with the generalized Hamiltonian analogous to the XXZ Heisenberg model, normally describing a system of spins in condensed matter physics. Subsequently, we study both the homogenous cosmological sector and linear perturbations of such a test field. In the homogenous sector, we find that nonlinearity of the field phase space is becoming relevant for large volumes of the Universe and can lead to a recollapse, and possibly also at very high energies, leading to the phase of a bounce. Quantization of the field is performed in the limit where the nontrivial nature of its phase space can be neglected, while there is a nonvanishing contribution from the Lorentz symmetry breaking term of the Hamiltonian. As a result, in the leading order of the XXZ anisotropy parameter, we find that the inflationary spectral index remains unmodified with respect to the standard case but the total amplitude of perturbations is subject to a correction. The Bunch-Davies vacuum state also becomes appropriately corrected. The proposed new approach is bringing cosmology and condensed matter physics closer together, which may turn out to be beneficial for both disciplines.
Bojowald, Martin
2005-01-01
Quantum gravity is expected to be necessary in order to understand situations where classical general relativity breaks down. In particular in cosmology one has to deal with initial singularities, i.e., the fact that the backward evolution of a classical space-time inevitably comes to an end after a finite amount of proper time. This presents a breakdown of the classical picture and requires an extended theory for a meaningful description. Since small length scales and high curvatures are involved, quantum effects must play a role. Not only the singularity itself but also the surrounding space-time is then modified. One particular realization is loop quantum cosmology, an application of loop quantum gravity to homogeneous systems, which removes classical singularities. Its implications can be studied at different levels. Main effects are introduced into effective classical equations which allow to avoid interpretational problems of quantum theory. They give rise to new kinds of early universe phenomenology with applications to inflation and cyclic models. To resolve classical singularities and to understand the structure of geometry around them, the quantum description is necessary. Classical evolution is then replaced by a difference equation for a wave function which allows to extend space-time beyond classical singularities. One main question is how these homogeneous scenarios are related to full loop quantum gravity, which can be dealt with at the level of distributional symmetric states. Finally, the new structure of space-time arising in loop quantum gravity and its application to cosmology sheds new light on more general issues such as time.
Bojowald, Martin
2008-01-01
Quantum gravity is expected to be necessary in order to understand situations in which classical general relativity breaks down. In particular in cosmology one has to deal with initial singularities, i.e., the fact that the backward evolution of a classical spacetime inevitably comes to an end after a finite amount of proper time. This presents a breakdown of the classical picture and requires an extended theory for a meaningful description. Since small length scales and high curvatures are involved, quantum effects must play a role. Not only the singularity itself but also the surrounding spacetime is then modified. One particular theory is loop quantum cosmology, an application of loop quantum gravity to homogeneous systems, which removes classical singularities. Its implications can be studied at different levels. The main effects are introduced into effective classical equations, which allow one to avoid the interpretational problems of quantum theory. They give rise to new kinds of early-universe phenomenology with applications to inflation and cyclic models. To resolve classical singularities and to understand the structure of geometry around them, the quantum description is necessary. Classical evolution is then replaced by a difference equation for a wave function, which allows an extension of quantum spacetime beyond classical singularities. One main question is how these homogeneous scenarios are related to full loop quantum gravity, which can be dealt with at the level of distributional symmetric states. Finally, the new structure of spacetime arising in loop quantum gravity and its application to cosmology sheds light on more general issues, such as the nature of time.
The screening Horndeski cosmologies
Starobinsky, Alexei A.; Sushkov, Sergey V.; Volkov, Mikhail S.
2016-06-06
We present a systematic analysis of homogeneous and isotropic cosmologies in a particular Horndeski model with Galileon shift symmetry, containing also a Λ-term and a matter. The model, sometimes called Fab Five, admits a rich spectrum of solutions. Some of them describe the standard late time cosmological dynamic dominated by the Λ-term and matter, while at the early times the universe expands with a constant Hubble rate determined by the value of the scalar kinetic coupling. For other solutions the Λ-term and matter are screened at all times but there are nevertheless the early and late accelerating phases. The model also admits bounces, as well as peculiar solutions describing “the emergence of time”. Most of these solutions contain ghosts in the scalar and tensor sectors. However, a careful analysis reveals three different branches of ghost-free solutions, all showing a late time acceleration phase. We analyse the dynamical stability of these solutions and find that all of them are stable in the future, since all their perturbations stay bounded at late times. However, they all turn out to be unstable in the past, as their perturbations grow violently when one approaches the initial spacetime singularity. We therefore conclude that the model has no viable solutions describing the whole of the cosmological history, although it may describe the current acceleration phase. We also check that the flat space solution is ghost-free in the model, but it may acquire ghost in more general versions of the Horndeski theory.
Galileons on cosmological backgrounds
Goon, Garrett; Hinterbichler, Kurt; Trodden, Mark E-mail: kurthi@physics.upenn.edu
2011-12-01
We construct four-dimensional effective field theories of a generalized DBI galileon field, the dynamics of which naturally take place on a Friedmann-Robertson-Walker spacetime. The theories are invariant under non-linear symmetry transformations, which can be thought of as being inherited from five-dimensional bulk Killing symmetries via the probe brane technique through which they are constructed. The resulting model provides a framework in which to explore the cosmological role that galileons may play as the universe evolves.
Stochastic processes in cosmology
NASA Astrophysics Data System (ADS)
Cáceres, Manuel O.; Diaz, Mario C.; Pullin, Jorge A.
1987-08-01
The behavior of a radiation filled de Sitter universe in which the equation of state is perturbed by a stochastic term is studied. The corresponding two-dimensional Fokker-Planck equation is solved. The finiteness of the cosmological constant appears to be a necessary condition for the stability of the model which undergoes an exponentially expanding state. Present address: Facultad de Matemática Astronomía y Física, Universidad Nacional de Córdoba, Laprida 854, 5000 Códoba, Argentina.
DOE R&D Accomplishments Database
Wilczek, Frank; Turner, Michael S.
1990-09-01
If Peccei-Quinn (PQ) symmetry is broken after inflation, the initial axion angle is a random variable on cosmological scales; based on this fact, estimates of the relic-axion mass density give too large a value if the axion mass is less than about 10-6 eV. This bound can be evaded if the Universe underwent inflation after PQ symmetry breaking and if the observable Universe happens to be a region where the initial axion angle was atypically small, .1 . (ma/10-6eV)0.59. We show consideration of fluctuations induced during inflation severely constrains the latter alternative.
Chamseddine, Ali H.; Mukhanov, Viatcheslav; Vikman, Alexander E-mail: viatcheslav.Mukhanov@lmu.de
2014-06-01
We consider minimal extensions of the recently proposed Mimetic Dark Matter and show that by introducing a potential for the mimetic non-dynamical scalar field we can mimic nearly any gravitational properties of the normal matter. In particular, the mimetic matter can provide us with inflaton, quintessence and even can lead to a bouncing nonsingular universe. We also investigate the behaviour of cosmological perturbations due to a mimetic matter. We demonstrate that simple mimetic inflation can produce red-tilted scalar perturbations which are largely enhanced over gravity waves.
NASA Astrophysics Data System (ADS)
Krishnan, Chethan; Raju, Avinash; Roy, Shubho; Thakur, Somyadip
2014-02-01
We construct cosmological solutions of higher spin gravity in 2+1 dimensional de Sitter space. We show that a consistent thermodynamics can be obtained for their horizons by demanding appropriate holonomy conditions. This is equivalent to demanding the integrability of the Euclidean boundary conformal field theory partition function, and it reduces to Gibbons-Hawking thermodynamics in the spin-2 case. By using the prescription of Maldacena, we relate the thermodynamics of these solutions to those of higher spin black holes in AdS3.
McFadden, Paul; Skenderis, Kostas
2010-01-15
We propose a holographic description of four-dimensional single-scalar inflationary universes, and show how cosmological observables, such as the primordial power spectrum, are encoded in the correlation functions of a three-dimensional quantum field theory (QFT). The holographic description correctly reproduces standard inflationary predictions in the regime where a perturbative quantization of fluctuations is justified. In the opposite regime, wherein gravity is strongly coupled at early times, we propose a holographic description in terms of perturbative large N QFT. Initiating a holographic phenomenological approach, we show that models containing only two parameters, N and a dimensionful coupling constant, are capable of satisfying the current observational constraints.
NASA Technical Reports Server (NTRS)
Turner, Michael S.; Wilczek, Frank
1991-01-01
If Peccei-Quinn (PQ) symmetry is broken after inflation, the initial axion angle is a random variable on cosmological scales; based on this fact, estimates of the relic-axion mass density give too large a value if the axion mass is less than about 10 to the -6th eV. This bound can be evaded if the universe underwent inflation after PQ-symmetry breaking and if the observable universe happens to be a region where the initial axion angle was atypically small. Consideration of fluctuations induced during inflation severely constrains the latter alternative is shown.
Supersymmetric quantum cosmology
Macias, Alfredo; Camacho, Abel
2009-05-01
We address the canonical quantization in the framework of N = 1 simple supergravity for the case of Gowdy T{sup 3} cosmological models. It will be proved that there exist physical states in the minisuperspace sector of the theory. Our result will be confronted against the so-called no-physical states conjecture and in this way it will be proved that this conjecture is based upon an assumption involving the constraint equations and initial-value hypersurface which, in general, is not valid.
Cosmology of bifundamental fields
Vachaspati, Tanmay
2009-01-15
If a field theory contains gauged, non-Abelian, bifundamental fields, i.e. fields that are charged under two separate non-Abelian gauge groups, the transition from a deconfined phase to a hadronic phase may be frustrated. Similar frustration may occur in non-Abelian gauge models containing matter only in higher dimensional representations, e.g. models with pure glue, or if ordinary quarks are confined by two flux tubes, as implied in the triangular configuration of baryons within QCD. In a cosmological setting, such models can lead to the formation of a web of confining electric flux tubes that can potentially have observational signatures.
Cosmological special relativity
NASA Astrophysics Data System (ADS)
Carmeli, M.
1996-03-01
Recently we presented a new special relativity theory for cosmology in which it was assumed that gravitation can be neglected and thus the bubble constant can be taken as a constant. The theory was presented in a six-dimensional hvperspace. three for the ordinary space and three for the velocities. In this paper we reduce our hyperspace to four dimensions by assuming that the three-dimensional space expands only radially, thus one is left with the three dimensions of ordinary space and one dimension of the radial velocity.
NASA Astrophysics Data System (ADS)
Gill, Stuart P. D.; Knebe, Alexander; Gibson, Brad K.; Flynn, Chris; Ibata, Rodrigo A.; Lewis, Geraint F.
2003-04-01
An adaptive multi grid approach to simulating the formation of structure from collisionless dark matter is described. MLAPM (Multi-Level Adaptive Particle Mesh) is one of the most efficient serial codes available on the cosmological "market" today. As part of Swinburne University's role in the development of the Square Kilometer Array, we are implementing hydrodynamics, feedback, and radiative transfer within the MLAPM adaptive mesh, in order to simulate baryonic processes relevant to the interstellar and intergalactic media at high redshift. We will outline our progress to date in applying the existing MLAPM to a study of the decay of satellite galaxies within massive host potentials.
NASA Technical Reports Server (NTRS)
Gregory, Ruth
1988-01-01
The effect of an infinite cosmic string on a cosmological background is investigated. It is found that the metric is approximately a scaled version of the empty space string metric, i.e., conical in nature. Results are used to place bounds on the amount of cylindrical gravitational radiation currently emitted by such a string. The gravitational radiation equations are then analyzed explicitly and it is shown that even initially large disturbances are rapidly damped as the expansion proceeds. The implications of the gravitational radiation background and the limitations of the quadrupole formula are discussed.
Republication of: Relativistic cosmology
NASA Astrophysics Data System (ADS)
Robertson, H. P.
2012-08-01
This is a reprinting of the paper by Howard Percy Robertson, first published in 1933 in Rev. Mod. Phys., that is a very authoritative summary of relativistic cosmology at the stage at which it was up to 1933. The paper has been selected by the Editors of General Relativity and Gravitation for re-publication in the Golden Oldies series of the journal. This republication is accompanied by an editorial note written by George Ellis, and by Robertson's biography, compiled by Andrzej Krasinski from printed sources.
NASA Astrophysics Data System (ADS)
Rasanen, Syksy
The thesis consists of three research papers and an introduction which provides background and also contains some new observations not included in the papers. In the thesis I consider certain questions in the new field of brane cosmology. The basic idea of brane cosmology is that the visible universe is a four- dimensional slice in higher-dimensional spacetime. I give a self-contained introduction to the field, starting from the Randall-Sundrum model and proceeding to the general case of brane gravity and cosmology in the case of one extra dimension. I emphasise the main result of studies of brane gravity: it is possible to obtain approximately four-dimensional gravity independent of the size of the extra dimension, in contrast to set-ups where the observers are not localised in the extra dimension. I proceed to examine a new and promising brave cosmology set-up, the ekpyrotic scenario, in detail. The ekpyrotic scenario aims to be a comprehensive model of the primordial universe and has been presented as an alternative to the prominent scenarios, inflation and pre-big bang. I give an overview of these three scenarios of the primordial universe. I then present the starting point of the ekpyrotic scenario and the construction of the four-dimensional effective theory. After briefly discussing the internal problems of the four-dimensional effective theory, I proceed to the far more serious problems of the four- dimensional construction itself. I conclude that the four-dimensional effective theory does not give a correct description even at a qualitative level. I then discuss some problems faced by the five-dimensional approach, and comment on the spin-off known as the “cyclic model of the universe”. I conclude that the ekpyrotic scenario is a welcome new idea but that most work done thus far is not solid. Careful analysis in the five-dimensional setting is needed to promote the scenario from an interesting concept to a working model with testable predictions.
Jones, Aled; Bugge, Carol
2006-09-01
In this paper, we aim to explore the benefits of triangulation and to expose the positive contribution of using 'triangulation for completeness' within a study of a complex concept, namely patient participation during healthcare interaction. Complex concepts, such as patient participation, are often the focus of nursing research. Triangulation has been proposed as a technique for studying complexity but, although debates about triangulation are becoming more prevalent in the literature, there is little deliberation about the process through which triangulation for completeness, with its claims of forming more comprehensive and rigorous descriptions of concepts through use of multiple data sources, yields it purported benefits. A seminar series, held between 2001 and 2003, brought together researchers actively involved in the study of patient participation in healthcare consultations. The group came from diverse methodological traditions and had undertaken research with a range of informants and a range of methods. The various studies used triangulation at different levels: within studies, across studies and across disciplines. Our examples support theoretical arguments that triangulation for completeness can lead to a more holistic understanding of a concept and can improve scientific rigour. Furthermore, we suggest that triangulation can improve research skills for individuals. Our examples suggest that the process through which understanding is enhanced is discursive and centres on discussions of convergent and unique findings; rigour is improved is through challenging findings, being encouraged to explain aspects of your research that may be taken for granted and improving transparency; and individual researcher's skills and abilities are improved is through a process of discussion and reflexivity. Triangulation for completeness, on various levels, can improve the quality and utility of research about complex concepts through a range of discursive processes
Cosmology: Recent and future developments
Joshua A. Frieman
2003-01-15
The precision with which the cosmological parameters have been determined has made dramatic progress in just the last two years. The author reviews this recent observational progress, highlights some of the key questions facing cosmology in the new millennium, and briefly discusses some of the projects now being mounted or contemplated to address them.
Rolling Tachyon in Nonlocal Cosmology
Joukovskaya, L.
2007-11-20
Nonlocal cosmological models derived from String Field Theory are considered. A new method for constructing rolling tachyon solutions in the FRW metric in two field configuration is proposed and solutions of the Friedman equations with nonlocal operator are presented. The cosmological properties of these solutions are discussed.
Turner, Michael S.
1997-03-01
The Hubble constant sets the size and age of the Universe, and, together with independent determinations of the age, provides a consistency check of the standard cosmology. The Hubble constant also provides an important test of our most attractive paradigm for extending the standard cosmology, inflation and cold dark matter.
Is cosmology a historical science?
NASA Astrophysics Data System (ADS)
Grignon, Claude
2012-06-01
To explain the formation and the evolution of the Universe, cosmology settles universal laws. In this respect, cosmology belongs to the category of the nomothetic sciences, which write and think in mathematics. But cosmology is also akin to the historical sciences; like archaeology, geology or the biology of evolution, cosmology infers history from the vestiges of the past; moreover, it is not an experimental but an observational science. Due to this ambivalence, cosmology confronts divergent epistemological options. Nomothetic and historical sciences use indeed different, even opposite conceptions of such fundamental notions as time, causality and chance. Is it possible to make the history of the Universe intelligible without referring to the narrative conception of history congruent with the course of the historical world?.
Higher dimensional loop quantum cosmology
NASA Astrophysics Data System (ADS)
Zhang, Xiangdong
2016-07-01
Loop quantum cosmology (LQC) is the symmetric sector of loop quantum gravity. In this paper, we generalize the structure of loop quantum cosmology to the theories with arbitrary spacetime dimensions. The isotropic and homogeneous cosmological model in n+1 dimensions is quantized by the loop quantization method. Interestingly, we find that the underlying quantum theories are divided into two qualitatively different sectors according to spacetime dimensions. The effective Hamiltonian and modified dynamical equations of n+1 dimensional LQC are obtained. Moreover, our results indicate that the classical big bang singularity is resolved in arbitrary spacetime dimensions by a quantum bounce. We also briefly discuss the similarities and differences between the n+1 dimensional model and the 3+1 dimensional one. Our model serves as a first example of higher dimensional loop quantum cosmology and offers the possibility to investigate quantum gravity effects in higher dimensional cosmology.
More problems for Newtonian cosmology
NASA Astrophysics Data System (ADS)
Wallace, David
2017-02-01
I point out a radical indeterminism in potential-based formulations of Newtonian gravity once we drop the condition that the potential vanishes at infinity (as is necessary, and indeed celebrated, in cosmological applications). This indeterminism, which is well known in theoretical cosmology but has received little attention in foundational discussions, can be removed only by specifying boundary conditions at all instants of time, which undermines the theory's claim to be fully cosmological, i.e., to apply to the Universe as a whole. A recent alternative formulation of Newtonian gravity due to Saunders (Philosophy of Science 80 (2013) pp. 22-48) provides a conceptually satisfactory cosmology but fails to reproduce the Newtonian limit of general relativity in homogenous but anisotropic universes. I conclude that Newtonian gravity lacks a fully satisfactory cosmological formulation.
NASA Astrophysics Data System (ADS)
Reddy, D. R. K.; Anitha, S.; Umadevi, S.
2016-10-01
In this paper, we investigate Bianchi type VI0 universe filled with two minimally interacting fields, matter and anisotropic holographic dark energy components in the scalar-tensor theory of gravitation proposed by Saez and Ballester (Phys. Lett. A 113: 467, 1986). Solving the field equations of the theory using a relation between metric potentials and special law of variation for Hubble's parameter proposed by Bermann (Nuovo Cimento B 74:182, 1983) we have presented an anisotropic holographic dark energy model in this theory. The physical aspects of the model are also discussed.
NASA Astrophysics Data System (ADS)
Umadevi, S.; Ramesh, G.
2015-10-01
A spatially homogeneous and anisotropic Bianchi type-III universe filled with two minimally interacting fields is investigated: matter and holographic dark energy components in the framework of the Brans-Dicke (Phys. Rev. 124:925, 1961) theory of gravitation. To obtain determinate solutions of the field equations we have used (i) scalar expansion proportional to the shear scalar and (ii) special law of variation for Hubble's parameter proposed by Berman (Nuovo Comento B 74:182, 1983). Some physical and kinematical properties of the model are also discussed.
Triyanta; Zen, F. P.; Supardi; Wardaya, A. Y.
2010-12-23
Gauge theory, under the framework of quantum field theory, has successfully described three fundamental interactions: electromagnetic, weak, and strong interactions. Problems of describing the gravitational interaction in a similar manner has not been satisfied yet until now. Teleparallel gravity (TG) is one proposal describing gravitational field as a gauge field. This theory is quite new and it is equivalent to Einstein's general relativity. But as gravitational field in TG is expressed by torsion, rather than curvature, it gives an alternative framework for solving problems on gravity. This paper will present solution of the dynamical equation of abelian vector fields under the framework of TG in the Bianchi type I spacetime.
NASA Astrophysics Data System (ADS)
Ross, Charles H.
2005-04-01
Aristotle thought that the universe was finite and Earth centered. Newton thought that it was infinite. Einstein guessed that the universe was finite, spherical, static, warped, and closed. Hubble's 1930 discovery of the expanding universe, Penzias and Wilson's 1968 discovery of the isotropic CMB, and measurements on light element abundances, however, established a big bang origin. Vera Rubin's 1980 dark matter discovery significantly impacted contending theories. However, 1998 is the year when sufficiently accurate supernova and primordial deuterium data was available to truly explore the universe. CMB anisotropy measurements further extended our cosmological database in 2003. On the theoretical side, Friedmann's 1922 perturbation solution of Einstein's general relativity equations for a static universe has shaped the thought and direction in cosmology for the past 80 years. It describes 3D space as a dynamic function of time. However, 80 years of trying to fit Friedmann's solution to observational data has been a bumpy road - resulting in such counter-intuitive, but necessary, features as rapid inflation, precision tuning, esoteric dark matter, and an accelerating input of esoteric dark energy.
Particle physics and cosmology
Kolb, E.W.
1986-10-01
This series of lectures is about the role of particle physics in physical processes that occurred in the very early stages of the bug gang. Of particular interest is the role of particle physics in determining the evolution of the early Universe, and the effect of particle physics on the present structure of the Universe. The use of the big bang as a laboratory for placing limits on new particle physics theories will also be discussed. Section 1 reviews the standard cosmology, including primordial nucleosynthesis. Section 2 reviews the decoupling of weakly interacting particles in the early Universe, and discusses neutrino cosmology and the resulting limits that may be placed on the mass and lifetime of massive neutrinos. Section 3 discusses the evolution of the vacuum through phase transitions in the early Universe and the formation of topological defects in the transitions. Section 4 covers recent work on the generation of the baryon asymmetry by baryon-number violating reactions in Grand Unified Theories, and mentions some recent work on baryon number violation effects at the electroweak transition. Section 5 is devoted to theories of cosmic inflation. Finally, Section 6 is a discussion of the role of extra spatial dimensions in the evolution of the early Universe. 78 refs., 32 figs., 6 tabs.
The standard cosmological model
NASA Astrophysics Data System (ADS)
Scott, D.
2006-06-01
The Standard Model of Particle Physics (SMPP) is an enormously successful description of high-energy physics, driving ever more precise measurements to find "physics beyond the standard model", as well as providing motivation for developing more fundamental ideas that might explain the values of its parameters. Simultaneously, a description of the entire three-dimensional structure of the present-day Universe is being built up painstakingly. Most of the structure is stochastic in nature, being merely the result of the particular realization of the "initial conditions" within our observable Universe patch. However, governing this structure is the Standard Model of Cosmology (SMC), which appears to require only about a dozen parameters. Cosmologists are now determining the values of these quantities with increasing precision to search for "physics beyond the standard model", as well as trying to develop an understanding of the more fundamental ideas that might explain the values of its parameters. Although it is natural to see analogies between the two Standard Models, some intrinsic differences also exist, which are discussed here. Nevertheless, a truly fundamental theory will have to explain both the SMPP and SMC, and this must include an appreciation of which elements are deterministic and which are accidental. Considering different levels of stochasticity within cosmology may make it easier to accept that physical parameters in general might have a nondeterministic aspect.
Investigations in theoretical cosmology
NASA Astrophysics Data System (ADS)
Barnard, Michael James
This report is a compilation of research I have done in the field of cosmology while at the University of California, Davis. The topics are all closely linked to the physics of scalar fields in General Relativity. This thesis contains the text of two papers, both of which deal with the goals and motivations of future projects in observational cosmology. The first is an evaluation of the effect of future observations on constraints on the parameter space of the Albrecht- Skordis model of dark energy. These future data sets were found to be able of constraining the scalar field model parameters in ways consistent with the constraints on the phenomenological equation of state parameters used by the Dark Energy Task Force. The second paper used principle component analysis of the equation of state parameter on simulated future data sets to construct parameter spaces. Distributions of dark energy quintessence models were then projected into these parameter spaces; it was found that there is structure in the separation of these models that is marginally detectable by so called "Stage 4" experiments. Also included are a review of the derivation of the scale invariant primordial power spectrum and an evaluation of a model of open inflation as the cause of the low CMB quadrupole.
Peculiar cosmological velocities
Lewis, C.M.
1990-01-01
In the first section a gauge-invariant, variations formalism for investigating vector perturbations is set up, suitable for showing that there is no natural way that the usual scalar inflation field could give rise to vorticities. In the last two sections, a vector field A{sub {mu}} is coupled to the Einstein equations with a linearly perturbed Friedmann-Robertson-Walker (FRW) metric, constructed to generate first order vector perturbations. A working classical chaotic vector inflation is demonstrated and then quantum fluctuations of the field are used to constrain the cosmological perturbations. In particular, the vector momentum flux, T{sub 0i}, is tracked to the epoch where a radiation-dominated matter exists. Matching conditions using observational constraints of the cosmic microwave background radiation (CMBR) gives rise to a peculiar cosmological velocity of the order of 10{sup {minus}100}c. Amplification of this number, e.g., by breaking the conformal invariance of the field, could be used to generate cosmic magnetic fields using a dynamo mechanism.
NASA Astrophysics Data System (ADS)
Perkins, D. K.
2006-08-01
Microbes swarming on a sand grain planet or integral complex organisms evolving consciousness at the forefront of cosmic evolution? How is our new cosmology contributing to redefining who we see ourselves to be at the edge of the 21^st century, as globalization and capitalism speed forward? How is the evolution of stardust and the universe offering new paradigms of process and identity regarding the role, function and emergence of life in space-time? What are the cultural and philosophical questions that are arising and how might astronomy be contributing to the creation of new visions for cooperation and community at a global scale? What is the significance of including astronomy in K-12 education and what can it offer youth regarding values in light of the present world situation? Exploring our new cosmological concepts and the emergence of life at astronomical scales may offer much of valuable orientation toward reframing the human role in global evolution. Considering new insight from astrobiology each diverse species has a definitive role to play in the facilitation and functioning of the biosphere. Thus the question may arise: Is there any sort of ethic implied by natural science and offered by our rapidly expanding cosmic frontier?
Aspects of cosmological relativity.
NASA Astrophysics Data System (ADS)
Carmeli, M.
1999-07-01
The author reviews cosmological relativity, a new special theory of relativity that was recently developed for cosmology, and discusses in detail some of its aspects. He recalls that in this theory it is assumed that gravitation is negligible. Under this assumption, the receding velocities of galaxies and the distances between them in the Hubble expansion are united into a four-dimensional pseudo-Euclidean manifold, similarly to space and time in ordinary special relativity. The Hubble law is assumed and is written in an invariant way that enables one to derive a four-dimensional transformation which is similar to the Lorentz transformation. The parameter in the new transformation is the ratio between the cosmic time to the Hubble time. Accordingly, the new transformation relates physical quantities at different cosmic times in the limit of weak or negligible gravitation. The transformation is then applied to the problem of the expansion of the universe at the very early stage when gravity was negligible and thus the transformation is applicable. New applications of the theory are presented. The author shows that there is no need to assume the existence of galaxy dark matter; the Tully-Fisher law is derived from the theory. A completely new picture of the expanding universe is thus obtained and compared to the FRW one.
Cosmology with matter diffusion
Calogero, Simone; Velten, Hermano E-mail: velten@cce.ufes.br
2013-11-01
We construct a viable cosmological model based on velocity diffusion of matter particles. In order to ensure the conservation of the total energy-momentum tensor in the presence of diffusion, we include a cosmological scalar field φ which we identify with the dark energy component of the universe. The model is characterized by only one new degree of freedom, the diffusion parameter σ. The standard ΛCDM model can be recovered by setting σ = 0. If diffusion takes place (σ > 0) the dynamics of the matter and of the dark energy fields are coupled. We argue that the existence of a diffusion mechanism in the universe may serve as a theoretical motivation for interacting models. We constrain the background dynamics of the diffusion model with Supernovae, H(z) and BAO data. We also perform a perturbative analysis of this model in order to understand structure formation in the universe. We calculate the impact of diffusion both on the CMB spectrum, with particular attention to the integrated Sachs-Wolfe signal, and on the matter power spectrum P(k). The latter analysis places strong constraints on the magnitude of the diffusion mechanism but does not rule out the model.
NASA Astrophysics Data System (ADS)
Mahootian, F.
2009-12-01
The rapid convergence of advancing sensor technology, computational power, and knowledge discovery techniques over the past decade has brought unprecedented volumes of astronomical data together with unprecedented capabilities of data assimilation and analysis. A key result is that a new, data-driven "observational-inductive'' framework for scientific inquiry is taking shape and proving viable. The anticipated rise in data flow and processing power will have profound effects, e.g., confirmations and disconfirmations of existing theoretical claims both for and against the big bang model. But beyond enabling new discoveries can new data-driven frameworks of scientific inquiry reshape the epistemic ideals of science? The history of physics offers a comparison. The Bohr-Einstein debate over the "completeness'' of quantum mechanics centered on a question of ideals: what counts as science? We briefly examine lessons from that episode and pose questions about their applicability to cosmology. If the history of 20th century physics is any indication, the abandonment of absolutes (e.g., space, time, simultaneity, continuity, determinacy) can produce fundamental changes in understanding. The classical ideal of science, operative in both physics and cosmology, descends from the European Enlightenment. This ideal has for over 200 years guided science to seek the ultimate order of nature, to pursue the absolute theory, the "theory of everything.'' But now that we have new models of scientific inquiry powered by new technologies and driven more by data than by theory, it is time, finally, to relinquish dreams of a "final'' theory.
NASA Astrophysics Data System (ADS)
Sadeghnezhad, Naser; Nozari, Kourosh
2017-06-01
We extend the idea of mimetic gravity to a Randall-Sundrum II braneworld model. As for the 4-dimensional mimetic gravity, we isolate the conformal degree of freedom of 5-dimensional gravity in a covariant manner. We assume the bulk metric to be made up of a non-dynamical scalar field Φ and an auxiliary metric G˜AB so that GAB =G˜CDΦ,CΦ,DG˜AB where A , B , . . . are the bulk spacetime indices. Then we show that the induced conformal degree of freedom on the brane as an induced scalar field, plays the role of a mimetic field on the brane. In fact, we suppose that the scalar degree of freedom which mimics the dark sectors on the brane has its origin on the bulk scalar field, Φ. By adopting some suitable mimetic potentials on the brane, we show that this brane mimetic field explains the late time cosmic expansion in the favor of observational data: the equation of state parameter of this field crosses the cosmological constant line in near past from quintessence to phantom phase in a redshift well in the range of observation. We show also that this induced mimetic scalar field has the capability to explain initial time cosmological inflation. We study parameter space of the models numerically in order to constraint the models with Planck2015 data set.
Cosmological Physics Ground Rules and How to Evaluate Cosmologies
NASA Astrophysics Data System (ADS)
Dilworth, D. J.
2009-12-01
This paper is a simple reminder for cosmology enthusiasts of the bright line separating the laws of physics from science fiction. It provides some tools: rules, guidelines and a definition of space useful for examining cosmology science claims and concepts. It explains the stringent thresholds for an idea before it can accurately be called a scientific theory or hypothesis; and who bears the burden of proof for a theory. These simple tools provide solid ground so you may more easily examine cosmology claims to help make up your own mind which side of the science/science fiction line a specific claim belongs on.
Comparison between triangulated auroral altitude and precipitating electron energy flux
NASA Astrophysics Data System (ADS)
Sangalli, L.; Partamies, N. J.; Gustavsson, B.
2012-12-01
The MIRACLE network monitors auroral activity in the Fennoscandian sector of Europe. Network stations cover the range of 55° to 57° magnetic latitude North and span two hours in magnetic local time. Some of the MIRACLE network stations include digital all-sky cameras (ASC) with overlapping field-of-views at the latitude aurora occurs. The ASCs in this network operate at three different wavelengths: 427.8 nm (blue line), 557.7 nm (green line) and 630.0 nm (red line). These wavelengths are selected using narrow band filters. Red and blue lines images are recorded once per minute and green line images every 20 s. On January 31, 2001 multiple discrete arcs were observed at the zenith of the ASC located in Muonio (67.9° N, 23.6° E) and were visible in other stations. The peak auroral emission is estimated using triangulation between pairs of stations and compared with precipitating electron energy fluxes inverted from ASC images and measured in situ on the DMSP satellite.
Comparison between triangulated auroral altitude and precipitating electron energy flux
NASA Astrophysics Data System (ADS)
Sangalli, L.; Partamies, N. J.; Gustavsson, B.
2013-12-01
The MIRACLE network monitors auroral activity in the Fennoscandian sector of Europe. Network stations cover the range of 55° to 57° magnetic latitude North and span two hours in magnetic local time. Some of the MIRACLE network stations include digital all-sky cameras (ASC) with overlapping field-of-views at the latitude aurora occurs. The ASCs in this network operate at three different wavelengths: 427.8 nm (blue line), 557.7 nm (green line) and 630.0 nm (red line). These wavelengths are selected using narrow band filters. Red and blue lines images are recorded once per minute and green line images every 20 s. On January 31, 2001 multiple discrete arcs were observed at the zenith of the ASC located in Muonio (67.9° N, 23.6° E) and were visible in other stations. The peak auroral emission is estimated using triangulation between pairs of stations and compared with precipitating electron energy fluxes inverted from ASC images and measured in situ on the DMSP satellite.
A DELAUNAY TRIANGULATION APPROACH FOR SEGMENTING CLUMPS OF NUCLEI
Wen, Quan; Chang, Hang; Parvin, Bahram
2009-05-07
Cell-based fluorescence imaging assays have the potential to generate massive amount of data, which requires detailed quantitative analysis. Often, as a result of fixation, labeled nuclei overlap and create a clump of cells. However, it is important to quantify phenotypic read out on a cell-by-cell basis. In this paper, we propose a novel method for decomposing clumps of nuclei using high-level geometric constraints that are derived from low-level features of maximum curvature computed along the contour of each clump. Points of maximum curvature are used as vertices for Delaunay triangulation (DT), which provides a setof edge hypotheses for decomposing a clump of nuclei. Each hypothesis is subsequently tested against a constraint satisfaction network for a near optimum decomposition. The proposed method is compared with other traditional techniques such as the watershed method with/without markers. The experimental results show that our approach can overcome the deficiencies of the traditional methods and is very effective in separating severely touching nuclei.
Beta-function B-spline smoothing on triangulations
NASA Astrophysics Data System (ADS)
Dechevsky, Lubomir T.; Zanaty, Peter
2013-03-01
In this work we investigate a novel family of Ck-smooth rational basis functions on triangulations for fitting, smoothing, and denoising geometric data. The introduced basis function is closely related to a recently introduced general method introduced in utilizing generalized expo-rational B-splines, which provides Ck-smooth convex resolutions of unity on very general disjoint partitions and overlapping covers of multidimensional domains with complex geometry. One of the major advantages of this new triangular construction is its locality with respect to the star-1 neighborhood of the vertex on which the said base is providing Hermite interpolation. This locality of the basis functions can be in turn utilized in adaptive methods, where, for instance a local refinement of the underlying triangular mesh affects only the refined domain, whereas, in other method one needs to investigate what changes are occurring outside of the refined domain. Both the triangular and the general smooth constructions have the potential to become a new versatile tool of Computer Aided Geometric Design (CAGD), Finite and Boundary Element Analysis (FEA/BEA) and Iso-geometric Analysis (IGA).
Biofilm thickness variability investigated with a laser triangulation sensor.
Okkerse, W J; Ottengraf, S P; Osinga-Kuipers, B
2000-12-20
Measurement of the surface roughness and thickness of biological films is laborious and usually destructive, thus hampering research in this area. We developed a laser triangulation sensor (LTS) set-up for the fast and nondestructive measurement of these biofilm parameters during growth. Using LTS measurements, the morphological development of a dichloromethane-(DCM) degrading biofilm cultured on a wetted-wall column was studied. The measurements show that the biofilm develops faster at the entrance of the reactor. The biofilm consisted of a base film in which microbial colonies were embedded. The biofilm-surface area gradually increased by 23% compared to the bare surface due to the formation of a large number of these colonies. The number and shape of these colonies were followed in time. Using LTS measurements, biofilms distinctly different in surface roughness could be distinguished in a laboratory trickling filter removing DCM from a waste gas. The consequences of the observed surface characteristics for the reaction-diffusion process in the biofilm and for the falling film hydrodynamics are discussed.