Quantum corrections for a cosmological string solution
Behrndt, K.
1994-08-01
The author investigates quantum corrections for a cosmological solution of the string effective action. Starting point is a classical solution containing an antisymmetric tensor field, a dilaton and a modulus field which has singularities in the scalar fields. As a first step he quantizes the scalar fields near the singularity with the result that the singularities disappear and that in general non-perturbative quantum corrections form a potential in the scalar fields.
Loop Quantum Cosmology: holonomy corrections to inflationary models
Artymowski, Michal; Lalak, Zygmunt; Szulc, Lukasz
2009-01-15
In the recent years the quantization methods of Loop Quantum Gravity have been successfully applied to the homogeneous and isotropic Friedmann-Robertson-Walker space-times. The resulting theory, called Loop Quantum Cosmology (LQC), resolves the Big Bang singularity by replacing it with the Big Bounce. We argue that the LQC holonomy corrections generate also certain corrections to field theoretical inflationary scenarios. These corrections imply that in the LQC the effective sonic horizon becomes infinite at some point after the bounce and that the scale of the inflationary potential implied by the COBE normalisation increases. The evolution of scalar fields immediately after the Bounce becomes modified in an interesting way. We point out that one can use COBE normalisation to establish an upper bound on the quantum of length of LQG. LQC corrections other than the holonomy one are assumed to be subdominant.
Cosmological implications of quantum corrections and higher-derivative extension
NASA Astrophysics Data System (ADS)
Chialva, Diego; Mazumdar, Anupam
2015-01-01
We discuss the challenges for the early universe cosmology from quantum corrections, and in particular higher-derivative terms, in the gravitational and inflaton sectors of the models. The work is divided in two parts. In the first one we review the already well-known issues due to quantum corrections to the inflaton potential, in particular focusing on chaotic/slow-roll single-field models. We will point out some issues concerning the proposed mechanisms to cope with the corrections, and also argue how the presence of higher-derivative corrections could be problematic for those mechanisms. In the second part we will more directly focus on higher-derivative corrections. We will show how, in order to discuss a number of high-energy phenomena relevant to inflation (such as its actual onset) one has to deal with energy scales where the derivative expansion breaks down, presenting problems such as quantum vacuum instability and ghosts. To discuss such phenomena in the convenient framework of the effective theory, one must then abandon the derivative expansion and resort to the full nonlocal formulation of the theory, which is in fact equivalent to re-integrating back the relevant physics, but with the benefit of using a more compact single-field formalism. Finally, we will briefly discuss possible advantages offered by the presence of higher derivatives and a nonlocal theory to build better controlled UV models of inflation.
On the correctness of cosmology from quantum potential
NASA Astrophysics Data System (ADS)
Lashin, E. I.
2016-02-01
We examine in detail the cosmology based on quantal (Bohmian) trajectories as suggested in a recent study [A. F. Ali and S. Das, Phys. Lett. B 741, 276 (2014)]. We disagree with the conclusions regarding predicting the value of the cosmological constant Λ and evading the Big Bang singularity. Furthermore, we show that the approach of using a quantum corrected Raychaudhuri equation (QRE), as suggested in A. F. Ali and S. Das, Phys. Lett. B 741, 276 (2014), is unsatisfactory, because, essentially, it uses the Raychaudhuri equation (RE), which is a kinematical equation, in order to predict dynamics. In addition, even within this inconsistent framework, the authors have adopted unjustified assumptions and carried out incorrect steps leading to doubtful conclusions.
Non-Gaussian features from the inverse volume corrections in loop quantum cosmology
NASA Astrophysics Data System (ADS)
Li, Li-Fang; Cai, Rong-Gen; Guo, Zong-Kuan; Hu, Bin
2012-08-01
In this paper we study the non-Gaussian features of the primordial fluctuations in loop quantum cosmology with the inverse volume corrections. The detailed analysis is performed in the single field slow-roll inflationary models. However, our results reflect the universal characteristics of bispectrum in loop quantum cosmology. The main corrections to the scalar bispectrum come from two aspects: one is the modifications to the standard Bunch-Davies vacuum, and the other is the corrections to the background dependent variables, such as slow-roll parameters. Our calculations show that the loop quantum corrections make fNL of the inflationary models increase 0.1%. Moreover, we find that two new shapes of non-Gaussian signal arise, which we name F1 and F2. The former gives a unique loop quantum feature, which is less correlated with the local, equilateral, and single types, while the latter is highly correlated with the local one.
Quantum corrections to the cosmological evolution of conformally coupled fields
Cembranos, Jose A.R.; Olive, Keith A.; Peloso, Marco; Uzan, Jean-Philippe E-mail: olive@physics.umn.edu E-mail: uzan@iap.fr
2009-07-01
Because the source term for the equations of motion of a conformally coupled scalar field, such as the dilaton, is given by the trace of the matter energy momentum tensor, it is commonly assumed to vanish during the radiation dominated epoch in the early universe. As a consequence, such fields are generally frozen in the early universe. Here we compute the finite temperature radiative correction to the source term and discuss its consequences on the evolution of such fields in the early universe. We discuss in particular, the case of scalar tensor theories of gravity which have general relativity as an attractor solution. We show that, in some cases, the universe can experience an early phase of contraction, followed by a non-singular bounce, and standard expansion. This can have interesting consequences for the abundance of thermal relics; for instance, it can provide a solution to the gravitino problem. We conclude by discussing the possible consequences of the quantum corrections to the evolution of the dilaton.
Two-loop quantum gravity corrections to the cosmological constant in Landau gauge
NASA Astrophysics Data System (ADS)
Hamada, Ken-ji; Matsuda, Mikoto
2016-03-01
The anomalous dimensions of the Planck mass and the cosmological constant are calculated in a renormalizable quantum conformal gravity with a single dimensionless coupling, which is formulated using dimensional regularization on the basis of Hathrell's works for conformal anomalies. The dynamics of the traceless tensor field is handled by the Weyl action, while that of the conformal-factor field is described by the induced Wess-Zumino actions, including the Riegert action as the kinetic term. Loop calculations are carried out in Landau gauge in order to reduce the number of Feynman diagrams as well as to avoid some uncertainty. Especially, we calculate two-loop quantum gravity corrections to the cosmological constant. It suggests that there is a dynamical solution to the cosmological constant problem.
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).
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.
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.
Gauge invariant cosmological perturbation equations with corrections from loop quantum gravity
Bojowald, Martin; Hossain, Golam Mortuza; Kagan, Mikhail; Shankaranarayanan, S.
2009-02-15
A consistent implementation of quantum gravity is expected to change the familiar notions of space, time, and the propagation of matter in drastic ways. This will have consequences on very small scales, but also gives rise to correction terms in evolution equations of modes relevant for observations. In particular, the evolution of inhomogeneities in the very early Universe should be affected. In this paper consistent evolution equations for gauge-invariant perturbations in the presence of inverse triad corrections of loop quantum gravity are derived. Some immediate effects are pointed out, for instance, concerning conservation of power on large scales and nonadiabaticity. It is also emphasized that several critical corrections can only be seen to arise in a fully consistent treatment where the gauge freedom of canonical gravity is not fixed before implementing quantum corrections. In particular, metric modes must be allowed to be inhomogeneous: it is not consistent to assume only matter inhomogeneities on a quantum-corrected homogeneous background geometry. In this way, stringent consistency conditions arise for possible quantization ambiguities, which will eventually be further constrained observationally.
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.
Perfect Quantum Cosmological Bounce.
Gielen, Steffen; Turok, Neil
2016-07-01
We study quantum cosmology with conformal matter comprising a perfect radiation fluid and a number of conformally coupled scalar fields. Focusing initially on the collective coordinates (minisuperspace) associated with homogeneous, isotropic backgrounds, we are able to perform the quantum gravity path integral exactly. The evolution describes a "perfect bounce", in which the Universe passes smoothly through the singularity. We extend the analysis to spatially flat, anisotropic universes, treated exactly, and to generic inhomogeneous, anisotropic perturbations treated at linear and nonlinear order. This picture provides a natural, unitary description of quantum mechanical evolution across a cosmological bounce. We provide evidence for a semiclassical description in which all fields pass "around" the cosmological singularity along complex classical paths. PMID:27447496
Perfect Quantum Cosmological Bounce
NASA Astrophysics Data System (ADS)
Gielen, Steffen; Turok, Neil
2016-07-01
We study quantum cosmology with conformal matter comprising a perfect radiation fluid and a number of conformally coupled scalar fields. Focusing initially on the collective coordinates (minisuperspace) associated with homogeneous, isotropic backgrounds, we are able to perform the quantum gravity path integral exactly. The evolution describes a "perfect bounce", in which the Universe passes smoothly through the singularity. We extend the analysis to spatially flat, anisotropic universes, treated exactly, and to generic inhomogeneous, anisotropic perturbations treated at linear and nonlinear order. This picture provides a natural, unitary description of quantum mechanical evolution across a cosmological bounce. We provide evidence for a semiclassical description in which all fields pass "around" the cosmological singularity along complex classical paths.
Tachyon matter in loop quantum cosmology
NASA Astrophysics Data System (ADS)
Sen, A. A.
2006-08-01
An analytical approach for studying the cosmological scenario with a homogeneous tachyon field within the framework of loop quantum gravity is developed. Our study is based on the semiclassical regime where space time can be approximated as a continuous manifold, but matter Hamiltonian gets nonperturbative quantum corrections. A formal correspondence between classical and loop quantum cosmology is also established. The Hamilton-Jacobi method for getting exact solutions is constructed and some exact power law as well as bouncing solutions are presented.
Will Quantum Cosmology Resurrect Chaotic Inflation Model?
NASA Astrophysics Data System (ADS)
Kim, Sang Pyo; Kim, Won
2016-07-01
The single field chaotic inflation model with a monomial power greater than one seems to be ruled out by the recent Planck and WMAP CMB data while Starobinsky model with a higher curvature term seems to be a viable model. Higher curvature terms being originated from quantum fluctuations, we revisit the quantum cosmology of the Wheeler-DeWitt equation for the chaotic inflation model. The semiclassical cosmology emerges from quantum cosmology with fluctuations of spacetimes and matter when the wave function is peaked around the semiclassical trajectory with quantum corrections a la the de Broglie-Bohm pilot theory.
Quantum coherent states in cosmology
NASA Astrophysics Data System (ADS)
Ziaeepour, Houri
2015-07-01
Coherent states consist of superposition of infinite number of particles and do not have a classical analogue. We study their evolution in a FLRW cosmology and show that only when full quantum corrections are considered, they may survive the expansion of the Universe and form a global condensate. This state of matter can be the origin of accelerating expansion of the Universe, generally called dark energy, and inflation in the early universe. Additionally, such a quantum pool may be the ultimate environment for decoherenceat shorter distances. If dark energy is a quantum coherent state, its dominant contribution to the total energy of the Universe at present provides a low entropy state which may be necessary as an initial condition for a new Big Bang in the framework of bouncing cosmology models.
DaPbrowski, Mariusz P.; Kiefer, Claus; Sandhoefer, Barbara
2006-08-15
We apply the formalism of quantum cosmology to models containing a phantom field. Three models are discussed explicitly: a toy model, a model with an exponential phantom potential, and a model with phantom field accompanied by a negative cosmological constant. In all these cases we calculate the classical trajectories in configuration space and give solutions to the Wheeler-DeWitt equation in quantum cosmology. In the cases of the toy model and the model with exponential potential we are able to solve the Wheeler-DeWitt equation exactly. For comparison, we also give the corresponding solutions for an ordinary scalar field. We discuss, in particular, the behavior of wave packets in minisuperspace. For the phantom field these packets disperse in the region that corresponds to the big-rip singularity. This thus constitutes a genuine quantum region at large scales, described by a regular solution of the Wheeler-DeWitt equation. For the ordinary scalar field, the big-bang singularity is avoided. Some remarks on the arrow of time in phantom models as well as on the relation of phantom models to loop quantum cosmology are given.
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. PMID:25582917
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.
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.
Supersymmetric quantum cosmological billiards
NASA Astrophysics Data System (ADS)
Kleinschmidt, Axel; Koehn, Michael; Nicolai, Hermann
2009-09-01
D=11 supergravity near a spacelike singularity admits a cosmological billiard description based on the hyperbolic Kac-Moody group E10. The quantization of this system via the supersymmetry constraint is shown to lead to wave functions involving automorphic (Maass wave) forms under the modular group W+(E10)≅PSL2(O) with Dirichlet boundary conditions on the billiard domain. A general inequality for the Laplace eigenvalues of these automorphic forms implies that the wave function of the Universe is generically complex and always tends to zero when approaching the initial singularity. We discuss possible implications of this result for the question of singularity resolution in quantum cosmology and comment on the differences with other approaches.
Quantum cosmological metroland model
NASA Astrophysics Data System (ADS)
Anderson, Edward; Franzen, Anne
2010-02-01
Relational particle mechanics is useful for modelling whole-universe issues such as quantum cosmology or the problem of time in quantum gravity, including some aspects outside the reach of comparably complex mini-superspace models. In this paper, we consider the mechanics of pure shape and not scale of four particles on a line, so that the only physically significant quantities are ratios of relative separations between the constituents' physical objects. Many of our ideas and workings extend to the N-particle case. As such models' configurations resemble depictions of metro lines in public transport maps, we term them 'N-stop metrolands'. This 4-stop model's configuration space is a 2-sphere, from which our metroland mechanics interpretation is via the 'cubic' tessellation. This model yields conserved quantities which are mathematically SO(3) objects like angular momenta but are physically relative dilational momenta (i.e. coordinates dotted with momenta). We provide and interpret various exact and approximate classical and quantum solutions for 4-stop metroland; from these results one can construct expectations and spreads of shape operators that admit interpretations as relative sizes and the 'homogeneity of the model universe's contents', and also objects of significance for the problem of time in quantum gravity (e.g. in the naïve Schrödinger and records theory timeless approaches).
Quantum cosmology on the worldsheet
Cooper, A.R.; Susskind, L.; Thorlacius, L.
1991-08-01
Two-dimensional quantum gravity coupled to conformally invariant matter central c > 25 provides a toy model for quantum gravity in four dimensions. Two-dimensional quantum cosmology can thus be studied in terms of string theory in background fields. The large scale cosmological constant depends on non-linear dynamics in the string theory target space and does not appear to be suppressed by wormhole effects. 13 refs.
Initial conditions and quantum cosmology
NASA Technical Reports Server (NTRS)
Hartle, James B.
1987-01-01
A theory of initial conditions is necessary for a complete explanation of the presently observed large scale structural features of the universe, and a quantum theory of cosmology is probably needed for its formulation. The kinematics of quantum cosmology are reviewed, and some candidates for a law of initial conditions are discussed. The proposal that the quantum state of a closed universe is the natural analog of the ground state for closed cosmologies and is specified by a Euclidean sum over histories is sketched. When implemented in simple models, this proposal is consistent with the most important large-scale observations.
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.
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.
Varying constants quantum cosmology
Leszczyńska, Katarzyna; Balcerzak, Adam; Dabrowski, Mariusz P. E-mail: abalcerz@wmf.univ.szczecin.pl
2015-02-01
We discuss minisuperspace models within the framework of varying physical constants theories including Λ-term. In particular, we consider the varying speed of light (VSL) theory and varying gravitational constant theory (VG) using the specific ansätze for the variability of constants: c(a) = c{sub 0} a{sup n} and G(a)=G{sub 0} a{sup q}. We find that most of the varying c and G minisuperspace potentials are of the tunneling type which allows to use WKB approximation of quantum mechanics. Using this method we show that the probability of tunneling of the universe ''from nothing'' (a=0) to a Friedmann geometry with the scale factor a{sub t} is large for growing c models and is strongly suppressed for diminishing c models. As for G varying, the probability of tunneling is large for G diminishing, while it is small for G increasing. In general, both varying c and G change the probability of tunneling in comparison to the standard matter content (cosmological term, dust, radiation) universe models.
Quantum Weyl invariance and cosmology
NASA Astrophysics Data System (ADS)
Dabholkar, Atish
2016-09-01
Equations for cosmological evolution are formulated in a Weyl invariant formalism to take into account possible Weyl anomalies. Near two dimensions, the renormalized cosmological term leads to a nonlocal energy-momentum tensor and a slowly decaying vacuum energy. A natural generalization to four dimensions implies a quantum modification of Einstein field equations at long distances. It offers a new perspective on time-dependence of couplings and naturalness with potentially far-reaching consequences for the cosmological constant problem, inflation, and dark energy.
Quantum cosmology near two dimensions
NASA Astrophysics Data System (ADS)
Bautista, Teresa; Dabholkar, Atish
2016-08-01
We consider a Weyl-invariant formulation of gravity with a cosmological constant in d -dimensional spacetime and show that near two dimensions the classical action reduces to the timelike Liouville action. We show that the renormalized cosmological term leads to a nonlocal quantum momentum tensor which satisfies the Ward identities in a nontrivial way. The resulting evolution equations for an isotropic, homogeneous universe lead to slowly decaying vacuum energy and power-law expansion. We outline the implications for the cosmological constant problem, inflation, and dark energy.
Quantum cosmology with nontrivial topologies
Vargas, T.
2008-10-10
Quantum creation of a universe with a nontrivial spatial topology is considered. Using the Euclidean functional integral prescription, we calculate the wave function of such a universe with cosmological constant and without matter. The minisuperspace path integral is calculated in the semiclassical approximation, and it is shown that in order to include the nontrivial topologies in the path integral approach to quantum cosmology, it is necessary to generalize the sum over compact and smooth 4-manifolds to sum over finite-volume compact 4-orbifolds.
Covariant entropy bound and loop quantum cosmology
Ashtekar, Abhay; Wilson-Ewing, Edward
2008-09-15
We examine Bousso's covariant entropy bound conjecture in the context of radiation filled, spatially flat, Friedmann-Robertson-Walker models. The bound is violated near the big bang. However, the hope has been that quantum gravity effects would intervene and protect it. Loop quantum cosmology provides a near ideal setting for investigating this issue. For, on the one hand, quantum geometry effects resolve the singularity and, on the other hand, the wave function is sharply peaked at a quantum corrected but smooth geometry, which can supply the structure needed to test the bound. We find that the bound is respected. We suggest that the bound need not be an essential ingredient for a quantum gravity theory but may emerge from it under suitable circumstances.
Decoherence in quantum mechanics and quantum cosmology
NASA Technical Reports Server (NTRS)
Hartle, James B.
1992-01-01
A sketch of the quantum mechanics for closed systems adequate for cosmology is presented. This framework is an extension and clarification of that of Everett and builds on several aspects of the post-Everett development. It especially builds on the work of Zeh, Zurek, Joos and Zeh, and others on the interactions of quantum systems with the larger universe and on the ideas of Griffiths, Omnes, and others on the requirements for consistent probabilities of histories.
Loop quantum Brans-Dicke cosmology
NASA Astrophysics Data System (ADS)
Zhang, Xiangdong; Artymowski, Michal; Ma, Yongge
2013-04-01
The spatially flat and isotropic cosmological model of Brans-Dicke theory with coupling parameter ω≠-(3)/(2) is quantized by the approach of loop quantum cosmology. An interesting feature of this model is that although the Brans-Dicke scalar field is nonminimally coupled with curvature, it can still play the role of an emergent time variable. In the quantum theory, the classical differential equation which represents cosmological evolution is replaced by a quantum difference equation. The effective Hamiltonian and modified dynamical equations of loop quantum Brans-Dicke cosmology are also obtained, which lay a foundation for the phenomenological investigation to possible quantum gravity effects in cosmology. The effective equations indicate that the classical big bang singularity is again replaced by a quantum bounce in loop quantum Brans-Dicke cosmology.
Loop quantum cosmology: an overview
NASA Astrophysics Data System (ADS)
Ashtekar, Abhay
2009-04-01
A brief overview of loop quantum cosmology of homogeneous isotropic models is presented with emphasis on the origin of and subtleties associated with the resolution of big bang and big crunch singularities. These results bear out the remarkable intuition that John Wheeler had. Discussion is organized at two levels. The the main text provides a bird’s eye view of the subject that should be accessible to non-experts. Appendices address conceptual and technical issues that are often raised by experts in loop quantum gravity and string theory.
Gauge invariant quantum cosmology
NASA Technical Reports Server (NTRS)
Berger, Beverly K.
1987-01-01
The study of boundary conditions, the Hamiltonian constraint, reparameterization-invariance, and quantum dynamics, is presently approached by means of the path-integral quantization of minisuperspace models. The separation of the wave functions for expansion and contraction by the Feynman boundary conditions is such that there can be no interference between them. This is implemented by the choice of a contour in the complex plane, in order to define the phase of the square-root Arnowitt, Deser, and Misner (1960) Hamiltonian for expansion, collapse, and the classically forbidden region.
Large numbers hypothesis. IV - The cosmological constant and quantum physics
NASA Technical Reports Server (NTRS)
Adams, P. J.
1983-01-01
In standard physics quantum field theory is based on a flat vacuum space-time. This quantum field theory predicts a nonzero cosmological constant. Hence the gravitational field equations do not admit a flat vacuum space-time. This dilemma is resolved using the units covariant gravitational field equations. This paper shows that the field equations admit a flat vacuum space-time with nonzero cosmological constant if and only if the canonical LNH is valid. This allows an interpretation of the LNH phenomena in terms of a time-dependent vacuum state. If this is correct then the cosmological constant must be positive.
New ekpyrotic quantum cosmology
NASA Astrophysics Data System (ADS)
Lehners, Jean-Luc
2015-11-01
Ekpyrotic instantons describe the emergence of classical contracting universes out of the no-boundary quantum state. However, up to now these instantons ended in a big crunch singularity. We remedy this by adding a higher-derivative term, allowing a ghost condensate to form. This causes a smooth, non-singular bounce from the contracting phase into an expanding, kinetic-dominated phase. Remarkably, and although there is a non-trivial evolution during the bounce, the wavefunction of the universe is "classical" in a WKB sense just as much after the bounce as before. These new non-singular instantons can thus form the basis for a fully non-singular and calculable ekpyrotic history of the universe, from creation until now.
Vector fields and Loop Quantum Cosmology
Artymowski, Michał; Lalak, Zygmunt E-mail: Zygmunt.Lalak@fuw.edu.pl
2011-09-01
In the context of the Loop Quantum Cosmology we have analysed the holonomy correction to the classical evolution of the simplified Bianchi I model in the presence of vector fields. For the Universe dominated by a massive vector field or by a combination of a scalar field and a vector field a smooth transition between Kasner-like and Kasner-unlike solutions for a Bianchi I model has been demonstrated. In this case a lack of initial curvature singularity and a finite maximal energy density appear already at the level of General Relativity, which simulates a classical Big Bounce.
Quantum Vacuum Structure and Cosmology
Rafelski, Johann; Labun, Lance; Hadad, Yaron; Chen, Pisin; /Taiwan, Natl. Taiwan U. /KIPAC, Menlo Park /SLAC
2011-12-05
Contemporary physics faces three great riddles that lie at the intersection of quantum theory, particle physics and cosmology. They are: (1) The expansion of the universe is accelerating - an extra factor of two appears in the size; (2) Zero-point fluctuations do not gravitate - a matter of 120 orders of magnitude; and (3) The 'True' quantum vacuum state does not gravitate. The latter two are explicitly problems related to the interpretation and the physical role and relation of the quantum vacuum with and in general relativity. Their resolution may require a major advance in our formulation and understanding of a common unified approach to quantum physics and gravity. To achieve this goal we must develop an experimental basis and much of the discussion we present is devoted to this task. In the following, we examine the observations and the theory contributing to the current framework comprising these riddles. We consider an interpretation of the first riddle within the context of the universe's quantum vacuum state, and propose an experimental concept to probe the vacuum state of the universe.
Quantum inflationary minisuperspace cosmological models
Kim Sangpyo.
1991-01-01
The Wheeler-DeWitt equations for the Friedmann-Robertson-Walker cosmology conformally and minimally coupled to scalar fields with power-lay potential are expanded in the eigenstates of the scalar field parts. The gravitational parts become a diagonal matrix-valued differential equation for a conformal scalar field, and a coupled matrix-valued differential equation for a minimally coupled scalar field. The Cauchy initial value problem is defined with respect to the intrinsic timelike coordinate, and the wavefunctions incorporating initial data are constructed using the product integral formulation. The packetlike wavefunctions around classical turning points are shown possible in the product integral formulation, and the returning wavepackets near the returning point of the classical Friedmann-Robertson-Walker cosmology are constructed. The wavefunctions to the Wheeler-DeWitt equation minimally coupled to the scaler field are constructed by two differential methods, the master equation and the enlarged matrix equation. The spectrum for the wavefunctions regular at the infinite size of universe is found, and these are interpreted as the Hawking-Page spectrum of wormholes connecting two asymptotically Euclidean regions. The quantum Friedmann-Robertson-Walker cosmology is extended to the minimal scalar field with the inflationary potential having a first order phase transition. The Wheeler-DeWitt equation is expanded in the eigenstates of the scalar field, and the gravitational part becomes a coupled matrix-valued differential equation.
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 in 2 +1 dimension
NASA Astrophysics Data System (ADS)
Zhang, Xiangdong
2014-12-01
As a first step to generalize the structure of loop quantum cosmology to the theories with the spacetime dimension other than four, the isotropic model of loop quantum cosmology in 2 +1 dimension is studied in this paper. We find that the classical big bang singularity is again replaced by a quantum bounce in the model. The similarities and differences between the (2 +1 )-dimensional model and the (3 +1 )-dimensional one are also discussed.
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
Loop quantum cosmology with complex Ashtekar variables
NASA Astrophysics Data System (ADS)
Ben Achour, Jibril; Grain, Julien; Noui, Karim
2015-01-01
We construct and study loop quantum cosmology (LQC) when the Barbero-Immirzi parameter takes the complex value γ =+/- i. We refer to this new approach to quantum cosmology as complex LQC. This formulation is obtained via an analytic continuation of the Hamiltonian constraint (with no inverse volume corrections) from real γ to γ =+/- i, in the simple case of a flat FLRW Universe coupled to a massless scalar field with no cosmological constant. For this, we first compute the non-local curvature operator (defined by the trace of the holonomy of the connection around a fundamental plaquette) evaluated in an arbitrary spin j representation, and find a new close formula for its expression. This allows us to define explicitly a one parameter family of regularizations of the Hamiltonian constraint in LQC, parametrized by the spin j. It is immediate to see that any spin j regularization leads to a bouncing scenario. Then, motivated in particular by previous results on black hole thermodynamics, we perform the analytic continuation of the Hamiltonian constraint to values of the Barbero-Immirzi parameter given by γ =+/- i and to spins j=\\frac{1}{2}(-1+is) where s is real. Even if the area spectrum then becomes continuous, we show that the complex LQC defined in this way does also replace the initial big-bang singularity by a big-bounce. In addition to this, the maximal density and the minimal volume of the Universe are obviously independent of γ . Furthermore, the dynamics before and after the bounce is not symmetrical anymore, which makes a clear distinction between these two phases of the evolution of the Universe.
Onset of inflation in loop quantum cosmology
Germani, Cristiano; Nelson, William; Sakellariadou, Mairi
2007-08-15
Using a Liouville measure, similar to the one proposed recently by Gibbons and Turok, we investigate the probability that single-field inflation with a polynomial potential can last long enough to solve the shortcomings of the standard hot big bang model, within the semiclassical regime of loop quantum cosmology. We conclude that, for such a class of inflationary models and for natural values of the loop quantum cosmology parameters, a successful inflationary scenario is highly improbable.
Quantum hyperbolic geometry in loop quantum gravity with cosmological constant
NASA Astrophysics Data System (ADS)
Dupuis, Maïté; Girelli, Florian
2013-06-01
Loop quantum gravity (LQG) is an attempt to describe the quantum gravity regime. Introducing a nonzero cosmological constant Λ in this context has been a standing problem. Other approaches, such as Chern-Simons gravity, suggest that quantum groups can be used to introduce Λ into the game. Not much is known when defining LQG with a quantum group. Tensor operators can be used to construct observables in any type of discrete quantum gauge theory with a classical/quantum gauge group. We illustrate this by constructing explicitly geometric observables for LQG defined with a quantum group and show for the first time that they encode a quantized hyperbolic geometry. This is a novel argument pointing out the usefulness of quantum groups as encoding a nonzero cosmological constant. We conclude by discussing how tensor operators provide the right formalism to unlock the LQG formulation with a nonzero cosmological constant.
Aspects of Quantum Gravity in Cosmology
NASA Astrophysics Data System (ADS)
Rinaldi, Massimiliano
We review some aspects of quantum gravity in the context of cosmology. In particular, we focus on models with a phenomenology accessible to current and near-future observations, as the early Universe might be our only chance to peep through the quantum gravity realm.
Cosmology, the Quantum Universe, Spin and Spinors
NASA Astrophysics Data System (ADS)
Wolff, Milo
2001-03-01
A highly successful mathematical theory of spin has been developed by Paul Dirac and others (1928). Until recently there has been no successful physical description of spin or its origin. The electron's structure and its spin had been a mystery. Describing them and their cosmological implications is the role of this poster display. Spin is measured in units of angular momentum like rotating objects of human size. But particle spin is uniquely a quantum phenomenon because its value is fixed and cannot be calculated from mass or angular velocity. It will be shown that this occurs because spin is due to the behavior of the waves that form the electron structure. This is very easy to understand after you recognize that particles are 100% waves while mass and charge are properties of the waves in a space medium. The Greek concept of solid particles and charge is not correct. The Wave Structure of Matter was popular sixty years ago among the pioneers of quantum theory. Namely that matter consists of undulations in the fabric of space. The matter substances, mass and charge, are appearances or 'schaumkommen' as conjectured by Schröedinger. His prediction is consistent with quantum theory because QM does not depend on the existence of such substances. This poster describes how the spin of the electron arises out of the Quantum Wave Structure of Matter. The electron in particular is formed of a pair of spherical quantum waves, one inward and one outward. Spin is the result of spherical rotation of the inward wave of the electron at the electron center where it converts to the outward wave. Spherical rotation is a required condition to maintain proper phase relations of the in- and out- wave amplitudes. The spherical rotation, which is a unique property of 3D space, can be described using SU(2) group theory algebra. Thus the IN and OUT waves of the charged particle are a Dirac spinor of two elements. Surprisingly, the universe is constructed of binary elements like computer
Quantum cosmological consistency condition for inflation
Calcagni, Gianluca; Kiefer, Claus; Steinwachs, Christian F. E-mail: kiefer@thp.uni-koeln.de
2014-10-01
We investigate the quantum cosmological tunneling scenario for inflationary models. Within a path-integral approach, we derive the corresponding tunneling probability distribution. A sharp peak in this distribution can be interpreted as the initial condition for inflation and therefore as a quantum cosmological prediction for its energy scale. This energy scale is also a genuine prediction of any inflationary model by itself, as the primordial gravitons generated during inflation leave their imprint in the B-polarization of the cosmic microwave background. In this way, one can derive a consistency condition for inflationary models that guarantees compatibility with a tunneling origin and can lead to a testable quantum cosmological prediction. The general method is demonstrated explicitly for the model of natural inflation.
Gaussian state for the bouncing quantum cosmology
NASA Astrophysics Data System (ADS)
Mielczarek, Jakub; Piechocki, Włodzimierz
2012-10-01
We present results concerning propagation of the Gaussian state across the cosmological quantum bounce. The reduced phase space quantization of loop quantum cosmology is applied to the Friedman-Robertson-Walker universe with a free massless scalar field. Evolution of quantum moments of the canonical variables is investigated. The covariance turns out to be a monotonic function so it may be used as an evolution parameter having quantum origin. We show that for the Gaussian state the Universe is least quantum at the bounce. We propose explanation of this counter-intuitive feature using the entropy of squeezing. The obtained time dependence of entropy is in agreement with qualitative predictions based on von Neumann entropy for mixed states. We show that, for the considered Gaussian state, semiclassicality is preserved across the bounce, so there is no cosmic forgetfulness.
Cosmological implications of modified gravity induced by quantum metric fluctuations
NASA Astrophysics Data System (ADS)
Liu, Xing; Harko, Tiberiu; Liang, Shi-Dong
2016-08-01
We investigate the cosmological implications of modified gravities induced by the quantum fluctuations of the gravitational metric. If the metric can be decomposed as the sum of the classical and of a fluctuating part, of quantum origin, then the corresponding Einstein quantum gravity generates at the classical level modified gravity models with a non-minimal coupling between geometry and matter. As a first step in our study, after assuming that the expectation value of the quantum correction can be generally expressed in terms of an arbitrary second order tensor constructed from the metric and from the thermodynamic quantities characterizing the matter content of the Universe, we derive the (classical) gravitational field equations in their general form. We analyze in detail the cosmological models obtained by assuming that the quantum correction tensor is given by the coupling of a scalar field and of a scalar function to the metric tensor, and by a term proportional to the matter energy-momentum tensor. For each considered model we obtain the gravitational field equations, and the generalized Friedmann equations for the case of a flat homogeneous and isotropic geometry. In some of these models the divergence of the matter energy-momentum tensor is non-zero, indicating a process of matter creation, which corresponds to an irreversible energy flow from the gravitational field to the matter fluid, and which is direct consequence of the non-minimal curvature-matter coupling. The cosmological evolution equations of these modified gravity models induced by the quantum fluctuations of the metric are investigated in detail by using both analytical and numerical methods, and it is shown that a large variety of cosmological models can be constructed, which, depending on the numerical values of the model parameters, can exhibit both accelerating and decelerating behaviors.
Quantum coherence, wormholes, and the cosmological constant
Unruh, W.G. )
1989-08-15
Coleman has argued that if wormhole solutions to the Euclidean action coupled to matter dominate the Euclidean path integral for quantum gravity, they do not lead to a loss of quantum coherence for wave functions in our Universe. Furthermore, they also lead to the prediction that the ultimate'' cosmological constant is zero. I analyze the assumptions that go into this result and argue that the presence of wormhole solutions does lead to a loss of quantum coherence and, furthermore, completely destroys the Euclidean quantum theory by producing a highly nonlocal effective Euclidean action which is violently unbounded from below.
Quantum Steganography and Quantum Error-Correction
ERIC Educational Resources Information Center
Shaw, Bilal A.
2010-01-01
Quantum error-correcting codes have been the cornerstone of research in quantum information science (QIS) for more than a decade. Without their conception, quantum computers would be a footnote in the history of science. When researchers embraced the idea that we live in a world where the effects of a noisy environment cannot completely be…
Warm inflationary model in loop quantum cosmology
Herrera, Ramon
2010-06-15
A warm inflationary universe model in loop quantum cosmology is studied. In general we discuss the condition of inflation in this framework. By using a chaotic potential, V({phi}){proportional_to}{phi}{sup 2}, we develop a model where the dissipation coefficient {Gamma}={Gamma}{sub 0}=constant. We use recent astronomical observations for constraining the parameters appearing in our model.
Towards Noncommutative Supersymmetric Quantum Cosmology
NASA Astrophysics Data System (ADS)
Sabido, M.; Guzmán, W.; Socorro, J.
2010-12-01
In this work a construction of supersymmetric noncommutative cosmology is presented. We start with a ``noncommutative'' deformation of the minisuperspace variables, and by using the time reparametrization invariance of the noncommutative bosonic model we proceed to construct a super field description of the model.
Future singularities and teleparallelism in loop quantum cosmology
Bamba, Kazuharu; Haro, Jaume de; Odintsov, Sergei D. E-mail: jaime.haro@upc.edu
2013-02-01
We demonstrate how holonomy corrections in loop quantum cosmology (LQC) prevent the Big Rip singularity by introducing a quadratic modification in terms of the energy density ρ in the Friedmann equation in the Friedmann-Lemaître-Robertson-Walker (FLRW) space-time in a consistent and useful way. In addition, we investigate whether other kind of singularities like Type II,III and IV singularities survive or are avoided in LQC when the universe is filled by a barotropic fluid with the state equation P = −ρ−f(ρ), where P is the pressure and f(ρ) a function of ρ. It is shown that the Little Rip cosmology does not happen in LQC. Nevertheless, the occurrence of the Pseudo-Rip cosmology, in which the phantom universe approaches the de Sitter one asymptotically, is established, and the corresponding example is presented. It is interesting that the disintegration of bound structures in the Pseudo-Rip cosmology in LQC always takes more time than that in Einstein cosmology. Our investigation on future singularities is generalized to that in modified teleparallel gravity, where LQC and Brane Cosmology in the Randall-Sundrum scenario are the best examples. It is remarkable that F(T) gravity may lead to all the kinds of future singularities including Little Rip.
Quantum error correction beyond qubits
NASA Astrophysics Data System (ADS)
Aoki, Takao; Takahashi, Go; Kajiya, Tadashi; Yoshikawa, Jun-Ichi; Braunstein, Samuel L.; van Loock, Peter; Furusawa, Akira
2009-08-01
Quantum computation and communication rely on the ability to manipulate quantum states robustly and with high fidelity. To protect fragile quantum-superposition states from corruption through so-called decoherence noise, some form of error correction is needed. Therefore, the discovery of quantum error correction (QEC) was a key step to turn the field of quantum information from an academic curiosity into a developing technology. Here, we present an experimental implementation of a QEC code for quantum information encoded in continuous variables, based on entanglement among nine optical beams. This nine-wave-packet adaptation of Shor's original nine-qubit scheme enables, at least in principle, full quantum error correction against an arbitrary single-beam error.
Quantum Coherence Arguments for Cosmological Scale
Lindesay, James; /SLAC
2005-05-27
Homogeneity and correlations in the observed CMB are indicative of some form of cosmological coherence in early times. Quantum coherence in the early universe would be expected to give space-like phase coherence to any effects sourced to those times. If dark energy de-coherence is assumed to occur when the rate of expansion of the relevant cosmological scale parameter in the Friedmann-Lemaitre equations is no longer supra-luminal, a critical energy density is immediately defined. It is shown that the general class of dynamical models so defined necessarily requires a spatially flat cosmology in order to be consistent with observed structure formation. The basic assumption is that the dark energy density which is fixed during de-coherence is to be identified with the cosmological constant. It is shown for the entire class of models that the expected amplitude of fluctuations driven by the dark energy de-coherence process is of the order needed to evolve into the fluctuations observed in cosmic microwave background radiation and galactic clustering. The densities involved during de-coherence which correspond to the measured dark energy density turn out to be of the electroweak symmetry restoration scale. In an inflationary cosmology, this choice of the scale parameter in the FL equations directly relates the scale of dark energy decoherence to the De Sitter scales (associated with the positive cosmological constants) at both early and late times.
Uniqueness of measures in loop quantum cosmology
Hanusch, Maximilian
2015-09-15
In Ashtekar and Campiglia [Classical Quantum Gravity 29, 242001 (2012)], residual diffeomorphisms have been used to single out the standard representation of the reduced holonomy-flux algebra in homogeneous loop quantum cosmology (LQC). We show that, in the homogeneous isotropic case, unitarity of the translations with respect to the extended ℝ-action (exponentiated reduced fluxes in the standard approach) singles out the Bohr measure on both the standard quantum configuration space ℝ{sub Bohr} as well as on the Fleischhack one (ℝ⊔ℝ{sub Bohr}). Thus, in both situations, the same condition singles out the standard kinematical Hilbert space of LQC.
Loop quantum cosmology and the fate of cosmological singularities
NASA Astrophysics Data System (ADS)
Singh, Parampreet
2014-09-01
Singularities in general relativity such as the big bang and big crunch, and exotic singularities such as the big rip are the boundaries of the classical spacetimes. These events are marked by a divergence in the curvature invariants and the breakdown of the geodesic evolution. Recent progress on implementing techniques of loop quantum gravity to cosmological models reveals that such singularities may be generically resolved because of the quantum gravitational effects. Due to the quantum geometry, which replaces the classical differential geometry at the Planck scale, the big bang is replaced by a big bounce without any assumptions on the matter content or any fine tuning. In this manuscript, we discuss some of the main features of this approach and the results on the generic resolution of singularities for the isotropic as well as anisotropic models. Using effective spacetime description of the quantum theory, we show the way quantum gravitational effects lead to the universal bounds on the energy density, the Hubble rate and the anisotropic shear. We discuss the geodesic completeness in the effective spacetime and the resolution of all of the strong singularities. It turns out that despite the bounds on energy density and the Hubble rate, there can be divergences in the curvature invariants. However such events are geodesically extendible, with tidal forces not strong enough to cause inevitable destruction of the in-falling objects.
Exact solutions for a big bounce in loop quantum cosmology
Mielczarek, Jakub; Stachowiak, Tomasz; Szydlowski, Marek
2008-06-15
In this paper we study the flat (k=0) cosmological Friedmann-Robertson-Walker model with holonomy corrections of loop quantum gravity. The considered universe contains a massless scalar field and the cosmological constant {lambda}. We find analytical solutions for this model in different configurations and investigate its dynamical behavior in the whole phase space. Such an approach might be significant e.g. as a phenomenological reference for a further, fully quantum treatment. We show the explicit influence of {lambda} on the qualitative and quantitative character of solutions. Even in the case of positive {lambda} the oscillating solutions without the initial and final singularity appear as a generic case for some quantization schemes.
Hořava-Lifshitz quantum cosmology
NASA Astrophysics Data System (ADS)
Bertolami, Orfeu; Zarro, Carlos A. D.
2011-08-01
In this work, a minisuperspace model for the projectable Hořava-Lifshitz gravity without the detailed-balance condition is investigated. The Wheeler-DeWitt equation is derived and its solutions are studied and discussed for some particular cases where, due to Hořava-Lifshitz gravity, there is a “potential barrier” nearby a=0. For a vanishing cosmological constant, a normalizable wave function of the Universe is found. When the cosmological constant is nonvanishing, the WKB method is used to obtain solutions for the wave function of the Universe. Using the Hamilton-Jacobi equation, one discusses how the transition from quantum to classical regime occurs and, for the case of a positive cosmological constant, the scale factor is shown to grow exponentially, hence recovering the general relativity behavior for the late Universe.
Shape space methods for quantum cosmological triangleland
NASA Astrophysics Data System (ADS)
Anderson, Edward
2011-05-01
With toy modelling of conceptual aspects of quantum cosmology and the problem of time in quantum gravity in mind, I study the classical and quantum dynamics of the pure-shape (i.e. scale-free) triangle formed by 3 particles in 2- d. I do so by importing techniques to the triangle model from the corresponding 4 particles in 1- d model, using the fact that both have 2-spheres for shape spaces, though the latter has a trivial realization whilst the former has a more involved Hopf (or Dragt) type realization. I furthermore interpret the ensuing Dragt-type coordinates as shape quantities: a measure of anisoscelesness, the ellipticity of the base and apex's moments of inertia, and a quantity proportional to the area of the triangle. I promote these quantities at the quantum level to operators whose expectation and spread are then useful in understanding the quantum states of the system. Additionally, I tessellate the 2-sphere by its physical interpretation as the shape space of triangles, and then use this as a back-cloth from which to read off the interpretation of dynamical trajectories, potentials and wavefunctions. I include applications to timeless approaches to the problem of time and to the role of uniform states in quantum cosmological modelling.
Further corrections to the theory of cosmological recombination
NASA Technical Reports Server (NTRS)
Krolik, Julian H.
1990-01-01
Krolik (1989) pointed out that frequency redistribution due to scattering is more important than cosmological expansion in determining the Ly-alpha frequency profile during cosmological recombination, and that its effects substantially modify the rate of recombination. Although the first statement is true, the second statement is not: a basic symmetry of photon scattering leads to identical cancellations which almost completely erase the effects of both coherent and incoherent scattering. Only a small correction due to atomic recoil alters the line profile from the prediction of pure cosmological expansion, so that the pace of cosmological recombination can be well approximated by ignoring Ly-alpha scattering.
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.
Supersymmetric quantum cosmology: a `Socratic' guide
NASA Astrophysics Data System (ADS)
Moniz, Paulo Vargas
2014-01-01
By adequately adapting a `knowledge by enquire' approach, an appraisal of what supersymmetric quantum cosmology (SQC) entails ( viz., some of the difficulties but also current successes and motivation) is subsequently presented. More concretely, the basics of SQC are briefly reviewed in a pedagogical manner. The purpose is twofold: (i) promote SQC as a promising line where to conduct research work and (ii) provide an introduction to the essential computational framework. Directions still open to be explored are pointed out.
Dynamical Casimir effect and quantum cosmology
NASA Astrophysics Data System (ADS)
Brevik, I.; Milton, K. A.; Odintsov, S. D.; Osetrin, K. E.
2000-09-01
We apply the background field method and the effective action formalism to describe the four-dimensional dynamical Casimir effect. Our picture corresponds to the consideration of quantum cosmology for an expanding FRW universe (the boundary conditions act as a moving mirror) filled by a quantum massless GUT which is conformally invariant. We consider cases in which the static Casimir energy is attractive and repulsive. Inserting the simplest possible inertial term, we find, in the adiabatic (and semiclassical) approximation, the dynamical evolution of the scale factor and the dynamical Casimir stress analytically and numerically [for SU(2) super Yang-Mills theory]. Alternative kinetic energy terms are explored in the Appendix.
Generalized effective description of loop quantum cosmology
NASA Astrophysics Data System (ADS)
Ashtekar, Abhay; Gupt, Brajesh
2015-10-01
The effective description of loop quantum cosmology (LQC) has proved to be a convenient platform to study phenomenological implications of the quantum bounce that resolves the classical big bang singularity. Originally, this description was derived using Gaussian quantum states with small dispersions. In this paper we present a generalization to incorporate states with large dispersions. Specifically, we derive the generalized effective Friedmann and Raychaudhuri equations and propose a generalized effective Hamiltonian which are being used in an ongoing study of the phenomenological consequences of a broad class of quantum geometries. We also discuss an interesting interplay between the physics of states with larger dispersions in standard LQC, and of sharply peaked states in (hypothetical) LQC theories with larger area gap.
Interpretation and Predictability of Quantum Mechanics and Quantum Cosmology
NASA Astrophysics Data System (ADS)
Wada, Sumio
A non-probabilistic interpretation of quantum mechanics asserts that we get a prediction only when a wave function has a peak. Taking this interpretation seriously, we discuss how to find a peak in the wave function of the universe, by using some minisuperspace models with homogeneous degrees of freedom and also a model with cosmological perturbations. Then we show how to recover our classical picture of the universe from the quantum theory, and comment on the physical meaning of the backreaction equation.
Cosmological inflation and the quantum measurement problem
NASA Astrophysics Data System (ADS)
Martin, Jérôme; Vennin, Vincent; Peter, Patrick
2012-11-01
According to cosmological inflation, the inhomogeneities in our Universe are of quantum-mechanical origin. This scenario is phenomenologically very appealing as it solves the puzzles of the standard hot big bang model and naturally explains why the spectrum of cosmological perturbations is almost scale invariant. It is also an ideal playground to discuss deep questions among which is the quantum measurement problem in a cosmological context. Although the large squeezing of the quantum state of the perturbations and the phenomenon of decoherence explain many aspects of the quantum-to-classical transition, it remains to understand how a specific outcome can be produced in the early Universe, in the absence of any observer. The continuous spontaneous localization (CSL) approach to quantum mechanics attempts to solve the quantum measurement question in a general context. In this framework, the wave function collapse is caused by adding new nonlinear and stochastic terms to the Schrödinger equation. In this paper, we apply this theory to inflation, which amounts to solving the CSL parametric oscillator case. We choose the wave function collapse to occur on an eigenstate of the Mukhanov-Sasaki variable and discuss the corresponding modified Schrödinger equation. Then, we compute the power spectrum of the perturbations and show that it acquires a universal shape with two branches, one which remains scale invariant and one with nS=4, a spectral index in obvious contradiction with the cosmic microwave background anisotropy observations. The requirement that the non-scale-invariant part be outside the observational window puts stringent constraints on the parameter controlling the deviations from ordinary quantum mechanics. Due to the absence of a CSL amplification mechanism in field theory, this also has the consequence that the collapse mechanism of the inflationary fluctuations is not efficient. Then, we determine the collapse time. On small scales the collapse is
Large classical universes emerging from quantum cosmology
Pinto-Neto, Nelson
2009-04-15
It is generally believed that one cannot obtain a large universe from quantum cosmological models without an inflationary phase in the classical expanding era because the typical size of the universe after leaving the quantum regime should be around the Planck length, and the standard decelerated classical expansion after that is not sufficient to enlarge the universe in the time available. For instance, in many quantum minisuperspace bouncing models studied in the literature, solutions where the universe leaves the quantum regime in the expanding phase with appropriate size have negligible probability amplitude with respect to solutions leaving this regime around the Planck length. In this paper, I present a general class of moving Gaussian solutions of the Wheeler-DeWitt equation where the velocity of the wave in minisuperspace along the scale factor axis, which is the new large parameter introduced in order to circumvent the above-mentioned problem, induces a large acceleration around the quantum bounce, forcing the universe to leave the quantum regime sufficiently big to increase afterwards to the present size, without needing any classical inflationary phase in between, and with reasonable relative probability amplitudes with respect to models leaving the quantum regime around the Planck scale. Furthermore, linear perturbations around this background model are free of any trans-Planckian problem.
Inflation with the Starobinsky potential in loop quantum cosmology
NASA Astrophysics Data System (ADS)
Bonga, Béatrice; Gupt, Brajesh
2016-06-01
A self-consistent pre-inflationary extension of the inflationary scenario with the Starobinsky potential, favored by Planck data, is studied using techniques from loop quantum cosmology (LQC). The results are compared with the quadratic potential previously studied. Planck scale completion of the inflationary paradigm and observable signatures of LQC are found to be robust under the change of the inflation potential. The entire evolution, from the quantum bounce all the way to the end of inflation, is compatible with observations. Occurrence of desired slow-roll phase is almost inevitable and natural initial conditions exist for both the background and perturbations for which the resulting power spectrum agrees with recent observations. There exist initial data for which the quantum gravitational corrections to the power spectrum are potentially observable.
Inflationary cosmology from quantum conformal gravity
NASA Astrophysics Data System (ADS)
Jizba, Petr; Kleinert, Hagen; Scardigli, Fabio
2015-06-01
We analyze the functional integral for quantum conformal gravity and show that, with the help of a Hubbard-Stratonovich transformation, the action can be broken into a local quadratic-curvature theory coupled to a scalar field. A one-loop effective-action calculation reveals that strong fluctuations of the metric field are capable of spontaneously generating a dimensionally transmuted parameter which, in the weak-field sector of the broken phase, induces a Starobinsky-type f( R)-model with a gravi-cosmological constant. A resulting non-trivial relation between Starobinsky's parameter and the gravi-cosmological constant is highlighted and implications for cosmic inflation are briefly discussed and compared with the recent PLANCK and BICEP2 data.
Matter bounce loop quantum cosmology from F (R ) gravity
NASA Astrophysics Data System (ADS)
Odintsov, S. D.; Oikonomou, V. K.
2014-12-01
Using the reconstruction method, we investigate which F (R ) theories, with or without the presence of matter fluids, can produce the matter bounce scenario of holonomy corrected loop quantum cosmology. We focus our study in two limits of the cosmic time, the large cosmic time limit and the small cosmic time limit. For the former, we find that, in the presence of noninteracting and nonrelativistic matter, the F (R ) gravity that reproduces the late time limit of the matter bounce solution is actually the Einstein-Hilbert gravity plus a power law term. In the early time limit, since it corresponds to large spacetime curvatures, assuming that the Jordan frame is described by a general metric that, when it is conformally transformed to the Einstein frame, produces an accelerating Friedmann-Robertson-Walker metric, we find explicitly the scalar field dependence on time. After demonstrating that the solution in the Einstein frame is indeed accelerating, we calculate the spectral index derived from the Einstein frame scalar-tensor counterpart theory of the F (R ) theory and compare it with the Planck experiment data. In order to implement the resulting picture, we embed the F (R ) gravity explicitly in a loop quantum cosmology framework by introducing holonomy corrections to the F (R ) gravity. In this way, the resulting inflation picture corresponding to the F (R ) gravity can be corrected in order that it coincides to some extent with the current experimental data.
Improved Quantum Metrology Using Quantum Error Correction
NASA Astrophysics Data System (ADS)
Dür, W.; Skotiniotis, M.; Fröwis, F.; Kraus, B.
2014-02-01
We consider quantum metrology in noisy environments, where the effect of noise and decoherence limits the achievable gain in precision by quantum entanglement. We show that by using tools from quantum error correction this limitation can be overcome. This is demonstrated in two scenarios, including a many-body Hamiltonian with single-qubit dephasing or depolarizing noise and a single-body Hamiltonian with transversal noise. In both cases, we show that Heisenberg scaling, and hence a quadratic improvement over the classical case, can be retained. Moreover, for the case of frequency estimation we find that the inclusion of error correction allows, in certain instances, for a finite optimal interrogation time even in the asymptotic limit.
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.
Quantum Error Correction for Metrology
NASA Astrophysics Data System (ADS)
Sushkov, Alex; Kessler, Eric; Lovchinsky, Igor; Lukin, Mikhail
2014-05-01
The question of the best achievable sensitivity in a quantum measurement is of great experimental relevance, and has seen a lot of attention in recent years. Recent studies [e.g., Nat. Phys. 7, 406 (2011), Nat. Comms. 3, 1063 (2012)] suggest that in most generic scenarios any potential quantum gain (e.g. through the use of entangled states) vanishes in the presence of environmental noise. To overcome these limitations, we propose and analyze a new approach to improve quantum metrology based on quantum error correction (QEC). We identify the conditions under which QEC allows one to improve the signal-to-noise ratio in quantum-limited measurements, and we demonstrate that it enables, in certain situations, Heisenberg-limited sensitivity. We discuss specific applications to nanoscale sensing using nitrogen-vacancy centers in diamond in which QEC can significantly improve the measurement sensitivity and bandwidth under realistic experimental conditions.
Novel Numerical Approaches to Loop Quantum Cosmology
NASA Astrophysics Data System (ADS)
Diener, Peter
2015-04-01
Loop Quantum Gravity (LQG) is an (as yet incomplete) approach to the quantization of gravity. When applied to symmetry reduced cosmological spacetimes (Loop Quantum Cosmology or LQC) one of the predictions of the theory is that the Big Bang is replaced by a Big Bounce, i.e. a previously existing contracting universe underwent a bounce at finite volume before becoming our expanding universe. The evolution equations of LQC take the form of difference equations (with the discretization given by the theory) that in the large volume limit can be approximated by partial differential equations (PDEs). In this talk I will first discuss some of the unique challenges encountered when trying to numerically solve these difference equations. I will then present some of the novel approaches that have been employed to overcome the challenges. I will here focus primarily on the Chimera scheme that takes advantage of the fact that the LQC difference equations can be approximated by PDEs in the large volume limit. I will finally also briefly discuss some of the results that have been obtained using these numerical techniques by performing simulations in regions of parameter space that were previously unreachable. This work is supported by a grant from the John Templeton Foundation and by NSF grant PHYS1068743.
Interpretation and predictability of quantum mechanics and quantum cosmology
Wada, S.
1988-06-01
A non-probabilistic interpretation of quantum mechanics asserts that the authors get a prediction only when a wave function has a peak. Taking this interpretation seriously, the authors discuss how to find a peak in the wave function of the universe, by using some minisuperspace models. With homogeneous degrees of freedom and also a model with cosmological perturbations. Then the authors show how to recover their classical picture of the universe from the quantum theory, and comment on the physical meaning of the backreaction equation.
Interacting Ricci Logarithmic Entropy-Corrected Holographic Dark Energy in Brans-Dicke Cosmology
NASA Astrophysics Data System (ADS)
Pasqua, Antonio; Khomenko, Iuliia
2013-11-01
In the derivation of Holographic Dark Energy (HDE), the area law of the black hole entropy assumes a crucial role. However, the entropy-area relation can be modified including some quantum effects, motivated from the Loop Quantum Gravity (LQG), string theory and black hole physics. In this paper, we study the cosmological implications of the interacting logarithmic entropy-corrected HDE (LECHDE) model in the framework of Brans-Dicke (BD) cosmology. As system’s infrared (IR) cut-off, we choose the average radius of Ricci scalar curvature, i.e. R -1/2. We obtain the Equation of State (EoS) parameter ω D , the deceleration parameter q and the evolution of energy density parameter of our model in a non-flat universe. Moreover, we study the limiting cases corresponding to our model without corrections and to the Einstein’s gravity.
Bogolyubov's integrals of motion in quantum cosmology and gravity
Pervushin, V. N. Zinchuk, V. A.
2007-03-15
Quantum cosmology and gravity are defined here as the primary and secondary quantizations of the energy constraints by analogy with the historical formulation of quantum field theory given in the 20th century. A new fact is that both the Universe and its matter are created from stable vacuum obtained by the Bogolyubov transformations applied to description of quantum superfluid liquid. We show that the quantum gravity makes it possible to explain topical problems of cosmology by the cosmological creation of both universes and particles from Bogolyubov's vacuum.
Quantum reduced loop gravity and the foundation of loop quantum cosmology
NASA Astrophysics Data System (ADS)
Alesci, Emanuele; Cianfrani, Francesco
2016-06-01
Quantum reduced loop gravity is a promising framework for linking loop quantum gravity and the effective semiclassical dynamics of loop quantum cosmology. We review its basic achievements and its main perspectives, outlining how it provides a quantum description of the Universe in terms of a cuboidal graph which constitutes the proper framework for applying loop techniques in a cosmological setting.
Quantum nonthermal radiation of nonstationary rotating de Sitter cosmological model
NASA Astrophysics Data System (ADS)
Meitei, Irom Ablu; Singh, T. Ibungochouba; Singh, K. Yugindro
2014-08-01
Using the Hamilton-Jacobi method a study of quantum nonthermal radiation of nonstationary rotating de Sitter cosmological model is carried out. It is shown that there exist seas of positive and negative energy states in the vicinity of the cosmological event horizon and there also exists a forbidden energy gap between the two seas. The forbidden energy gap vanishes on the surface of the cosmological event horizon so that the positive and negative energy levels overlap. The width of the forbidden energy gap and the energy of the particle at the cosmological event horizon are found to depend on the cosmological constant, the rotation parameter, positions of the particle and the cosmological event horizon, angular momentum of the particle, evaporation rate and shape of the cosmological event horizon. The tunneling probability of the emitted particles constituting Hawking radiation is also deduced for stationary nonrotating de Sitter cosmological model and the standard Hawking temperature is recovered.
Embedding loop quantum cosmology without piecewise linearity
NASA Astrophysics Data System (ADS)
Engle, Jonathan
2013-04-01
An important goal is to understand better the relation between full loop quantum gravity (LQG) and the simplified, reduced theory known as loop quantum cosmology (LQC), directly at the quantum level. Such a firmer understanding would increase confidence in the reduced theory as a tool for formulating predictions of the full theory, as well as permitting lessons from the reduced theory to guide further development in the full theory. This paper constructs an embedding of the usual state space of LQC into that of standard LQG, that is, LQG based on piecewise analytic paths. The embedding is well defined even prior to solving the diffeomorphism constraint, at no point is a graph fixed and at no point is the piecewise linear category used. This motivates for the first time a definition of operators in LQC corresponding to holonomies along non-piecewise linear paths, without changing the usual kinematics of LQC in any way. The new embedding intertwines all operators corresponding to such holonomies, and all elements in its image satisfy an operator equation which classically implies homogeneity and isotropy. The construction is made possible by a recent result proven by Fleischhack. Communicated by P Singh
Observational exclusion of a consistent loop quantum cosmology scenario
NASA Astrophysics Data System (ADS)
Bolliet, Boris; Barrau, Aurélien; Grain, Julien; Schander, Susanne
2016-06-01
It is often argued that inflation erases all the information about what took place before it started. Quantum gravity, relevant in the Planck era, seems therefore mostly impossible to probe with cosmological observations. In general, only very ad hoc scenarios or hyper fine-tuned initial conditions can lead to observationally testable theories. Here we consider a well-defined and well-motivated candidate quantum cosmology model that predicts inflation. Using the most recent observational constraints on the cosmic microwave background B-modes, we show that the model is excluded for all its parameter space, without any tuning. Some important consequences are drawn for the deformed algebra approach to loop quantum cosmology. We emphasize that neither loop quantum cosmology in general nor loop quantum gravity are disfavored by this study but their falsifiability is established.
Quantum corrections to the Mukhanov-Sasaki equations
NASA Astrophysics Data System (ADS)
Castelló Gomar, Laura; Mena Marugán, Guillermo A.; Martín-Benito, Mercedes
2016-05-01
Recently, a lot of attention has been paid to the modifications of the power spectrum of primordial fluctuations caused by quantum cosmology effects. The origin of these modifications is corrections to the Mukhanov-Sasaki equations that govern the propagation of the primeval cosmological perturbations. The specific form of these corrections depends on a series of details of the quantization approach and of the prescription followed to implement it. Generally, the complexity of the theoretical quantum formulation is simplified in practice appealing to a semiclassical or effective approximation in order to perform concrete numerical computations. In this work, we introduce technical tools and design a procedure to deal with these quantum corrections beyond the most direct approximations employed so far in the literature. In particular, by introducing an interaction picture, we extract the quantum dynamics of the homogeneous geometry in absence of scalar field potential and inhomogeneities, dynamics that has been intensively studied and that can be integrated. The rest of our analysis focuses on the interaction evolution, putting forward methods to cope with it. The ultimate aim is to develop treatments that increase our ability to discriminate between the predictions of different quantization proposals for cosmological perturbations.
Loop quantum cosmology of Bianchi type I models
NASA Astrophysics Data System (ADS)
Ashtekar, Abhay; Wilson-Ewing, Edward
2009-04-01
The “improved dynamics” of loop quantum cosmology is extended to include anisotropies of the Bianchi type I model. As in the isotropic case, a massless scalar field serves as a relational time parameter. However, the extension is nontrivial because one has to face several conceptual subtleties as well as technical difficulties. These include a better understanding of the relation between loop quantum gravity and loop quantum cosmology, handling novel features associated with the nonlocal field strength operator in presence of anisotropies, and finding dynamical variables that make the action of the Hamiltonian constraint manageable. Our analysis provides a conceptually complete description that overcomes limitations of earlier works. We again find that the big-bang singularity is resolved by quantum geometry effects but, because of the presence of Weyl curvature, Planck scale physics is now much richer than in the isotropic case. Since the Bianchi I models play a key role in the Belinskii, Khalatnikov, Lifshitz conjecture on the nature of generic spacelike singularities in general relativity, the quantum dynamics of Bianchi I cosmologies is likely to provide considerable intuition about the fate of generic spacelike singularities in quantum gravity. Finally, we show that the quantum dynamics of Bianchi I cosmologies projects down exactly to that of the Friedmann model. This opens a new avenue to relate more complicated models to simpler ones, thereby providing a new tool to relate the quantum dynamics of loop quantum gravity to that of loop quantum cosmology.
Loop quantum cosmology of Bianchi type I models
Ashtekar, Abhay; Wilson-Ewing, Edward
2009-04-15
The ''improved dynamics'' of loop quantum cosmology is extended to include anisotropies of the Bianchi type I model. As in the isotropic case, a massless scalar field serves as a relational time parameter. However, the extension is nontrivial because one has to face several conceptual subtleties as well as technical difficulties. These include a better understanding of the relation between loop quantum gravity and loop quantum cosmology, handling novel features associated with the nonlocal field strength operator in presence of anisotropies, and finding dynamical variables that make the action of the Hamiltonian constraint manageable. Our analysis provides a conceptually complete description that overcomes limitations of earlier works. We again find that the big-bang singularity is resolved by quantum geometry effects but, because of the presence of Weyl curvature, Planck scale physics is now much richer than in the isotropic case. Since the Bianchi I models play a key role in the Belinskii, Khalatnikov, Lifshitz conjecture on the nature of generic spacelike singularities in general relativity, the quantum dynamics of Bianchi I cosmologies is likely to provide considerable intuition about the fate of generic spacelike singularities in quantum gravity. Finally, we show that the quantum dynamics of Bianchi I cosmologies projects down exactly to that of the Friedmann model. This opens a new avenue to relate more complicated models to simpler ones, thereby providing a new tool to relate the quantum dynamics of loop quantum gravity to that of loop quantum cosmology.
Thermoelectric Corrections to Quantum Measurement
NASA Astrophysics Data System (ADS)
Bergfield, Justin; Ratner, Mark; Stafford, Charles; di Ventra, Massimiliano
The voltage and temperature measured by a floating probe of a nonequilibrium quantum system is shown to exhibit nontrivial thermoelectric corrections at finite temperature. Using a realistic model of a scanning thermal microscope to calculate the voltage and temperature distributions, we predict quantum temperature variations along graphene nanoribbons subject to a thermal bias which are not simply related to the local density of states. Experimentally, the wavelength of the oscillations can be tuned over several orders of magnitude by gating/doping, bringing quantum temperature oscillations within reach of the spatial resolution of existing measurement techniques. We also find that the Peltier cooling/heating which causes the temperature oscillations can lead to significant errors in voltage measurements for a wide range of system.
Fabris, Júlio C.; Pelinson, Ana M.; Salles, Filipe de O.; Shapiro, Ilya L. E-mail: ana.pelinson@gmail.com E-mail: shapiro@fisica.ufjf.br
2012-02-01
The dynamics of metric perturbations is explored in the gravity theory with anomaly-induced quantum corrections. Our first purpose is to derive the equation for gravitational waves in this theory on the general homogeneous and isotropic background, and then verify the stability of such background with respect to metric perturbations. The problem under consideration has several interesting applications. Our first purpose is to explore the stability of the classical cosmological solutions in the theory with quantum effects taken into account. There is an interesting literature about stability of Minkowski and de Sitter spaces and here we extend the consideration also to the radiation and matter dominated cosmologies. Furthermore, we analyze the behavior of metric perturbations during inflationary period, in the stable phase of the Modified Starobinsky inflation.
NASA Astrophysics Data System (ADS)
Paranjape, Aseem
A consistent approach to cosmology requires an explicit averaging of the Einstein equations, to describe a homogeneous and isotropic geometry. Such an averaging will in general modify the Einstein equations. The averaging procedure due to Buchert has attracted considerable attention recently since it offers the tantalizing hope of explaining the phenomenon of dark energy through such corrections. This approach has been criticized, however, on the grounds that its effects may be gauge artifacts. We apply the fully covariant formalism of Zalaletdinov's macroscopic gravity and show that, after making some essential gauge choices, the cosmological equations receive space-time scalar corrections which are therefore observable in principle, and further, that the broad structure of these corrections is identical to those derived by Buchert.
Power-Law Entropy-Corrected HDE and NADE in Brans-Dicke Cosmology
NASA Astrophysics Data System (ADS)
Sheykhi, A.; Karami, K.; Jamil, M.; Kazemi, E.; Haddad, M.
2012-06-01
Considering the power-law corrections to the black hole entropy, which appear in dealing with the entanglement of quantum fields inside and outside the horizon, the holographic energy density is modified accordingly. In this paper we study the power-law entropy-corrected holographic dark energy in the framework of Brans-Dicke theory. We investigate the cosmological implications of this model in detail. We also perform the study for the new agegraphic dark energy model and calculate some relevant cosmological parameters and their evolution. As a result we find that this model can provide the present cosmic acceleration and even the equation of state parameter of this model can cross the phantom line w D =-1 provided the model parameters are chosen suitably.
Genericness of inflation in isotropic loop quantum cosmology.
Date, Ghanashyam; Hossain, Golam Mortuza
2005-01-14
Nonperturbative corrections from loop quantum cosmology (LQC) to the scalar matter sector are already known to imply inflation. We prove that the LQC modified scalar field generates exponential inflation in the small scale factor regime, for all positive definite potentials, independent of initial conditions and independent of ambiguity parameters. For positive semidefinite potentials it is always possible to choose, without fine-tuning, a value of one of the ambiguity parameters such that exponential inflation results, provided zeros of the potential are approached at most as a power law in the scale factor. In conjunction with the generic occurrence of bounce at small volumes, particle horizon is absent, thus eliminating the horizon problem of the standard big bang model. PMID:15698059
Covariant effective action for loop quantum cosmology a la Palatini
Olmo, Gonzalo J.; Singh, Parampreet E-mail: psingh@perimeterinstitute.ca
2009-01-15
In loop quantum cosmology, non-perturbative quantum gravity effects lead to the resolution of the big bang singularity by a quantum bounce without introducing any new degrees of freedom. Though fundamentally discrete, the theory admits a continuum description in terms of an effective Hamiltonian. Here we provide an algorithm to obtain the corresponding effective action, establishing in this way the covariance of the theory for the first time. This result provides new insights on the continuum properties of the discrete structure of quantum geometry and opens new avenues to extract physical predictions such as those related to gauge invariant cosmological perturbations.
Shortcomings of the big bounce derivation in loop quantum cosmology
Cianfrani, Francesco; Montani, Giovanni
2010-07-15
We give a prescription to define in loop quantum gravity the electric field operator related to the scale factor of a homogeneous and isotropic cosmological space-time. This procedure allows us to link the fundamental theory with its cosmological implementation. In view of the conjugate relation existing between holonomies and fluxes, the edge length and the area of surfaces in the fiducial metric satisfy a duality condition. As a consequence, the area operator has a discrete spectrum also in loop quantum cosmology. This feature makes the super-Hamiltonian regularization an open issue of the whole formulation.
Comparing codes for error corrected quantum annealing
NASA Astrophysics Data System (ADS)
Mishra, Anurag; Albash, Tameem; Paz, Gerardo; Lidar, Daniel
2015-03-01
Previous work on the D-Wave Two (DW2) device has demonstrated the effectiveness of using error correction and suppression for quantum annealers. As the size of a quantum annealer increases, error correction becomes crucial for improved performance. We introduce a new type of code for error correction tailored to the hardware graph of the DW2, discuss the result of benchmarking this code on qubit chains, discuss various new decoding methods, and compare the performance to previous quantum annealing correction schemes.
Superbounce and loop quantum cosmology ekpyrosis from modified gravity
NASA Astrophysics Data System (ADS)
Oikonomou, V. K.
2015-09-01
As is known, in modified cosmological theories of gravity many of the cosmologies which could not be generated by standard Einstein gravity, can be consistently described by theories. Using known reconstruction techniques, we investigate which theories can lead to a Hubble parameter describing two types of cosmological bounces, the superbounce model, related to supergravity and non-supersymmetric models of contracting ekpyrosis and also the Loop Quantum Cosmology modified ekpyrotic model. Since our method is an approximate method, we investigate the problem at large and small curvatures. As we evince, both models yield power law reconstructed gravities, with the most interesting new feature being that both lead to accelerating cosmologies, in the large curvature approximation. The mathematical properties of the some Friedmann-Robertson-Walker spacetimes , that describe superbounce-like cosmologies are also pointed out, with regards to the group of curvature collineations.
Quantum cosmological perturbations of multiple fluids
NASA Astrophysics Data System (ADS)
Peter, Patrick; Pinto-Neto, N.; Vitenti, Sandro D. P.
2016-01-01
The formalism to treat quantization and evolution of cosmological perturbations of multiple fluids is described. We first construct the Lagrangian for both the gravitational and matter parts, providing the necessary relevant variables and momenta leading to the quadratic Hamiltonian describing linear perturbations. The final Hamiltonian is obtained without assuming any equations of motions for the background variables. This general formalism is applied to the special case of two fluids, having in mind the usual radiation and matter mix which made most of our current Universe history. Quantization is achieved using an adiabatic expansion of the basis functions. This allows for an unambiguous definition of a vacuum state up to the given adiabatic order. Using this basis, we show that particle creation is well defined for a suitable choice of vacuum and canonical variables, so that the time evolution of the corresponding quantum fields is unitary. This provides constraints for setting initial conditions for an arbitrary number of fluids and background time evolution. We also show that the common choice of variables for quantization can lead to an ill-defined vacuum definition. Our formalism is not restricted to the case where the coupling between fields is small, but is only required to vary adiabatically with respect to the ultraviolet modes, thus paving the way to consistent descriptions of general models not restricted to single-field (or fluid).
Triangulated loop quantum cosmology: Bianchi IX universe and inhomogeneous perturbations
Battisti, Marco Valerio; Marciano, Antonino; Rovelli, Carlo
2010-03-15
We develop the triangulated version of loop quantum cosmology, recently introduced in the literature. We focus on the dipole cosmology, where space is a three-sphere and the triangulation is formed by two tetrahedra. We show that the discrete fiducial connection has a simple and appealing geometrical interpretation and we correct the ansatz on the relation between the model variables and the Friedmann-Robertson-Walker scale factor. The modified ansatz leads to the convergence of the Hamiltonian constraint to the continuum one. We then ask which degrees of freedom are captured by this model. We show that the model is rich enough to describe the (anisotropic) Bianchi IX universe, and give the explicit relation between the Bianchi IX variables and the variables of the model. We discuss the possibility of using this path in order to define the quantization of the Bianchi IX universe. The model contains more degrees of freedom than Bianchi IX, and therefore captures some inhomogeneous degrees of freedom as well. Inhomogeneous degrees of freedom can be expanded in representations of the SU(2) Bianchi IX isometry group, and the dipole model captures the lowest integer representation of these, connected to hyperspherical harmonic of angular momentum j=1.
Anti-de Sitter universe dynamics in loop quantum cosmology
Bentivegna, Eloisa; Pawlowski, Tomasz
2008-06-15
A model for a flat isotropic universe with a negative cosmological constant {lambda} and a massless scalar field as sole matter content is studied within the framework of loop quantum cosmology. By application of the methods introduced for the model with {lambda}=0, the physical Hilbert space and the set of Dirac observables are constructed. As in that case, the scalar field plays here the role of an emergent time. The properties of the system are found to be similar to those of the k=1 Friedmann-Robertson-Walker (FRW) model: for small energy densities, the quantum dynamics reproduces the classical one, whereas, due to modifications at near-Planckian densities, the big bang and big crunch singularities are replaced by a quantum bounce connecting deterministically the large semiclassical epochs. Thus in loop quantum cosmology the evolution is qualitatively cyclic.
Anti-de Sitter universe dynamics in loop quantum cosmology
NASA Astrophysics Data System (ADS)
Bentivegna, Eloisa; Pawlowski, Tomasz
2008-06-01
A model for a flat isotropic universe with a negative cosmological constant Λ and a massless scalar field as sole matter content is studied within the framework of loop quantum cosmology. By application of the methods introduced for the model with Λ=0, the physical Hilbert space and the set of Dirac observables are constructed. As in that case, the scalar field plays here the role of an emergent time. The properties of the system are found to be similar to those of the k=1 Friedmann-Robertson-Walker (FRW) model: for small energy densities, the quantum dynamics reproduces the classical one, whereas, due to modifications at near-Planckian densities, the big bang and big crunch singularities are replaced by a quantum bounce connecting deterministically the large semiclassical epochs. Thus in loop quantum cosmology the evolution is qualitatively cyclic.
Quantum Corrections to Entropic Gravity
NASA Astrophysics Data System (ADS)
Chen, Pisin; Wang, Chiao-Hsuan
2013-12-01
The entropic gravity scenario recently proposed by Erik Verlinde reproduced Newton's law of purely classical gravity yet the key assumptions of this approach all have quantum mechanical origins. As is typical for emergent phenomena in physics, the underlying, more fundamental physics often reveals itself as corrections to the leading classical behavior. So one naturally wonders: where is ħ hiding in entropic gravity? To address this question, we first revisit the idea of holographic screen as well as entropy and its variation law in order to obtain a self-consistent approach to the problem. Next we argue that as the concept of minimal length has been invoked in the Bekenstein entropic derivation, the generalized uncertainty principle (GUP), which is a direct consequence of the minimal length, should be taken into consideration in the entropic interpretation of gravity. Indeed based on GUP it has been demonstrated that the black hole Bekenstein entropy area law must be modified not only in the strong but also in the weak gravity regime where in the weak gravity limit the GUP modified entropy exhibits a logarithmic correction. When applying it to the entropic interpretation, we demonstrate that the resulting gravity force law does include sub-leading order correction terms that depend on ħ. Such deviation from the classical Newton's law may serve as a probe to the validity of entropic gravity.
Quantum Corrections to Entropic Gravity
NASA Astrophysics Data System (ADS)
Chen, Pisin; Wang, Chiao-Hsuan
2013-01-01
The entropic gravity scenario recently proposed by Erik Verlinde reproduced Newton's law of purely classical gravity yet the key assumptions of this approach all have quantum mechanical origins. As is typical for emergent phenomena in physics, the underlying, more fundamental physics often reveals itself as corrections to the leading classical behavior. So one naturally wonders: where is ℏ hiding in entropic gravity? To address this question, we first revisit the idea of holographic screen as well as entropy and its variation law in order to obtain a self-consistent approach to the problem. Next we argue that since the concept of minimal length has been invoked in the Bekenstein entropic derivation, the generalized uncertainty principle (GUP), which is a direct consequence of the minimal length, should be taken into consideration in the entropic interpretation of gravity. Indeed based on GUP it has been demonstrated that the black hole Bekenstein entropy area law must be modified not only in the strong but also in the weak gravity regime where in the weak gravity limit the GUP modified entropy exhibits a logarithmic correction. When applying it to the entropic interpretation, we demonstrate that the resulting gravity force law does include sub-leading order correction terms that depend on ℏ. Such deviation from the classical Newton's law may serve as a probe to the validity of entropic gravity.
GRAVITATIONAL LENSING CORRECTIONS IN FLAT {Lambda}CDM COSMOLOGY
Kantowski, Ronald; Chen Bin; Dai Xinyu E-mail: Bin.Chen-1@ou.ed
2010-08-01
We compute the deflection angle to order (m/r {sub 0}){sup 2} and m/r{sub 0} x {Lambda}r {sup 2}{sub 0} for a light ray traveling in a flat {Lambda}CDM cosmology that encounters a completely condensed mass region. We use a Swiss cheese model for the inhomogeneities and find that the most significant correction to the Einstein angle occurs not because of the nonlinear terms but instead occurs because the condensed mass is embedded in a background cosmology. The Swiss cheese model predicts a decrease in the deflection angle of {approx}2% for weakly lensed galaxies behind the rich cluster A1689 and that the reduction can be as large as {approx}5% for similar rich clusters at z {approx} 1. Weak-lensing deflection angles caused by galaxies can likewise be reduced by as much as {approx}4%. We show that the lowest order correction in which {Lambda} appears is proportional to m/r{sub 0} x {radical}({Lambda}r{sub 0}{sup 2}) and could cause as much as a {approx}0.02% increase in the deflection angle for light that passes through a rich cluster. The lowest order nonlinear correction in the mass is proportional to m/r{sub 0}x{radical}(m/r{sub 0}) and can increase the deflection angle by {approx}0.005% for weak lensing by galaxies.
Cosmological constraints on a classical limit of quantum gravity
Easson, Damien A.; Trodden, Mark; Schuller, Frederic P.; Wohlfarth, Mattias N.R.
2005-08-15
We investigate the cosmology of a recently proposed deformation of Einstein gravity, emerging from quantum gravity heuristics. The theory is constructed to have de Sitter space as a vacuum solution, and thus to be relevant to the accelerating universe. However, this solution turns out to be unstable, and the true phase space of cosmological solutions is significantly more complex, displaying two late-time power-law attractors - one accelerating and the other dramatically decelerating. It is also shown that nonaccelerating cosmologies sit on a separatrix between the two basins of attraction of these attractors. Hence it is impossible to pass from a decelerating cosmology to an accelerating one, as required in standard cosmology for consistency with nucleosynthesis and structure formation and compatibility with the data inferred from supernovae Ia. We point out that alternative models of the early universe, such as the one investigated here might provide possible ways to circumvent these requirements.
Loop corrections and graceful exit in string cosmology
NASA Astrophysics Data System (ADS)
Foffa, Stefano; Maggiore, Michele; Sturani, Riccardo
1999-07-01
We examine the effect of perturbative string loops on the cosmological pre-big-bang evolution. We study loop corrections derived from heterotic string theory compactified on a ZN orbifold and we consider the effect of the all-order loop corrections to the Kähler potential and of the corrections to gravitational couplings, including both threshold corrections and corrections due to the mixed Kähler-gravitational anomaly. We find that string loops can drive the evolution into the region of the parameter space where a graceful exit is in principle possible, and we find solutions that, in the string frame, connect smoothly the superinflationary pre-big-bang evolution to a phase where the curvature and the derivative of the dilaton are decreasing. We also find that at a critical coupling the loop corrections to the Kähler potential induce a ghost-like instability, i.e. the kinetic term of the dilaton vanishes. This is similar to what happens in Seiberg-Witten theory and signals the transition to a new regime where the light modes in the effective action are different and are related to the original ones by S-duality. In a string context, this means that we enter a D-brane dominated phase.
On the Convergence in Effective Loop Quantum Cosmology
Corichi, Alejandro; Vukasinac, Tatjana; Zapata, Jose Antonio
2010-07-12
In Loop Quantum Cosmology (LQC) there is a discreteness parameter {lambda}, that has been heuristically associated to a fundamental granularity of quantum geometry. It is also possible to consider {lambda} as a regulator in the same spirit as that used in lattice field theory, where it specifies a regular lattice in the real line. A particular quantization of the k = 0 FLRW loop cosmological model yields a completely solvable model, known as solvable loop quantum cosmology(sLQC). In this contribution, we consider effective classical theories motivated by sLQC and study their {lambda}-dependence, with a special interest on the limit {lambda}{yields}0 and the role of the evolution parameter in the convergence of such limit.
Cosmology from group field theory formalism for quantum gravity.
Gielen, Steffen; Oriti, Daniele; Sindoni, Lorenzo
2013-07-19
We identify a class of condensate states in the group field theory (GFT) formulation of quantum gravity that can be interpreted as macroscopic homogeneous spatial geometries. We then extract the dynamics of such condensate states directly from the fundamental quantum GFT dynamics, following the procedure used in ordinary quantum fluids. The effective dynamics is a nonlinear and nonlocal extension of quantum cosmology. We also show that any GFT model with a kinetic term of Laplacian type gives rise, in a semiclassical (WKB) approximation and in the isotropic case, to a modified Friedmann equation. This is the first concrete, general procedure for extracting an effective cosmological dynamics directly from a fundamental theory of quantum geometry. PMID:23909305
Quantum error correction with trapped ions
NASA Astrophysics Data System (ADS)
Schindler, Philipp
Quantum computers promise exponential speed-up compared to their classical counterparts for certain problems. Unfortunately, the states required for quantum computation are fragile and lose their quantum properties with growing system size. In a milestone work, it has been shown that quantum error correction can overcome this problem and enable arbitrary long and arbitrary high quality quantum algorithms. However, current experiments are not able to fulfill the requirements to employ useful quantum error correction procedures. In this talk, I will first review past proof-of-principle experiments in trapped ion quantum information processors. Building on that, I will sketch a way towards a medium-sized trapped ion system that will be capable of running an error correction procedure that outperforms it constituents.
The consistent histories approach to loop quantum cosmology
NASA Astrophysics Data System (ADS)
Craig, David A.
2016-06-01
We review the application of the consistent (or decoherent) histories formulation of quantum theory to canonical loop quantum cosmology. Conventional quantum theory relies crucially on “measurements” to convert unrealized quantum potentialities into physical outcomes that can be assigned probabilities. In the early universe and other physical contexts in which there are no observers or measuring apparatus (or indeed, in any closed quantum system), what criteria determine which alternative outcomes may be realized and what their probabilities are? In the consistent histories formulation it is the vanishing of interference between the branch wave functions describing alternative histories — as determined by the system’s decoherence functional — that determines which alternatives may be assigned probabilities. We describe the consistent histories formulation and how it may be applied to canonical loop quantum cosmology, describing in detail the application to homogeneous and isotropic cosmological models with scalar matter. We show how the theory may be used to make definite physical predictions in the absence of “observers”. As an application, we demonstrate how the theory predicts that loop quantum models “bounce” from large volume to large volume, while conventional “Wheeler-DeWitt”-quantized universes are invariably singular. We also briefly indicate the relation to other work.
Optimized entanglement-assisted quantum error correction
Taghavi, Soraya; Brun, Todd A.; Lidar, Daniel A.
2010-10-15
Using convex optimization, we propose entanglement-assisted quantum error-correction procedures that are optimized for given noise channels. We demonstrate through numerical examples that such an optimized error-correction method achieves higher channel fidelities than existing methods. This improved performance, which leads to perfect error correction for a larger class of error channels, is interpreted in at least some cases by quantum teleportation, but for general channels this interpretation does not hold.
Tensor Networks and Quantum Error Correction
NASA Astrophysics Data System (ADS)
Ferris, Andrew J.; Poulin, David
2014-07-01
We establish several relations between quantum error correction (QEC) and tensor network (TN) methods of quantum many-body physics. We exhibit correspondences between well-known families of QEC codes and TNs, and demonstrate a formal equivalence between decoding a QEC code and contracting a TN. We build on this equivalence to propose a new family of quantum codes and decoding algorithms that generalize and improve upon quantum polar codes and successive cancellation decoding in a natural way.
Foliated Quantum Error-Correcting Codes.
Bolt, A; Duclos-Cianci, G; Poulin, D; Stace, T M
2016-08-12
We show how to construct a large class of quantum error-correcting codes, known as Calderbank-Steane-Shor codes, from highly entangled cluster states. This becomes a primitive in a protocol that foliates a series of such cluster states into a much larger cluster state, implementing foliated quantum error correction. We exemplify this construction with several familiar quantum error-correction codes and propose a generic method for decoding foliated codes. We numerically evaluate the error-correction performance of a family of finite-rate Calderbank-Steane-Shor codes known as turbo codes, finding that they perform well over moderate depth foliations. Foliated codes have applications for quantum repeaters and fault-tolerant measurement-based quantum computation. PMID:27563942
Foliated Quantum Error-Correcting Codes
NASA Astrophysics Data System (ADS)
Bolt, A.; Duclos-Cianci, G.; Poulin, D.; Stace, T. M.
2016-08-01
We show how to construct a large class of quantum error-correcting codes, known as Calderbank-Steane-Shor codes, from highly entangled cluster states. This becomes a primitive in a protocol that foliates a series of such cluster states into a much larger cluster state, implementing foliated quantum error correction. We exemplify this construction with several familiar quantum error-correction codes and propose a generic method for decoding foliated codes. We numerically evaluate the error-correction performance of a family of finite-rate Calderbank-Steane-Shor codes known as turbo codes, finding that they perform well over moderate depth foliations. Foliated codes have applications for quantum repeaters and fault-tolerant measurement-based quantum computation.
Separate universes in loop quantum cosmology: Framework and applications
NASA Astrophysics Data System (ADS)
Wilson-Ewing, Edward
2016-06-01
I present a streamlined review of how the separate universe approach to cosmological perturbation theory can be used to study the dynamics of long-wavelength scalar perturbations in loop quantum cosmology (LQC), and then use it to calculate how long-wavelength curvature perturbations evolve across the LQC bounce assuming a constant equation of state. A similar calculation is possible for tensor modes using results from a complementary approach to cosmological perturbation theory in LQC based on an effective Hamiltonian constraint. An interesting result is that the tensor-to-scalar ratio can be suppressed or amplified by quantum gravity effects during the bounce, depending on the equation of state of the matter field dominating the dynamics. In particular, if the equation of state lies between ‑ 1/3 and 1, the value of the tensor-to-scalar ratio will be suppressed during the bounce, in some cases significantly.
Evolutionary quantum cosmology in a gauge-fixed picture
Vakili, Babak
2011-05-15
We study the classical and quantum models of a flat Friedmann-Robertson-Walker space-time, coupled to a perfect fluid, in the context of the consensus and a gauge-fixed Lagrangian frameworks. It is shown that, either in the usual or in the gauge-fixed actions, the evolution of the Universe based on the classical cosmology represents a late time power law expansion, coming from a big-bang singularity in which the scale factor goes to zero for the standard matter, and tending towards a big-rip singularity in which the scale factor diverges for the phantom fluid. We then employ the familiar canonical quantization procedure in the given cosmological setting to find the cosmological wave functions in the corresponding minisuperspace. Using a gauge-fixed (reduced) Lagrangian, we show that it may lead to a Schroedinger equation for the quantum-mechanical description of the model under consideration, the eigenfunctions of which can be used to construct the time dependent wave function of the Universe. We use the resulting wave function in order to investigate the possibility of the avoidance of classical singularities due to quantum effects by means of the many-worlds and ontological interpretation of quantum cosmology.
Long distance quantum communication using quantum error correction
NASA Technical Reports Server (NTRS)
Gingrich, R. M.; Lee, H.; Dowling, J. P.
2004-01-01
We describe a quantum error correction scheme that can increase the effective absorption length of the communication channel. This device can play the role of a quantum transponder when placed in series, or a cyclic quantum memory when inserted in an optical loop.
Quantum resolution of cosmological singularities using AdS/CFT correspondence
NASA Astrophysics Data System (ADS)
Craps, Ben; Hertog, Thomas; Turok, Neil
2012-08-01
The AdS/CFT correspondence allows us to map a dynamical cosmology to a dual quantum field theory living on the boundary of spacetime. Specifically, we study a five-dimensional model cosmology in type IIB supergravity, where the dual theory is an unstable deformation of N=4 supersymmetric SU(N) gauge theory on IR×S3. A one-loop computation shows that the coupling governing the instability is asymptotically free, so quantum corrections cannot turn the potential around. The big crunch singularity in the bulk occurs when a boundary scalar field runs to infinity, in finite time. Consistent quantum evolution requires that we impose boundary conditions at infinite scalar field, i.e. a self-adjoint extension of the system. We find that quantum spreading of the homogeneous mode of the boundary scalar leads to a natural UV cutoff in particle production as the wave function for the homogeneous mode bounces back from infinity. However a perturbative calculation indicates that despite this, the logarithmic running of the boundary coupling governing the instability generally leads to significant particle production across the bounce. This prevents the wave packet of the homogeneous boundary scalar to return close to its initial form. Translating back to the bulk theory, we conclude that a quantum transition from a big crunch to a big bang is an improbable outcome of cosmological evolution in this class of five-dimensional models.
Reconstructing the evolution of the Universe from loop quantum cosmology scalar fields
NASA Astrophysics Data System (ADS)
Oikonomou, V. K.
2016-08-01
We extend the scalar-tensor reconstruction techniques for classical cosmology frameworks, in the context of loop quantum cosmology. After presenting in some detail how the equations are generalized in the loop quantum cosmology case, we discuss which new features and limitations the quantum framework introduces, and we use various illustrative examples in order to demonstrate how the method works. As we show, the energy density has two different classes of solutions, and one of these yields the correct classical limit, while the second captures the quantum phenomena. We study in detail the scalar tensor reconstruction method for both of these solutions. We also discuss some scenarios for which the Hubble rate becomes unbounded at finite time, which corresponds for example to the case in which the big rip occurs. As we show, this issue is nontrivial and we discuss how this case should be treated in a consistent way. Finally, we investigate how the classical stability conditions for the scalar-tensor solutions are generalized in the loop quantum framework.
Effective dynamics in Bianchi type II loop quantum cosmology
NASA Astrophysics Data System (ADS)
Corichi, Alejandro; Montoya, Edison
2012-05-01
We numerically investigate the solutions to the effective equations of the Bianchi II model within the “improved” loop quantum cosmology dynamics. The matter source is a massless scalar field. We perform a systematic study of the space of solutions, and focus on the behavior of several geometrical observables. We show that the big bang singularity is replaced by a bounce and the pointlike singularities do not saturate the energy density bound. There are up to three directional bounces in the scale factors, one global bounce in the expansion, the shear presents up to four local maxima and can be zero at the bounce. This allows for solutions with density larger than the maximal density for the isotropic and Bianchi I cases. The asymptotic behavior is shown to behave like that of a Bianchi I model, and the effective solutions connect anisotropic solutions even when the shear is zero at the bounce. All known facts of Bianchi I are reproduced. In the “vacuum limit,” solutions are such that almost all the dynamics is due to the anisotropies. Since Bianchi II plays an important role in the Bianchi IX model and the Belinskii, Khalatnikov, Lifshitz conjecture, our results can provide an intuitive understanding of the behavior in the vicinity of general spacelike singularities, when loop-geometric corrections are present.
Quantum Gravity corrections and entropy at the Planck time
Basilakos, Spyros; Vagenas, Elias C.; Das, Saurya E-mail: saurya.das@uleth.ca
2010-09-01
We investigate the effects of Quantum Gravity on the Planck era of the universe. In particular, using different versions of the Generalized Uncertainty Principle and under specific conditions we find that the main Planck quantities such as the Planck time, length, mass and energy become larger by a factor of order 10−10{sup 4} compared to those quantities which result from the Heisenberg Uncertainty Principle. However, we prove that the dimensionless entropy enclosed in the cosmological horizon at the Planck time remains unchanged. These results, though preliminary, indicate that we should anticipate modifications in the set-up of cosmology since changes in the Planck era will be inherited even to the late universe through the framework of Quantum Gravity (or Quantum Field Theory) which utilizes the Planck scale as a fundamental one. More importantly, these corrections will not affect the entropic content of the universe at the Planck time which is a crucial element for one of the basic principles of Quantum Gravity named Holographic Principle.
The perturbed universe in the deformed algebra approach of loop quantum cosmology
NASA Astrophysics Data System (ADS)
Grain, Julien
2016-06-01
Loop Quantum Cosmology (LQC) is a tentative approach to model the universe down to the Planck era where quantum gravity settings are needed. The quantization of the universe as a dynamical spacetime is inspired by Loop Quantum Gravity (LQG) ideas. In addition, LQC could bridge contact with astronomical observations, and thus potentially investigate quantum cosmology modelings in the light of observations. To do so however, modeling both the background evolution and its perturbations is needed. The latter described cosmic inhomogeneities that are the main cosmological observables. In this context, we present the so-called deformed algebra approach implementing the quantum corrections to the perturbed universe at an effective level by taking great care of gauge issues. We particularly highlight that in this framework, the algebra of hypersurface deformation receives quantum corrections, and we discuss their meaning. The primordial power spectra of scalar and tensor inhomogeneities are then presented, assuming initial conditions are set in the contracting phase preceding the quantum bounce and the well-known expanding phase of the cosmic history. These spectra are subsequently propagated to angular power spectra of the anisotropies of the cosmic microwave background. It is then shown that regardless of the choice for the initial conditions inside the effective approach for the background evolution (except that they are set in the contracting phase), the predicted angular power spectra of the polarized B-modes exceed the upper bound currently set by observations. The exclusion of this specific version of LQC establishes the falsifiability of the approach, though one shall not conclude here that either LQC or LQG excluded.
Quantum supersymmetric cosmology and its hidden Kac-Moody structure
NASA Astrophysics Data System (ADS)
Damour, Thibault; Spindel, Philippe
2013-08-01
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 an SO(3)-homogeneous (Bianchi IX) cosmological model. The quantization of the homogeneous gravitino field leads to a 64-dimensional fermionic Hilbert space. 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 sub-algebra of the rank-3 hyperbolic Kac-Moody algebra AE3. Some exponentials of these operators generate a spinorial extension of the Weyl group of AE3 which describe (in the small wavelength limit) the chaotic quantum evolution of the universe near the cosmological singularity.
Relativistic wavepackets in classically chaotic quantum cosmological billiards
NASA Astrophysics Data System (ADS)
Koehn, Michael
2012-03-01
Close to a spacelike singularity, pure gravity and supergravity in 4 to 11 spacetime dimensions admit a cosmological billiard description based on hyperbolic Kac-Moody groups. We investigate the quantum cosmological billiards of relativistic wavepackets towards the singularity, employing flat and hyperbolic space descriptions for the quantum billiards. We find that the strongly chaotic classical billiard motion of four-dimensional pure gravity corresponds to a spreading wavepacket subject to successive redshifts and tending to zero as the singularity is approached. We discuss the possible implications of these results in the context of singularity resolution and compare them with those of known semiclassical approaches. As an aside, we obtain exact solutions for the one-dimensional relativistic quantum billiards with moving walls.
Measure problem in slow roll inflation and loop quantum cosmology
Corichi, Alejandro; Karami, Asieh
2011-05-15
We consider the measure problem in standard slow-roll inflationary models from the perspective of loop quantum cosmology (LQC). Following recent results by Ashtekar and Sloan, we study the probability of having enough e-foldings and focus on its dependence on the quantum gravity scale, including the transition of the theory to the limit where general relativity (GR) is recovered. Contrary to the standard expectation, the probability of having enough inflation, that is close to 1 in LQC, grows and tends to 1 as one approaches the GR limit. We study the origin of the tension between these results with those by Gibbons and Turok, and offer an explanation that brings these apparent contradictory results into a coherent picture. As we show, the conflicting results stem from different choices of initial conditions for the computation of probability. The singularity-free scenario of loop quantum cosmology offers a natural choice of initial conditions, and suggests that enough inflation is generic.
Quantum annealing correction for random Ising problems
NASA Astrophysics Data System (ADS)
Pudenz, Kristen L.; Albash, Tameem; Lidar, Daniel A.
2015-04-01
We demonstrate that the performance of a quantum annealer on hard random Ising optimization problems can be substantially improved using quantum annealing correction (QAC). Our error correction strategy is tailored to the D-Wave Two device. We find that QAC provides a statistically significant enhancement in the performance of the device over a classical repetition code, improving as a function of problem size as well as hardness. Moreover, QAC provides a mechanism for overcoming the precision limit of the device, in addition to correcting calibration errors. Performance is robust even to missing qubits. We present evidence for a constructive role played by quantum effects in our experiments by contrasting the experimental results with the predictions of a classical model of the device. Our work demonstrates the importance of error correction in appropriately determining the performance of quantum annealers.
Quantum Corrections to the 'Atomistic' MOSFET Simulations
NASA Technical Reports Server (NTRS)
Asenov, Asen; Slavcheva, G.; Kaya, S.; Balasubramaniam, R.
2000-01-01
We have introduced in a simple and efficient manner quantum mechanical corrections in our 3D 'atomistic' MOSFET simulator using the density gradient formalism. We have studied in comparison with classical simulations the effect of the quantum mechanical corrections on the simulation of random dopant induced threshold voltage fluctuations, the effect of the single charge trapping on interface states and the effect of the oxide thickness fluctuations in decanano MOSFETs with ultrathin gate oxides. The introduction of quantum corrections enhances the threshold voltage fluctuations but does not affect significantly the amplitude of the random telegraph noise associated with single carrier trapping. The importance of the quantum corrections for proper simulation of oxide thickness fluctuation effects has also been demonstrated.
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.
Tanaka, Tomo; Amemiya, Fumitoshi; Shimano, Masahiro; Harada, Tomohiro; Tamaki, Takashi
2011-05-15
In loop quantum cosmology, the Hamiltonian reduces to a finite difference operator and quantum dynamics are controlled by the difference equation. In this framework, Bojowald [M. Bojowald, Phys. Rev. Lett. 86, 5227 (2001).] showed that the initial singularity is absent in the twofold sense: (i) the spectrum of the inverse scale factor operator is bounded from above; (ii) the wave function of the Universe can be uniquely extended beyond the point which was the initial singularity in classical theory. In this paper, we study the initial singularity in this sense and the large-volume limit against the ambiguities in the discretization and the operator ordering within a homogeneous, isotropic and spatially flat model with the cosmological constant. We find that the absence of the singularity strongly depends on the choice of the operator ordering and the requirement for the absence singles out a very small class of orderings. Moreover we find a general ordering rule required for the absence of the singularity. We also find that the large-volume limit naturally recovers a smooth wave function in the discretization where each step corresponds to a fixed volume increment but not in the one where each step corresponds to a fixed area increment. If loop quantum cosmology is to be a phenomenological realization of full loop quantum gravity, these results are important to fix the theoretical ambiguities.
Quantum gravity and the holographic dark energy cosmology
NASA Astrophysics Data System (ADS)
Nastase, Horatiu
2016-04-01
The holographic dark energy model is obtained from a cosmological constant generated by generic quantum gravity effects giving a minimum length. By contrast, the usual bound for the energy density to be limited by the formation of a black hole simply gives the Friedmann equation. The scale of the current cosmological constant relative to the inflationary scale is an arbitrary parameter characterizing initial conditions, which however can be fixed by introducing a physical principle during inflation, as a function of the number of e-folds and the inflationary scale.
Classical and quantum aspects of brane-world cosmology
Cordero, Ruben; Rojas, Efrain
2011-10-14
We give a brief overview of several models in brane-world cosmology. In particular, we focus on the asymmetric DGP and Regge-Teiltelboim models. We present the associated equations of motion governing the dynamics of the brane and their corresponding Friedmann-like equations. In order to develop the quantum Regge-Teiltelboim type cosmology we construct its Ostrogradski Hamiltonian formalism which naturally leads to the corresponding Wheeler-DeWitt equation. In addition, we comment on possible generalizations for these models including second order derivative geometrical terms.
Error suppression and correction for quantum annealing
NASA Astrophysics Data System (ADS)
Lidar, Daniel
While adiabatic quantum computing and quantum annealing enjoy a certain degree of inherent robustness against excitations and control errors, there is no escaping the need for error correction or suppression. In this talk I will give an overview of our work on the development of such error correction and suppression methods. We have experimentally tested one such method combining encoding, energy penalties and decoding, on a D-Wave Two processor, with encouraging results. Mean field theory shows that this can be explained in terms of a softening of the closing of the gap due to the energy penalty, resulting in protection against excitations that occur near the quantum critical point. Decoding recovers population from excited states and enhances the success probability of quantum annealing. Moreover, we have demonstrated that using repetition codes with increasing code distance can lower the effective temperature of the annealer. References: K.L. Pudenz, T. Albash, D.A. Lidar, ``Error corrected quantum annealing with hundreds of qubits'', Nature Commun. 5, 3243 (2014). K.L. Pudenz, T. Albash, D.A. Lidar, ``Quantum annealing correction for random Ising problems'', Phys. Rev. A. 91, 042302 (2015). S. Matsuura, H. Nishimori, T. Albash, D.A. Lidar, ``Mean Field Analysis of Quantum Annealing Correction''. arXiv:1510.07709. W. Vinci et al., in preparation.
Theory of quantum error-correcting codes
Knill, E.; Laflamme, R.
1997-02-01
Quantum error correction will be necessary for preserving coherent states against noise and other unwanted interactions in quantum computation and communication. We develop a general theory of quantum error correction based on encoding states into larger Hilbert spaces subject to known interactions. We obtain necessary and sufficient conditions for the perfect recovery of an encoded state after its degradation by an interaction. The conditions depend only on the behavior of the logical states. We use them to give a recovery-operator-independent definition of error-correcting codes. We relate this definition to four others: the existence of a left inverse of the interaction, an explicit representation of the error syndrome using tensor products, perfect recovery of the completely entangled state, and an information theoretic identity. Two notions of fidelity and error for imperfect recovery are introduced, one for pure and the other for entangled states. The latter is more appropriate when using codes in a quantum memory or in applications of quantum teleportation to communication. We show that the error for entangled states is bounded linearly by the error for pure states. A formal definition of independent interactions for qubits is given. This leads to lower bounds on the number of qubits required to correct e errors and a formal proof that the classical bounds on the probability of error of e-error-correcting codes applies to e-error-correcting quantum codes, provided that the interaction is dominated by an identity component. {copyright} {ital 1997} {ital The American Physical Society}
Relativistic quantum corrections to laser wakefield acceleration.
Zhu, Jun; Ji, Peiyong
2010-03-01
The influence of quantum effects on the interaction of intense laser fields with plasmas is investigated by using a hydrodynamic model based on the framework of the relativistic quantum theory. Starting from the covariant Wigner function and Dirac equation, the hydrodynamic equations for relativistic quantum plasmas are derived. Based on the relativistic quantum hydrodynamic equations and Poisson equation, the perturbations of electron number densities and the electric field of the laser wakefield containing quantum effects are deduced. It is found that the corrections generated by the quantum effects to the perturbations of electron number densities and the accelerating field of the laser wakefield cannot be neglected. Quantum effects will suppress laser wakefields, which is a classical manifestation of quantum decoherence effects, however, the contribution of quantum effects for the laser wakefield correction will been partially counteracted by the relativistic effects. The analysis also reveals that quantum effects enlarge the effective frequencies of plasmas, and the quantum behavior appears a screening effect for plasma electrons. PMID:20365881
Relativistic quantum corrections to laser wakefield acceleration
Zhu Jun; Ji Peiyong
2010-03-15
The influence of quantum effects on the interaction of intense laser fields with plasmas is investigated by using a hydrodynamic model based on the framework of the relativistic quantum theory. Starting from the covariant Wigner function and Dirac equation, the hydrodynamic equations for relativistic quantum plasmas are derived. Based on the relativistic quantum hydrodynamic equations and Poisson equation, the perturbations of electron number densities and the electric field of the laser wakefield containing quantum effects are deduced. It is found that the corrections generated by the quantum effects to the perturbations of electron number densities and the accelerating field of the laser wakefield cannot be neglected. Quantum effects will suppress laser wakefields, which is a classical manifestation of quantum decoherence effects, however, the contribution of quantum effects for the laser wakefield correction will been partially counteracted by the relativistic effects. The analysis also reveals that quantum effects enlarge the effective frequencies of plasmas, and the quantum behavior appears a screening effect for plasma electrons.
Does loop quantum cosmology replace the big rip singularity by a non-singular bounce?
Haro, Jaume de
2012-11-01
It is stated that holonomy corrections in loop quantum cosmology introduce a modification in Friedmann's equation which prevent the big rip singularity. Recently in [1] it has been proved that this modified Friedmann equation is obtained in an inconsistent way, what means that the results deduced from it, in particular the big rip singularity avoidance, are not justified. The problem is that holonomy corrections modify the gravitational part of the Hamiltonian of the system leading, after Legendre's transformation, to a non covariant Lagrangian which is in contradiction with one of the main principles of General Relativity. A more consistent way to deal with the big rip singularity avoidance is to disregard modification in the gravitational part of the Hamiltonian, and only consider inverse volume effects [2]. In this case we will see that, not like the big bang singularity, the big rip singularity survives in loop quantum cosmology. Another way to deal with the big rip avoidance is to take into account geometric quantum effects given by the the Wheeler-De Witt equation. In that case, even though the wave packets spread, the expectation values satisfy the same equations as their classical analogues. Then, following the viewpoint adopted in loop quantum cosmology, one can conclude that the big rip singularity survives when one takes into account these quantum effects. However, the spreading of the wave packets prevents the recover of the semiclassical time, and thus, one might conclude that the classical evolution of the universe come to and end before the big rip is reached. This is not conclusive because. as we will see, it always exists other external times that allows us to define the classical and quantum evolution of the universe up to the big rip singularity.
Thermoelectric corrections to quantum voltage measurement
NASA Astrophysics Data System (ADS)
Bergfield, Justin P.; Stafford, Charles A.
2014-12-01
A generalization of Büttiker's voltage probe concept for nonzero temperatures is an open third terminal of a quantum thermoelectric circuit. An explicit analytic expression for the thermoelectric correction to an ideal quantum voltage measurement in linear response is derived and interpreted in terms of local Peltier cooling/heating within the nonequilibrium system. The thermoelectric correction is found to be large (up to ±24 % of the peak voltage) in a prototypical ballistic quantum conductor (graphene nanoribbon). The effects of measurement nonideality are also investigated. Our findings have important implications for precision local electrical measurements.
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.
Loop quantum cosmology with self-dual variables
NASA Astrophysics Data System (ADS)
Wilson-Ewing, Edward
2015-12-01
Using the complex-valued self-dual connection variables, the loop quantum cosmology of a closed Friedmann space-time coupled to a massless scalar field is studied. It is shown how the reality conditions can be imposed in the quantum theory by choosing a particular inner product for the kinematical Hilbert space. While holonomies of the self-dual Ashtekar connection are not well defined in the kinematical Hilbert space, it is possible to introduce a family of generalized holonomylike operators of which some are well defined; these operators in turn are used in the definition of the Hamiltonian constraint operator where the scalar field can be used as a relational clock. The resulting quantum theory is closely related, although not identical, to standard loop quantum cosmology constructed from the Ashtekar-Barbero variables with a real Immirzi parameter. Effective Friedmann equations are derived which provide a good approximation to the full quantum dynamics for sharply peaked states whose volume remains much larger than the Planck volume, and they show that for these states quantum gravity effects resolve the big-bang and big-crunch singularities and replace them by a nonsingular bounce. Finally, the loop quantization in self-dual variables of a flat Friedmann space-time is recovered in the limit of zero spatial curvature and is identical to the standard loop quantization in terms of the real-valued Ashtekar-Barbero variables.
NASA Astrophysics Data System (ADS)
Joe, Anton; Dadhich, Naresh; Singh, Parampreet
2015-04-01
The loop quantum dynamics of Kantowski-Sachs and the interior of higher genus black hole spacetimes with cosmological constant has some peculiar features not shared by various other spacetimes in loop quantum cosmolgy. As in the other cases, though the quantum geometric effects resolve the singularity and result in a bounce, after the bounce a spacetime with small spacetime curvature does not emerge at late times. Instead, asymptotically the spacetime has constant spacetime curvature with a product manifold. Interestingly, though the spacetime curvature of these asymptotic spacetimes is very high, the effective metric of these spacetimes is a solution to the Einstein field equations. Analysis of the components of the Ricci tensor shows that after the singularity resolution, the Kantowski-Sachs spacetimes lead to an effective charged Nariai, and, the higher genus black hole interior lead to an anti Bertotti-Robinson spacetime with an effective tachyonic charge. The asymptotic spacetimes have an effective cosmological constant which is different in magnitude, and sometimes even its sign, from the cosmological constant in the Kantwoski-Sachs and higher genus black hole metrics.
Bouncing loop quantum cosmology from F(T) gravity
NASA Astrophysics Data System (ADS)
Amorós, Jaume; de Haro, Jaume; Odintsov, Sergei D.
2013-05-01
The big bang singularity could be understood as a breakdown of Einstein’s general relativity at very high energies. By adopting this viewpoint, other theories that implement Einstein cosmology at high energies might solve the problem of the primeval singularity. One of them is loop quantum cosmology (LQC) with a small cosmological constant that models a universe moving along an ellipse, which prevents singularities like the big bang or the big rip, in the phase space (H,ρ), where H is the Hubble parameter and ρ the energy density of the universe. Using LQC one considers a model universe filled by radiation and matter where, due to the cosmological constant, there are a de Sitter and an anti-de Sitter solution. This means that one obtains a bouncing nonsingular universe which is in the contracting phase at early times. After leaving this phase, i.e., after bouncing, it passes trough a radiation- and matter-dominated phase and finally at late times it expands in an accelerated way (current cosmic acceleration). This model does not suffer from the horizon and flatness problems as in big bang cosmology, where a period of inflation that increases the size of our universe in more than 60 e-folds is needed in order to solve both problems. The model has two mechanisms to avoid these problems: the evolution of the universe through a contracting phase and a period of super inflation (H˙>0).
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.
Aspects of nonlocality in quantum field theory, quantum gravity and cosmology
NASA Astrophysics Data System (ADS)
Barvinsky, A. O.
2015-01-01
This paper contains a collection of essays on nonlocal phenomena in quantum field theory, gravity and cosmology. Mechanisms of nonlocal contributions to the quantum effective action are discussed within the covariant perturbation expansion in field strengths and spacetime curvatures. Euclidean version of the Schwinger-Keldysh technique for quantum expectation values is presented as a special rule of obtaining the nonlocal effective equations of motion for the mean quantum field from the Euclidean effective action. This rule is applied to a new model of ghost free nonlocal cosmology which can generate the de Sitter (dS) cosmological evolution at an arbitrary value of Λ — a model of dark energy with the dynamical scale selected by a kind of a scaling symmetry breaking mechanism. This model is shown to interpolate between the superhorizon phase of a scalar mediated gravity and the short distance general relativistic limit in a special metric frame related by a nonlocal conformal transformation to the original metric.
Loop quantum cosmology, non-Gaussianity, and CMB power asymmetry
NASA Astrophysics Data System (ADS)
Agullo, Ivan
2015-09-01
We argue that the anomalous power asymmetry observed in the cosmic microwave background (CMB) may have originated in a cosmic bounce preceding inflation. In loop quantum cosmology (LQC), the big bang singularity is generically replaced by a bounce due to quantum gravitational effects. We compute the spectrum of inflationary non-Gaussianity and show that strong correlation between observable scales and modes with longer (superhorizon) wavelength arise as a consequence of the evolution of perturbations across the LQC bounce. These correlations are strongly scale dependent and induce a dipole-dominated modulation on large angular scales in the CMB, in agreement with observations.
Cosmological implications of quantum entanglement in the multiverse
NASA Astrophysics Data System (ADS)
Kanno, Sugumi
2015-12-01
We explore the cosmological implications of quantum entanglement between two causally disconnected universes in the multiverse. We first consider two causally separated de Sitter spaces with a state which is initially entangled. We derive the reduced density matrix of our universe and compute the spectrum of vacuum fluctuations. We then consider the same system with an initially non-entangled state. We find that due to quantum interference scale dependent modulations may enter the spectrum for the case of initially non-entangled state. This gives rise to the possibility that the existence of causally disconnected universes may be experimentally tested by analyzing correlators in detail.
On a Continuum Limit for Loop Quantum Cosmology
Corichi, Alejandro; Vukasinac, Tatjana; Zapata, Jose Antonio
2008-03-06
The use of non-regular representations of the Heisenberg-Weyl commutation relations has proved to be useful for studying conceptual and technical issues in quantum gravity. Of particular relevance is the study of Loop Quantum Cosmology (LQC), symmetry reduced theory that is related to Loop Quantum Gravity, and that is based on a non-regular, polymeric representation. Recently, a soluble model was used by Ashtekar, Corichi and Singh to study the relation between Loop Quantum Cosmology and the standard Wheeler-DeWitt theory and, in particular, the passage to the limit in which the auxiliary parameter (interpreted as ''quantum geometry discreetness'') is sent to zero in hope to get rid of this 'regulator' that dictates the LQC dynamics at each 'scale'. In this note we outline the first steps toward reformulating this question within the program developed by the authors for studying the continuum limit of polymeric theories, which was successfully applied to simple systems such as a Simple Harmonic Oscillator.
Numerical analysis of the big bounce in loop quantum cosmology
Laguna, Pablo
2007-01-15
Loop quantum cosmology (LQC) homogeneous models with a massless scalar field show that the big-bang singularity can be replaced by a big quantum bounce. To gain further insight on the nature of this bounce, we study the semidiscrete loop quantum gravity Hamiltonian constraint equation from the point of view of numerical analysis. For illustration purposes, we establish a numerical analogy between the quantum bounces and reflections in finite difference discretizations of wave equations triggered by the use of nonuniform grids or, equivalently, reflections found when solving numerically wave equations with varying coefficients. We show that the bounce is closely related to the method for the temporal update of the system and demonstrate that explicit time-updates in general yield bounces. Finally, we present an example of an implicit time-update devoid of bounces and show back-in-time, deterministic evolutions that reach and partially jump over the big-bang singularity.
Generalized quantum gravity condensates for homogeneous geometries and cosmology
NASA Astrophysics Data System (ADS)
Oriti, Daniele; Pranzetti, Daniele; Ryan, James P.; Sindoni, Lorenzo
2015-12-01
We construct a generalized class of quantum gravity condensate states that allows the description of continuum homogeneous quantum geometries within the full theory. They are based on similar ideas already applied to extract effective cosmological dynamics from the group field theory formalism, and thus also from loop quantum gravity. However, they represent an improvement over the simplest condensates used in the literature, in that they are defined by an infinite superposition of graph-based states encoding in a precise way the topology of the spatial manifold. The construction is based on the definition of refinement operators on spin network states, written in a second quantized language. The construction also lends itself easily to application to the case of spherically symmetric quantum geometries.
Quantum Metrology Enhanced by Repetitive Quantum Error Correction
NASA Astrophysics Data System (ADS)
Unden, Thomas; Balasubramanian, Priya; Louzon, Daniel; Vinkler, Yuval; Plenio, Martin B.; Markham, Matthew; Twitchen, Daniel; Stacey, Alastair; Lovchinsky, Igor; Sushkov, Alexander O.; Lukin, Mikhail D.; Retzker, Alex; Naydenov, Boris; McGuinness, Liam P.; Jelezko, Fedor
2016-06-01
We experimentally demonstrate the protection of a room-temperature hybrid spin register against environmental decoherence by performing repeated quantum error correction whilst maintaining sensitivity to signal fields. We use a long-lived nuclear spin to correct multiple phase errors on a sensitive electron spin in diamond and realize magnetic field sensing beyond the time scales set by natural decoherence. The universal extension of sensing time, robust to noise at any frequency, demonstrates the definitive advantage entangled multiqubit systems provide for quantum sensing and offers an important complement to quantum control techniques.
Quantum Metrology Enhanced by Repetitive Quantum Error Correction.
Unden, Thomas; Balasubramanian, Priya; Louzon, Daniel; Vinkler, Yuval; Plenio, Martin B; Markham, Matthew; Twitchen, Daniel; Stacey, Alastair; Lovchinsky, Igor; Sushkov, Alexander O; Lukin, Mikhail D; Retzker, Alex; Naydenov, Boris; McGuinness, Liam P; Jelezko, Fedor
2016-06-10
We experimentally demonstrate the protection of a room-temperature hybrid spin register against environmental decoherence by performing repeated quantum error correction whilst maintaining sensitivity to signal fields. We use a long-lived nuclear spin to correct multiple phase errors on a sensitive electron spin in diamond and realize magnetic field sensing beyond the time scales set by natural decoherence. The universal extension of sensing time, robust to noise at any frequency, demonstrates the definitive advantage entangled multiqubit systems provide for quantum sensing and offers an important complement to quantum control techniques. PMID:27341218
Continuous quantum error correction through local operations
Mascarenhas, Eduardo; Franca Santos, Marcelo; Marques, Breno; Terra Cunha, Marcelo
2010-09-15
We propose local strategies to protect global quantum information. The protocols, which are quantum error-correcting codes for dissipative systems, are based on environment measurements, direct feedback control, and simple encoding of the logical qubits into physical qutrits whose decaying transitions are indistinguishable and equally probable. The simple addition of one extra level in the description of the subsystems allows for local actions to fully and deterministically protect global resources such as entanglement. We present codes for both quantum jump and quantum state diffusion measurement strategies and test them against several sources of inefficiency. The use of qutrits in information protocols suggests further characterization of qutrit-qutrit disentanglement dynamics, which we also give together with simple local environment measurement schemes able to prevent distillability sudden death and even enhance entanglement in situations in which our feedback error correction is not possible.
Dimensional jump in quantum error correction
NASA Astrophysics Data System (ADS)
Bombín, Héctor
2016-04-01
Topological stabilizer codes with different spatial dimensions have complementary properties. Here I show that the spatial dimension can be switched using gauge fixing. Combining 2D and 3D gauge color codes in a 3D qubit lattice, fault-tolerant quantum computation can be achieved with constant time overhead on the number of logical gates, up to efficient global classical computation, using only local quantum operations. Single-shot error correction plays a crucial role.
Towards self-correcting quantum memories
NASA Astrophysics Data System (ADS)
Michnicki, Kamil
This thesis presents a model of self-correcting quantum memories where quantum states are encoded using topological stabilizer codes and error correction is done using local measurements and local dynamics. Quantum noise poses a practical barrier to developing quantum memories. This thesis explores two types of models for suppressing noise. One model suppresses thermalizing noise energetically by engineering a Hamiltonian with a high energy barrier between code states. Thermalizing dynamics are modeled phenomenologically as a Markovian quantum master equation with only local generators. The second model suppresses stochastic noise with a cellular automaton that performs error correction using syndrome measurements and a local update rule. Several ways of visualizing and thinking about stabilizer codes are presented in order to design ones that have a high energy barrier: the non-local Ising model, the quasi-particle graph and the theory of welded stabilizer codes. I develop the theory of welded stabilizer codes and use it to construct a code with the highest known energy barrier in 3-d for spin Hamiltonians: the welded solid code. Although the welded solid code is not fully self correcting, it has some self correcting properties. It has an increased memory lifetime for an increased system size up to a temperature dependent maximum. One strategy for increasing the energy barrier is by mediating an interaction with an external system. I prove a no-go theorem for a class of Hamiltonians where the interaction terms are local, of bounded strength and commute with the stabilizer group. Under these conditions the energy barrier can only be increased by a multiplicative constant. I develop cellular automaton to do error correction on a state encoded using the toric code. The numerical evidence indicates that while there is no threshold, the model can extend the memory lifetime significantly. While of less theoretical importance, this could be practical for real
Non-Abelian quantum error correction
NASA Astrophysics Data System (ADS)
Feng, Weibo
A quantum computer is a proposed device which would be capable of initializing, coherently manipulating, and measuring quantum states with sufficient accuracy to carry out new kinds of computations. In the standard scenario, a quantum computer is built out of quantum bits, or qubits, two-level quantum systems which replace the ordinary classical bits of a classical computer. Quantum computation is then carried out by applying quantum gates, the quantum equivalent of Boolean logic gates, to these qubits. The most fundamental barrier to building a quantum computer is the inevitable errors which occur when carrying out quantum gates and the loss of quantum coherence of the qubits due to their coupling to the environment (decoherence). Remarkably, it has been shown that in a quantum computer such errors and decoherence can be actively fought using what is known as quantum error correction. A closely related proposal for fighting errors and decoherence in a quantum computer is to build the computer out of so-called topologically ordered states of matter. These are states of matter which allow for the storage and manipulation of quantum states with a built in protection from error and decoherence. The excitations of these states are non-Abelian anyons, particle-like excitations which satisfy non-Abelian statistics, meaning that when two excitations are interchanged the result is not the usual +1 and -1 associated with identical Bosons or Fermions, but rather a unitary operation which acts on a multidimensional Hilbert space. It is therefore possible to envision computing with these anyons by braiding their world-lines in 2+1-dimensional spacetime. In this Dissertation we present explicit procedures for a scheme which lives at the intersection of these two approaches. In this scheme we envision a functioning ``conventional" quantum computer consisting of an array of qubits and the ability to carry out quantum gates on these qubits. We then give explicit quantum circuits
Quantum corrections to inflaton and curvaton dynamics
Markkanen, Tommi; Tranberg, Anders E-mail: anders.tranberg@nbi.dk
2012-11-01
We compute the fully renormalized one-loop effective action for two interacting and self-interacting scalar fields in FRW space-time. We then derive and solve the quantum corrected equations of motion both for fields that dominate the energy density (such as an inflaton) and fields that do not (such as a subdominant curvaton). In particular, we introduce quantum corrected Friedmann equations that determine the evolution of the scale factor. We find that in general, gravitational corrections are negligible for the field dynamics. For the curvaton-type fields this leaves only the effect of the flat-space Coleman-Weinberg-type effective potential, and we find that these can be significant. For the inflaton case, both the corrections to the potential and the Friedmann equations can lead to behaviour very different from the classical evolution. Even to the point that inflation, although present at tree level, can be absent at one-loop order.
Loop quantum cosmology of k=1 FRW models
Ashtekar, Abhay; Pawlowski, Tomasz; Singh, Parampreet; Vandersloot, Kevin
2007-01-15
The closed, k=1, FRW model coupled to a massless scalar field is investigated in the framework of loop quantum cosmology using analytical and numerical methods. As in the k=0 case, the scalar field can be again used as emergent time to construct the physical Hilbert space and introduce Dirac observables. The resulting framework is then used to address a major challenge of quantum cosmology: resolving the big-bang singularity while retaining agreement with general relativity at large scales. It is shown that the framework fulfills this task. In particular, for states which are semiclassical at some late time, the big bang is replaced by a quantum bounce and a recollapse occurs at the value of the scale factor predicted by classical general relativity. Thus, the 'difficulties' pointed out by Green and Unruh in the k=1 case do not arise in a more systematic treatment. As in k=0 models, quantum dynamics is deterministic across the deep Planck regime. However, because it also retains the classical recollapse, in contrast to the k=0 case one is now led to a cyclic model. Finally, we clarify some issues raised by Laguna's recent work addressed to computational physicists.
Exotic singularities and spatially curved loop quantum cosmology
Singh, Parampreet; Vidotto, Francesca
2011-03-15
We investigate the occurrence of various exotic spacelike singularities in the past and the future evolution of k={+-}1 Friedmann-Robertson-Walker model and loop quantum cosmology using a sufficiently general phenomenological model for the equation of state. We highlight the nontrivial role played by the intrinsic curvature for these singularities and the new physics which emerges at the Planck scale. We show that quantum gravity effects generically resolve all strong curvature singularities including big rip and big freeze singularities. The weak singularities, which include sudden and big brake singularities, are ignored by quantum gravity when spatial curvature is negative, as was previously found for the spatially flat model. Interestingly, for the spatially closed model there exist cases where weak singularities may be resolved when they occur in the past evolution. The spatially closed model exhibits another novel feature. For a particular class of equation of state, this model also exhibits an additional physical branch in loop quantum cosmology, a baby universe separated from the parent branch. Our analysis generalizes previous results obtained on the resolution of strong curvature singularities in flat models to isotropic spacetimes with nonzero spatial curvature.
Trivial pursuits: studies in quantum field theory and squantum cosmology
Furlong, R.C.
1987-01-01
The author show that the nonrelativistic limit of the lambdaphi/sup 4/ theory is trivial in 1 + 3 dimensions; the renormalized coupling constant vanishes and the S matrix reduces to the unit matrix. Our result is consistent with, though not sufficient to establish, the triviality of the Lorentz-invariant theory. A necessary condition for the existence of a consistent non-trivial continuum quantum field theory in d = 4 is the existence of an ultraviolet-stable fixed point of the Gell-Mann-Low renormalization group. Since others have shown (non-perturbatively) that the existence of just such a fixed point is sufficient to guarantee the triviality of the continuum massless Wess-Zumino model, we conclude that this model cannot exist non-trivially in d = 4. The fact that most renormalization group blocking schemes include each site link in many block links can generate spurious interactions in the block system. A general method for avoiding this problem is formulated and applied to do a Monte Carlo renormalization group study of the SU(2)-Higgs model in four dimensions with a check 2 scale factor. Finally starting from the D'Eath equation, the Dirac square root of the Wheeler-De Witt equation, for N = 1 supergravity, we construct superminisuperspace models (and quasi-models) for supersymmetric quantum cosmology (squantum cosmology) compatibile with Friedmann-Robertson-Walker (FRW) cosmologies.
A Calculation of Cosmological Scale from Quantum Coherence
Lindesay, J
2004-07-23
We use general arguments to examine the energy scales for which a quantum coherent description of gravitating quantum energy units is necessary. The cosmological dark energy density is expected to decouple from the Friedman-Lemaitre energy density when the Friedman-Robertson-Walker scale expansion becomes sub-luminal at R = c, at which time the usual microscopic interactions of relativistic quantum mechanics (QED, QCD, etc) open new degrees of freedom. We assume that these microscopic interactions cannot signal with superluminal exchanges, only superluminal quantum correlations. The expected gravitational vacuum energy density at that scale would be expected to freeze out due to the loss of gravitational coherence. We define the vacuum energy which generates this cosmological constant to be that of a zero temperature Bose condensate at this gravitational de-coherence scale. We presume a universality throughout the universe in the available degrees of freedom determined by fundamental constants during its evolution. Examining the reverse evolution of the universe from the present, long before reaching Planck scale dynamics one expects major modifications from the de-coherent thermal equations of state, suggesting that the pre-coherent phase has global coherence properties. Since the arguments presented involve primarily counting of degrees of freedom, we expect the statistical equilibrium states of causally disconnected regions of space to be independently identical. Thus, there is no horizon problem associated with the lack of causal influences between spatially separated regions in this approach. The scale of the amplitude of fluctuations produced during de-coherence of cosmological vacuum energy are found to evolve to values consistent with those observed in cosmic microwave background radiation and galactic clustering.
Isotropic loop quantum cosmology with matter. II. The Lorentzian constraint
NASA Astrophysics Data System (ADS)
Hinterleitner, Franz; Major, Seth
2003-12-01
The Lorentzian Hamiltonian constraint is solved for isotropic loop quantum cosmology coupled to a massless scalar field. As in the Euclidean case, the discreteness of quantum geometry removes the classical singularity from the quantum Friedmann models. In spite of the absence of the classical singularity, a modified DeWitt initial condition is incompatible with a late-time smooth behavior. Further, the smooth behavior is recovered only for positive or negatives times but not both. An important feature, which is shared with the Euclidean case, is a minimal initial energy of the order of the Planck energy required for the system to evolve dynamically. By forming wave packets of the matter field, an explicit evolution in terms of an internal time is obtained.
Loop quantum cosmology: from pre-inflationary dynamics to observations
NASA Astrophysics Data System (ADS)
Ashtekar, Abhay; Barrau, Aurélien
2015-12-01
The Planck collaboration has provided us rich information about the early Universe, and a host of new observational missions will soon shed further light on the ‘anomalies’ that appear to exist on the largest angular scales. From a quantum gravity perspective, it is natural to inquire if one can trace back the origin of such puzzling features to Planck scale physics. Loop quantum cosmology provides a promising avenue to explore this issue because of its natural resolution of the big bang singularity. Thanks to advances over the last decade, the theory has matured sufficiently to allow concrete calculations of the phenomenological consequences of its pre-inflationary dynamics. In this article we summarize the current status of the ensuing two-way dialog between quantum gravity and observations.
Inflation in loop quantum cosmology: Dynamics and spectrum of gravitational waves
Mielczarek, Jakub; Cailleteau, Thomas; Grain, Julien; Barrau, Aurelien
2010-05-15
Loop quantum cosmology provides an efficient framework to study the evolution of the Universe beyond the classical Big Bang paradigm. Because of holonomy corrections, the singularity is replaced by a 'bounce'. The dynamics of the background is investigated into the details, as a function of the parameters of the model. In particular, the conditions required for inflation to occur are carefully considered and are shown to be generically met. The propagation of gravitational waves is then investigated in this framework. By both numerical and analytical approaches, the primordial tensor power spectrum is computed for a wide range of parameters. Several interesting features could be observationally probed.
Quintessence and (anti-)Chaplygin gas in loop quantum cosmology
Lamon, Raphael; Woehr, Andreas J.
2010-01-15
The concordance model of cosmology contains several unknown components such as dark matter and dark energy. Many proposals have been made to describe them by choosing an appropriate potential for a scalar field. We study four models in the realm of loop quantum cosmology: the Chaplygin gas, an inflationary and radiationlike potential, quintessence and an anti-Chaplygin gas. For the latter we show that all trajectories start and end with a type II singularity and, depending on the initial value, may go through a bounce. On the other hand the evolution under the influence of the first three scalar fields behaves classically at times far away from the big bang singularity and bounces as the energy density approaches the critical density.
Quintessence and (anti-)Chaplygin gas in loop quantum cosmology
NASA Astrophysics Data System (ADS)
Lamon, Raphael; Wöhr, Andreas J.
2010-01-01
The concordance model of cosmology contains several unknown components such as dark matter and dark energy. Many proposals have been made to describe them by choosing an appropriate potential for a scalar field. We study four models in the realm of loop quantum cosmology: the Chaplygin gas, an inflationary and radiationlike potential, quintessence and an anti-Chaplygin gas. For the latter we show that all trajectories start and end with a type II singularity and, depending on the initial value, may go through a bounce. On the other hand the evolution under the influence of the first three scalar fields behaves classically at times far away from the big bang singularity and bounces as the energy density approaches the critical density.
Mean Field Analysis of Quantum Annealing Correction
NASA Astrophysics Data System (ADS)
Matsuura, Shunji; Nishimori, Hidetoshi; Albash, Tameem; Lidar, Daniel A.
2016-06-01
Quantum annealing correction (QAC) is a method that combines encoding with energy penalties and decoding to suppress and correct errors that degrade the performance of quantum annealers in solving optimization problems. While QAC has been experimentally demonstrated to successfully error correct a range of optimization problems, a clear understanding of its operating mechanism has been lacking. Here we bridge this gap using tools from quantum statistical mechanics. We study analytically tractable models using a mean-field analysis, specifically the p -body ferromagnetic infinite-range transverse-field Ising model as well as the quantum Hopfield model. We demonstrate that for p =2 , where the phase transition is of second order, QAC pushes the transition to increasingly larger transverse field strengths. For p ≥3 , where the phase transition is of first order, QAC softens the closing of the gap for small energy penalty values and prevents its closure for sufficiently large energy penalty values. Thus QAC provides protection from excitations that occur near the quantum critical point. We find similar results for the Hopfield model, thus demonstrating that our conclusions hold in the presence of disorder.
Mean Field Analysis of Quantum Annealing Correction.
Matsuura, Shunji; Nishimori, Hidetoshi; Albash, Tameem; Lidar, Daniel A
2016-06-01
Quantum annealing correction (QAC) is a method that combines encoding with energy penalties and decoding to suppress and correct errors that degrade the performance of quantum annealers in solving optimization problems. While QAC has been experimentally demonstrated to successfully error correct a range of optimization problems, a clear understanding of its operating mechanism has been lacking. Here we bridge this gap using tools from quantum statistical mechanics. We study analytically tractable models using a mean-field analysis, specifically the p-body ferromagnetic infinite-range transverse-field Ising model as well as the quantum Hopfield model. We demonstrate that for p=2, where the phase transition is of second order, QAC pushes the transition to increasingly larger transverse field strengths. For p≥3, where the phase transition is of first order, QAC softens the closing of the gap for small energy penalty values and prevents its closure for sufficiently large energy penalty values. Thus QAC provides protection from excitations that occur near the quantum critical point. We find similar results for the Hopfield model, thus demonstrating that our conclusions hold in the presence of disorder. PMID:27314705
Quantum computations: algorithms and error correction
NASA Astrophysics Data System (ADS)
Kitaev, A. Yu
1997-12-01
Contents §0. Introduction §1. Abelian problem on the stabilizer §2. Classical models of computations2.1. Boolean schemes and sequences of operations2.2. Reversible computations §3. Quantum formalism3.1. Basic notions and notation3.2. Transformations of mixed states3.3. Accuracy §4. Quantum models of computations4.1. Definitions and basic properties4.2. Construction of various operators from the elements of a basis4.3. Generalized quantum control and universal schemes §5. Measurement operators §6. Polynomial quantum algorithm for the stabilizer problem §7. Computations with perturbations: the choice of a model §8. Quantum codes (definitions and general properties)8.1. Basic notions and ideas8.2. One-to-one codes8.3. Many-to-one codes §9. Symplectic (additive) codes9.1. Algebraic preparation9.2. The basic construction9.3. Error correction procedure9.4. Torus codes §10. Error correction in the computation process: general principles10.1. Definitions and results10.2. Proofs §11. Error correction: concrete procedures11.1. The symplecto-classical case11.2. The case of a complete basis Bibliography
NASA Astrophysics Data System (ADS)
Fitzpatrick, A. Liam; Kaplan, Jared
2016-05-01
We use results on Virasoro conformal blocks to study chaotic dynamics in CFT2 at large central charge c. The Lyapunov exponent λ L , which is a diagnostic for the early onset of chaos, receives 1 /c corrections that may be interpreted as {λ}_L=2π /β(1+12/c) . However, out of time order correlators receive other equally important 1 /c suppressed contributions that do not have such a simple interpretation. We revisit the proof of a bound on λ L that emerges at large c, focusing on CFT2 and explaining why our results do not conflict with the analysis leading to the bound. We also comment on relationships between chaos, scattering, causality, and bulk locality.
Quantum annealing correction with minor embedding
NASA Astrophysics Data System (ADS)
Vinci, Walter; Albash, Tameem; Paz-Silva, Gerardo; Hen, Itay; Lidar, Daniel A.
2015-10-01
Quantum annealing provides a promising route for the development of quantum optimization devices, but the usefulness of such devices will be limited in part by the range of implementable problems as dictated by hardware constraints. To overcome constraints imposed by restricted connectivity between qubits, a larger set of interactions can be approximated using minor embedding techniques whereby several physical qubits are used to represent a single logical qubit. However, minor embedding introduces new types of errors due to its approximate nature. We introduce and study quantum annealing correction schemes designed to improve the performance of quantum annealers in conjunction with minor embedding, thus leading to a hybrid scheme defined over an encoded graph. We argue that this scheme can be efficiently decoded using an energy minimization technique provided the density of errors does not exceed the per-site percolation threshold of the encoded graph. We test the hybrid scheme using a D-Wave Two processor on problems for which the encoded graph is a two-level grid and the Ising model is known to be NP-hard. The problems we consider are frustrated Ising model problem instances with "planted" (a priori known) solutions. Applied in conjunction with optimized energy penalties and decoding techniques, we find that this approach enables the quantum annealer to solve minor embedded instances with significantly higher success probability than it would without error correction. Our work demonstrates that quantum annealing correction can and should be used to improve the robustness of quantum annealing not only for natively embeddable problems but also when minor embedding is used to extend the connectivity of physical devices.
Quantum Error Correction with Biased Noise
NASA Astrophysics Data System (ADS)
Brooks, Peter
Quantum computing offers powerful new techniques for speeding up the calculation of many classically intractable problems. Quantum algorithms can allow for the efficient simulation of physical systems, with applications to basic research, chemical modeling, and drug discovery; other algorithms have important implications for cryptography and internet security. At the same time, building a quantum computer is a daunting task, requiring the coherent manipulation of systems with many quantum degrees of freedom while preventing environmental noise from interacting too strongly with the system. Fortunately, we know that, under reasonable assumptions, we can use the techniques of quantum error correction and fault tolerance to achieve an arbitrary reduction in the noise level. In this thesis, we look at how additional information about the structure of noise, or "noise bias," can improve or alter the performance of techniques in quantum error correction and fault tolerance. In Chapter 2, we explore the possibility of designing certain quantum gates to be extremely robust with respect to errors in their operation. This naturally leads to structured noise where certain gates can be implemented in a protected manner, allowing the user to focus their protection on the noisier unprotected operations. In Chapter 3, we examine how to tailor error-correcting codes and fault-tolerant quantum circuits in the presence of dephasing biased noise, where dephasing errors are far more common than bit-flip errors. By using an appropriately asymmetric code, we demonstrate the ability to improve the amount of error reduction and decrease the physical resources required for error correction. In Chapter 4, we analyze a variety of protocols for distilling magic states, which enable universal quantum computation, in the presence of faulty Clifford operations. Here again there is a hierarchy of noise levels, with a fixed error rate for faulty gates, and a second rate for errors in the distilled
Genericness of a big bounce in isotropic loop quantum cosmology.
Date, Ghanashyam; Hossain, Golam Mortuza
2005-01-14
The absence of isotropic singularity in loop quantum cosmology can be understood in an effective classical description as the Universe exhibiting a big bounce. We show that with a scalar matter field, the big bounce is generic in the sense that it is independent of quantization ambiguities and the details of scalar field dynamics. The volume of the Universe at the bounce point is parametrized by a single parameter. It provides a minimum length scale which serves as a cutoff for computations of density perturbations thereby influencing their amplitudes. PMID:15698060
NASA Astrophysics Data System (ADS)
Haggard, Hal; Han, Muxin; Kaminski, Wojciech; Riello, Aldo
2016-03-01
Prominent approaches to quantum gravity struggle when it comes to incorporating a positive cosmological constant in their models. Using quantization of a complex SL(2,C) Chern-Simons theory we include a cosmological constant, of either sign, into a model of quantum gravity.
Astrophysical Applications of Quantum Corrections to the Equation of State of a Plasma
NASA Technical Reports Server (NTRS)
Heckler, Andrew F.
1994-01-01
The quantum electrodynamic correction to the equation of state of a plasma at finite temperature is applied to the areas of solar physics and cosmology. A previously neglected, purely quantum term in the correction is found to change the equation of state in the solar core by -0.37%, which is roughly estimated to decrease the calculated high energy neutrino flux by about 2.2%. We also show that a previous calculation of the effect of this correction on big bang nucleosynthesis is incomplete, and we estimate the correction to the primordial helium abundance Y to be Delta A= 1.4 x 10(exp -4). A physical explanation for the correction is found in terms of corrections to the dispersion relation of the electron, positron, and photon.
Topics in quantum cryptography, quantum error correction, and channel simulation
NASA Astrophysics Data System (ADS)
Luo, Zhicheng
In this thesis, we mainly investigate four different topics: efficiently implementable codes for quantum key expansion [51], quantum error-correcting codes based on privacy amplification [48], private classical capacity of quantum channels [44], and classical channel simulation with quantum side information [49, 50]. For the first topic, we propose an efficiently implementable quantum key expansion protocol, capable of increasing the size of a pre-shared secret key by a constant factor. Previously, the Shor-Preskill proof [64] of the security of the Bennett-Brassard 1984 (BB84) [6] quantum key distribution protocol relied on the theoretical existence of good classical error-correcting codes with the "dual-containing" property. But the explicit and efficiently decodable construction of such codes is unknown. We show that we can lift the dual-containing constraint by employing the non-dual-containing codes with excellent performance and efficient decoding algorithms. For the second topic, we propose a construction of Calderbank-Shor-Steane (CSS) [19, 68] quantum error-correcting codes, which are originally based on pairs of mutually dual-containing classical codes, by combining a classical code with a two-universal hash function. We show, using the results of Renner and Koenig [57], that the communication rates of such codes approach the hashing bound on tensor powers of Pauli channels in the limit of large block-length. For the third topic, we prove a regularized formula for the secret key assisted capacity region of a quantum channel for transmitting private classical information. This result parallels the work of Devetak on entanglement assisted quantum communication capacity. This formula provides a new family protocol, the private father protocol, under the resource inequality framework that includes the private classical communication without the assisted secret keys as a child protocol. For the fourth topic, we study and solve the problem of classical channel
Primordial power spectra for scalar perturbations in loop quantum cosmology
NASA Astrophysics Data System (ADS)
Martín de Blas, Daniel; Olmedo, Javier
2016-06-01
We provide the power spectrum of small scalar perturbations propagating in an inflationary scenario within loop quantum cosmology. We consider the hybrid quantization approach applied to a Friedmann-Robertson-Walker spacetime with flat spatial sections coupled to a massive scalar field. We study the quantum dynamics of scalar perturbations on an effective background within this hybrid approach. We consider in our study adiabatic states of different orders. For them, we find that the hybrid quantization is in good agreement with the predictions of the dressed metric approach. We also propose an initial vacuum state for the perturbations, and compute the primordial and the anisotropy power spectrum in order to qualitatively compare with the current observations of Planck mission. We find that our vacuum state is in good agreement with them, showing a suppression of the power spectrum for large scale anisotropies. We compare with other choices already studied in the literature.
Zanzi, Andrea
2010-08-15
The chameleonic behavior of the string theory dilaton is suggested. Some of the possible consequences of the chameleonic string dilaton are analyzed in detail. In particular, (1) we suggest a new stringy solution to the cosmological constant problem and (2) we point out the nonequivalence of different conformal frames at the quantum level. In order to obtain these results, we start taking into account the (strong coupling) string loop expansion in the string frame (S-frame), therefore the so-called form factors are present in the effective action. The correct dark energy scale is recovered in the Einstein frame (E-frame) without unnatural fine-tunings and this result is robust against all quantum corrections, granted that we assume a proper structure of the S-frame form factors in the strong coupling regime. At this stage, the possibility still exists that a certain amount of fine-tuning may be required to satisfy some phenomenological constraints. Moreover in the E-frame, in our proposal, all the interactions are switched off on cosmological length scales (i.e., the theory is IR-free), while higher derivative gravitational terms might be present locally (on short distances) and it remains to be seen whether these facts clash with phenomenology. A detailed phenomenological analysis is definitely necessary to clarify these points.
Testing Quantum Mechanics with Observations of Causally Disconnected Cosmological Events
NASA Astrophysics Data System (ADS)
Friedman, Andrew S.; Kaiser, D. I.; Gallicchio, J.; Guth, A. H.
2014-01-01
We discuss a thought experiment which would leverage cosmology to test quantum mechanics using astronomical observations. Specifically, we aim to close the "settings-independence" loophole in experimental tests of Bell's inequality by choosing the detector settings (e.g. polarizer orientations) using real-time observations of causally disconnected cosmic sources. This would help close one of the most important remaining Bell test loopholes whereby a local hidden variable theory could mimic the quantum predictions if the experimental settings choices shared even a small correlation due to unknown local causal influences prior to the experiment. The talk will focus on the theoretical cosmology constraints needed to choose optimal sources for such an experiment, describing general conditions for pairs of cosmic events with arbitrary redshifts and angular separations to have shared causal pasts in Friedman-Lemaitre-Robertson-Walker universes with arbitrary curvature, including flat, dark energy dominated, accelerating universes like our own. While causally disjoint patches of the cosmic microwave background radiation at redshift z ~ 1090 could be used to set the detectors, z > 3.65 quasars observed at optical wavelengths are arguably the optimal candidate source pairs using present technology that meet the condition of having no shared causal past since the end of any period of inflation, 13.82 Gyr ago. Results are illustrated for our universe with causal structure animations to help visualize the intersections of past light cones for arbitrary event pairs.
Quantum cosmology: From hidden symmetries towards a new (supersymmetric) perspective
NASA Astrophysics Data System (ADS)
Jalalzadeh, S.; Rostami, T.; Moniz, P. V.
2016-02-01
We review pedagogically some of the basic essentials regarding recent results intertwining boundary conditions, the algebra of constraints and hidden symmetries in quantum cosmology. They were extensively published in Refs. [S. Jalalzadeh, S. M. M. Rasouli and P. V. Moniz, Phys. Rev. D 90 (2014) 023541, S. Jalalzadeh and P. V. Moniz, Phys. Rev. D 89 (2014), S. Jalalzadeh, T. Rostami and P. V. Moniz, Eur. Phys. J. C 75 (2015) 38, arXiv:gr-qc/1412.6439 and T. Rostami, S. Jalalzadeh and P. V. Moniz, Phys. Rev. D 92 (2015) 023526, arXiv:gr-qc/1507.04212], where complete discussions and full details can be found. More concretely, in Refs. [S. Jalalzadeh, S. M. M. Rasouli and P. V. Moniz, Phys. Rev. D 90 (2014) 023541, S. Jalalzadeh and P. V. Moniz, Phys. Rev. D 89 (2014) and S. Jalalzadeh, T. Rostami and P. V. Moniz, Eur. Phys. J. C 75 (2015) 38, arXiv:gr-qc/1412.6439] it has been shown that specific boundary conditions can be related to the algebra of Dirac observables. Moreover, a process afterwards associated to the algebra of existent hidden symmetries, from which the boundary conditions can be selected, was introduced. On the other hand, in Ref. [T. Rostami, S. Jalalzadeh and P. V. Moniz, Phys. Rev. D 92 (2015) 023526, arXiv:gr-qc/1507.04212] it was subsequently argued that some factor ordering choices can be extracted from the hidden symmetries structure of the minisuperspace model. In Refs. [S. Jalalzadeh, S. M. M. Rasouli and P. V. Moniz, Phys. Rev. D 90 (2014) 023541, S. Jalalzadeh and P. V. Moniz, Phys. Rev. D 89 (2014), S. Jalalzadeh, T. Rostami and P. V. Moniz, Eur. Phys. J. C 75 (2015) 38, arXiv:gr-qc/1412.6439 and T. Rostami, S. Jalalzadeh and P. V. Moniz, Phys. Rev. D 92 (2015) 023526, arXiv:gr-qc/1507.04212], we proceeded gradually towards less simple models, ranging from a FLRW model with a perfect fluid [S. Jalalzadeh, S. M. M. Rasouli and P. V. Moniz, Phys. Rev. D 90 (2014) 023541] up to a conformal scalar field content [T. Rostami, S. Jalalzadeh and
Electromagnetic quantum effects in higher-dimensional cosmological models
NASA Astrophysics Data System (ADS)
Kotanjyan, Anna; Sargsyan, Hayk; Simonyan, David; Saharian, Aram
2016-07-01
Among the most interesting directions in quantum field theory on curved spacetimes is the investigation of the influence of the gravitational field on the properties of the quantum vacuum. The corresponding problems are exactly solvable for highly symmetric background geometries only. In particular, the investigations of quantum effects in de Sitter (dS) and anti-de Sitter (AdS) spacetimes have attracted a great deal of attention. We consider electromagnetic quantum effects in higher-dimensional cosmological models. The two-point functions of the vector potential and of the field tensor for the electromagnetic field in background of dS and AdS spacetime are evaluated in arbitrary number of spatial dimensions. First we consider the two-point functions in the boundary-free geometry and then generalize the results in the presence of a reflecting boundary, for AdS spacetimes parallel to the AdS horizon. By using the expressions for the two-point functions of the field tensor, we investigate the vacuum expectation values of the electric field squared and of the energy-momentum tensor. Simple asymptotic expressions are provided for both cases, in particular for AdS geometry near the AdS boundary and horizon.
Loop Quantum Gravity and the Planck Regime of Cosmology
NASA Astrophysics Data System (ADS)
Ashtekar, Abhay
The very early universe provides the best arena we currently have to test quantum gravity theories. The success of the inflationary paradigm in accounting for the observed inhomogeneities in the cosmic microwave background already illustrates this point to a certain extent because the paradigm is based on quantum field theory on the curved cosmological space-times. However, this analysis excludes the Planck era because the background space-time satisfies Einstein's equations all the way back to the big bang singularity. Using techniques from loop quantum gravity, the paradigm has now been extended to a self-consistent theory from the Planck regime to the onset of inflation, covering some 11 orders of magnitude in curvature. In addition, for a narrow window of initial conditions, there are departures from the standard paradigm, with novel effects, such as a modification of the consistency relation involving the scalar and tensor power spectra and a new source for non-Gaussianities. The genesis of the large scale structure of the universe can be traced back to quantum gravity fluctuations in the Planck regime. This report provides a bird's eye view of these developments for the general relativity community.
Low Energy Quantum Gravity, the Cosmological Constant and Gauge Coupling Constants
NASA Astrophysics Data System (ADS)
Toms, David J.
Robinson and Wilczek have suggested that loop corrections in quantum gravity can alter the running gauge coupling constants from the behaviour found in the absence of gravity. Although their original calculation is not correct, the basic idea behind their paper has been re-examined recently for quantized Einstein-Maxwell theory with a cosmological constant. In this essay I discuss some of the issues surrounding the calculation and mention some of the implications. I argue that it is possible for a theory that is not conventionally asymptotically free to become so in the presence of gravity, and for gravity to lead to a new ultraviolet fixed point. This establishes a provocative link between the microscopic and macroscopic realms.
Loop quantum cosmology in Bianchi type I models: Analytical investigation
Chiou, D.-W.
2007-01-15
The comprehensive formulation for loop quantum cosmology in the spatially flat, isotropic model was recently constructed. In this paper, the methods are extended to the anisotropic Bianchi I cosmology. Both the precursor and the improved strategies are applied and the expected results are established: (i) the scalar field again serves as an internal clock and is treated as emergent time; (ii) the total Hamiltonian constraint is derived by imposing the fundamental discreteness and gives the evolution as a difference equation; and (iii) the physical Hilbert space, Dirac observables, and semiclassical states are constructed rigorously. It is also shown that the state in the kinematical Hilbert space associated with the classical singularity is decoupled in the difference evolution equation, indicating that the big bounce may take place when any of the area scales undergoes the vanishing behavior. The investigation affirms the robustness of the framework used in the isotropic model by enlarging its domain of validity and provides foundations to conduct the detailed numerical analysis.
Quantum Bianchi Type IX Cosmology in K-Essence Theory
NASA Astrophysics Data System (ADS)
Espinoza-García, Abraham; Socorro, J.; Pimentel, Luis O.
2014-09-01
We use one of the simplest forms of the K-essence theory and apply it to the anisotropic Bianchi type IX cosmological model, with a barotropic perfect fluid modeling the usual matter content. We show that the most important contribution of the scalar field occurs during a stiff matter phase. Also, we present a canonical quantization procedure of the theory which can be simplified by reinterpreting the scalar field as an exotic part of the total matter content. The solutions to the Wheeler-DeWitt equation were found using the Bohmian formulation Bohm (Phys. Rev. 85(2):166, 1952) of quantum mechanics, employing the amplitude-real-phase approach Moncrief and Ryan (Phys. Rev. D 44:2375, 1991), where the ansatz for the wave function is of the form Ψ( ℓ μ )= χ( ϕ) W( ℓ μ ), where S is the superpotential function, which plays an important role in solving the Hamilton-Jacobi equation.
Classical and quantum cosmology of Born-Infeld type models
NASA Astrophysics Data System (ADS)
Kamenshchik, Alexander; Kiefer, Claus; Kwidzinski, Nick
2016-04-01
We discuss Born-Infeld type fields (tachyon fields) in classical and quantum cosmology. We first partly review and partly extend the discussion of the classical solutions and focus in particular on the occurrence of singularities. For quantization, we employ geometrodynamics. In the case of constant potential, we discuss both Wheeler-DeWitt quantization and reduced quantization. We are able to give various solutions and discuss their asymptotics. For the case of general potential, we transform the Wheeler-DeWitt equation to a form where it leads to a difference equation. Such a difference equation was previously found in the quantization of black holes. We give explicit results for the cases of constant potential and inverse squared potential and point out special features possessed by solutions of the difference equation.
Condensates in Quantum Chromodynamics and the Cosmological Constant
Brodsky, Stanley J.; Shrock, Robert
2009-05-08
Casher and Susskind have noted that in the light-front description, spontaneous chiral symmetry breaking in quantum chromodynamics (QCD) is a property of hadronic wavefunctions and not of the vacuum. Here we show from several physical perspectives that, because of color confinement, quark and gluon QCD condensates are associated with the internal dynamics of hadrons. We discuss condensates using condensed matter analogues, the AdS/CFT correspondence, and the Bethe-Salpeter/Dyson-Schwinger approach for bound states. Our analysis is in agreement with the Casher and Susskind model and the explicit demonstration of 'in-hadron' condensates by Roberts et al., using the Bethe-Salpeter/Dyson-Schwinger formalism for QCD bound states. These results imply that QCD condensates give zero contribution to the cosmological constant, since all of the gravitational effects of the in-hadron condensates are already included in the normal contribution from hadron masses.
Experimental quantum error correction with high fidelity
NASA Astrophysics Data System (ADS)
Zhang, Jingfu; Gangloff, Dorian; Moussa, Osama; Laflamme, Raymond
2011-09-01
More than ten years ago a first step toward quantum error correction (QEC) was implemented [Phys. Rev. Lett.PRLTAO0031-900710.1103/PhysRevLett.81.2152 81, 2152 (1998)]. The work showed there was sufficient control in nuclear magnetic resonance to implement QEC, and demonstrated that the error rate changed from ɛ to ˜ɛ2. In the current work we reproduce a similar experiment using control techniques that have been since developed, such as the pulses generated by gradient ascent pulse engineering algorithm. We show that the fidelity of the QEC gate sequence and the comparative advantage of QEC are appreciably improved. This advantage is maintained despite the errors introduced by the additional operations needed to protect the quantum states.
Experimental quantum error correction with high fidelity
Zhang Jingfu; Gangloff, Dorian; Moussa, Osama; Laflamme, Raymond
2011-09-15
More than ten years ago a first step toward quantum error correction (QEC) was implemented [Phys. Rev. Lett. 81, 2152 (1998)]. The work showed there was sufficient control in nuclear magnetic resonance to implement QEC, and demonstrated that the error rate changed from {epsilon} to {approx}{epsilon}{sup 2}. In the current work we reproduce a similar experiment using control techniques that have been since developed, such as the pulses generated by gradient ascent pulse engineering algorithm. We show that the fidelity of the QEC gate sequence and the comparative advantage of QEC are appreciably improved. This advantage is maintained despite the errors introduced by the additional operations needed to protect the quantum states.
Error-corrected quantum annealing with hundreds of qubits
NASA Astrophysics Data System (ADS)
Pudenz, Kristen L.; Albash, Tameem; Lidar, Daniel A.
2014-02-01
Quantum information processing offers dramatic speedups, yet is susceptible to decoherence, whereby quantum superpositions decay into mutually exclusive classical alternatives, thus robbing quantum computers of their power. This makes the development of quantum error correction an essential aspect of quantum computing. So far, little is known about protection against decoherence for quantum annealing, a computational paradigm aiming to exploit ground-state quantum dynamics to solve optimization problems more rapidly than is possible classically. Here we develop error correction for quantum annealing and experimentally demonstrate it using antiferromagnetic chains with up to 344 superconducting flux qubits in processors that have recently been shown to physically implement programmable quantum annealing. We demonstrate a substantial improvement over the performance of the processors in the absence of error correction. These results pave the way towards large-scale noise-protected adiabatic quantum optimization devices, although a threshold theorem such as has been established in the circuit model of quantum computing remains elusive.
Quantum corrected spherical collapse: A phenomenological framework
Ziprick, Jonathan; Kunstatter, Gabor
2010-08-15
A phenomenological framework is presented for incorporating quantum gravity motivated corrections into the dynamics of spherically symmetric collapse. The effective equations are derived from a variational principle that guarantees energy conservation and the existence of a Birkhoff theorem. The gravitational potential can be chosen as a function of the areal radius to yield specific nonsingular static spherically symmetric solutions that generically have two horizons. For a specific choice of potential, the effective stress energy tensor violates only the dominant energy condition. The violations are maximum near the inner horizon and die off rapidly. A numerical study of the quantum corrected collapse of a spherically symmetric scalar field in this case reveals that the modified gravitational potential prevents the formation of a central singularity and ultimately yields a static, mostly vacuum, spacetime with two horizons. The matter 'piles up' on the inner horizon giving rise to mass inflation at late times. The Cauchy horizon is transformed into a null, weak singularity, but in contrast to Einstein gravity, the absence of a central singularity renders this null singularity stable.
Classical and quantum behavior of the generic cosmological solution
NASA Astrophysics Data System (ADS)
Imponente, Giovanni; Montani, Giovanni
2006-11-01
In the present paper we generalize the original work of C.W. Misner about the quantum dynamics of the Bianchi type IX geometry near the cosmological singularity. We extend the analysis to the generic inhomogeneous universe by solving the super-momentum constraint and outlining the dynamical decoupling of spatial points. Firstly, we discuss the classical evolution of the model in terms of the Hamilton-Jacobi approach as applied to the super-momentum and super-Hamiltonian constraints; then we quantize it in the approximation of a square potential well after an ADM reduction of the dynamics with respect to the super-momentum constraint only. Such a reduction relies on a suitable form for the generic three-metric tensor which allows the use of its three functions as the new spatial coordinates. We get a functional representation of the quantum dynamics which is equivalent to the Misner-like one when extended point by point, since the Hilbert space factorizes into ∞3 independent components due to the parametric role that the three-coordinates assume in the asymptotic potential term. Finally, we discuss the conditions for having a semiclassical behavior of the dynamics and we recognize that this already corresponds to having mean occupation numbers of order O(102).
An embedding of loop quantum cosmology in (b,v) variables into a full theory context
NASA Astrophysics Data System (ADS)
Bodendorfer, N.
2016-06-01
Loop quantum cosmology in (b, v) variables, which is governed by a unit step size difference equation, is embedded into a full theory context based on similar variables. A full theory context here means a theory of quantum gravity arrived at using the quantisation techniques used in loop quantum gravity, however based on a different choice of elementary variables and classical gauge fixing suggested by loop quantum cosmology. From the full theory perspective, the symmetry reduction is characterised by the vanishing of certain phase space functions which are implemented as operator equations in the quantum theory. The loop quantum cosmology dynamics arise as the action of the full theory Hamiltonian on maximally coarse states in the kernel of the reduction constraints. An application of this reduction procedure to spherical symmetry is also sketched, with similar results, but only one canonical pair in (b, v) form.
Method for quantum-jump continuous-time quantum error correction
NASA Astrophysics Data System (ADS)
Hsu, Kung-Chuan; Brun, Todd A.
2016-02-01
Continuous-time quantum error correction (CTQEC) is a technique for protecting quantum information against decoherence, where both the decoherence and error correction processes are considered continuous in time. Given any [[n ,k ,d
Bond additivity corrections for quantum chemistry methods
C. F. Melius; M. D. Allendorf
1999-04-01
In the 1980's, the authors developed a bond-additivity correction procedure for quantum chemical calculations called BAC-MP4, which has proven reliable in calculating the thermochemical properties of molecular species, including radicals as well as stable closed-shell species. New Bond Additivity Correction (BAC) methods have been developed for the G2 method, BAC-G2, as well as for a hybrid DFT/MP2 method, BAC-Hybrid. These BAC methods use a new form of BAC corrections, involving atomic, molecular, and bond-wise additive terms. These terms enable one to treat positive and negative ions as well as neutrals. The BAC-G2 method reduces errors in the G2 method due to nearest-neighbor bonds. The parameters within the BAC-G2 method only depend on atom types. Thus the BAC-G2 method can be used to determine the parameters needed by BAC methods involving lower levels of theory, such as BAC-Hybrid and BAC-MP4. The BAC-Hybrid method should scale well for large molecules. The BAC-Hybrid method uses the differences between the DFT and MP2 as an indicator of the method's accuracy, while the BAC-G2 method uses its internal methods (G1 and G2MP2) to provide an indicator of its accuracy. Indications of the average error as well as worst cases are provided for each of the BAC methods.
Multipartite Entanglement: Transformations, Quantum Secret Sharing, Quantum Error Correction
NASA Astrophysics Data System (ADS)
Helwig, Wolfram
conveniently described within the graph state formalism. Finally, we use the insight gained from entanglement in QSS schemes to derive necessary and sufficient conditions for quantum erasure channel and quantum error correction codes that satisfy the quantum Singleton bound, as these codes are closely related to ramp QSS schemes. This provides us with a very intuitive approach to codes for the quantum erasure channel, purely based on the entanglement required to protect information against losses by use of the parallel teleportation protocol.
Classical and quantum Big Brake cosmology for scalar field and tachyonic models
Kamenshchik, A. Yu.; Manti, S.
2013-02-21
We study a relation between the cosmological singularities in classical and quantum theory, comparing the classical and quantum dynamics in some models possessing the Big Brake singularity - the model based on a scalar field and two models based on a tachyon-pseudo-tachyon field . It is shown that the effect of quantum avoidance is absent for the soft singularities of the Big Brake type while it is present for the Big Bang and Big Crunch singularities. Thus, there is some kind of a classical - quantum correspondence, because soft singularities are traversable in classical cosmology, while the strong Big Bang and Big Crunch singularities are not traversable.
The entropy-corrected holographic dark energy in Brans-Dicke cosmology with varying mass fermions
NASA Astrophysics Data System (ADS)
Farajollahi, H.; Tayebi, F.
2013-07-01
We aim in this paper to study Brans-Dicke cosmology in the presence of varying mass fermions and a self-interaction potential. Furthermore, we also probe the entropy corrected holographic dark energy (ECHDE) in the model in two non-interacting and interacting scenarios. The model parameters are constrained by using the recent SNe Ia observational data and tested against observational data of Hubble parameter. For a comparison, we also constrained and tested the cosmological parameters in ΛCDM model with the same observational data. We show that in non of the scenarios the model prediction is better than ΛCDM model.
NASA Astrophysics Data System (ADS)
Pasqua, Antonio; Assaf, Khudhair A.; Aly, Ayman A.
2013-10-01
In this work, we study the power-law and the logarithmic entropy corrected versions of the Ricci Dark Energy (RDE) model in the framework of the Brans-Dicke cosmology non-minimally coupled with a chameleon scalar field ϕ. Considering the presence of interaction between Dark Energy (DE) and Dark Matter (DM), we derived the expressions of some relevant cosmological parameters, i.e. the equation of state parameter ω D , the deceleration parameter q and the evolution of the energy density parameter \\varOmega'D.
Russell, R J
2001-12-01
The sciences and the humanities, including theology, form an epistemic hierarchy that ensures both constraint and irreducibility. At the same time, theological methodology is analogous to scientific methodology, though with several important differences. This model of interaction between science and theology can be seen illustrated in a consideration of the relation between contemporary cosmology (Big Bang cosmology, cosmic inflation, and quantum cosmology) and Christian systematic and natural theology. In light of developments in cosmology, the question of origins has become theologically less interesting than that of the cosmic evolution of a contingent universe. PMID:11797742
Quantum-electrodynamics corrections in pionic hydrogen
Schlesser, S.; Le Bigot, E.-O.; Indelicato, P.; Pachucki, K.
2011-07-15
We investigate all pure quantum-electrodynamics corrections to the np{yields}1s, n=2-4 transition energies of pionic hydrogen larger than 1 meV, which requires an accurate evaluation of all relevant contributions up to order {alpha}{sup 5}. These values are needed to extract an accurate strong interaction shift from experiment. Many small effects, such as second-order and double vacuum polarization contribution, proton and pion self-energies, finite size and recoil effects are included with exact mass dependence. Our final value differs from previous calculations by up to {approx_equal}11 ppm for the 1s state, while a recent experiment aims at a 4 ppm accuracy.
Breeding quantum error-correcting codes
Dong Ying; Hu Dan; Yu Sixia
2010-02-15
The stabilizer code, one major family of quantum error-correcting codes (QECC), is specified by the joint eigenspace of a commuting set of Pauli observables. It turns out that noncommuting sets of Pauli observables can be used to construct more efficient QECCs, such as the entanglement-assisted QECCs, which are built directly from any linear classical codes whose detailed properties are needed to determine the parameters of the resulting quantum codes. Here we propose another family of QECCs, namely, the breeding QECCs, that also employ noncommuting sets of Pauli observables and can be built from any classical additive codes, either linear or nonlinear, with the advantage that their parameters can be read off directly from the corresponding classical codes. Besides, since nonlinear codes are generally more efficient than linear codes, our breeding codes have better parameters than those codes built from linear codes. The terminology is justified by the fact that our QECCs are related to the ordinary QECCs in exactly the same way that the breeding protocols are related to the hashing protocols in the entanglement purification.
Power-law entropy-corrected new holographic dark energy in Horava-Lifshitz cosmology
NASA Astrophysics Data System (ADS)
Borah, Bharat; Ansari, M.
2014-12-01
Purpose of this paper is to study power-law entropy-corrected holographic dark energy (PLECHDE) in the frame work of Horava-Lifshitz cosmology with Granda-Oliveros (G-O) IR-cutoff. Considering interacting and non-interacting scenario of PLECHDE with dark matter in a spatially non-flat universe, we investigate the cosmological implications of this model in detail. We obtain equation of state parameter, deceleration parameter and the evolution of dark energy density to explain the expansion of the universe. We also find out these parameters for Ricci scale. Finally, we find out a cosmological application of our work by evaluating a relation for the equation of state of dark energy for law red-shifts.
Loop Quantum Corrections to Statefinder Parameters of Dark Energy
NASA Astrophysics Data System (ADS)
Jamil, Mubasher; Momeni, D.; Myrzakulov, Ratbay
2013-09-01
In this paper, we have calculated the statefinder parameters for the Friedmann-Robertson-Walker (FRW) Universe in the gravitational framework of loop quantum cosmology (LQC). As examples, we study two types of dark energy models namely Holographic dark energy and New-Agegraphic dark energy.
Universal Scaling Laws in Quantum Theory and Cosmology
NASA Astrophysics Data System (ADS)
Rauscher, Elizabeth A.; Hurtak, James J.; Hurtak, D. E.
2013-09-01
We have developed a hyperdimensional geometry, Dn or Descartes space of dimensionality of n > 4, for our consideration n = 10. This model introduces a formation in terms of the conditions of constants as the space that allows us to calculate a unique set of scaling laws from the lower end scale of the quantum vacuum foam to the current universe. A group theoretical matrix formalism is made for the ten and eleven dimensional model of this space. For the eleven dimensional expressions of this geometry, a fundamental frequency is introduced and utilized as an additional condition on the topology. The constraints on the Dn space are imposed by the relationship of the universal constraints of nature expressed in terms of physical variables. The quantum foam picture can be related to the Fermi-Dirac vacuum model. Consideration is made for the lower limit of a universal size scaling from the Planck length, l = 10-33 cm, temporal component, t = 10-44 sec, density, 1093 gm/cm3 and additional Planck units of quantized variables. The upper limit of rotational frequency in the Dn space is given as 1043 Hz, as conditions or constraints that apply to the early universe which are expressed uniquely in terms of the universal constants, h, Planck's constant, the G, the gravitational constant and c, the velocity of light. We have developed a scaling law for cosmogenesis from the early universe to our present day universe. We plot the physical variables of the ten and eleven dimensional space versus a temporal evolution of these parameters. From this formalism, in order to maintain the compatibility of Einstein's General Relativity with the current model of cosmology, we replace Guth's inflationary model with a matter creation term. Also we have developed a fundamental scaling relationship between the "size scale" of organized matter with their associated fundamental frequency.
Condensates in quantum chromodynamics and the cosmological constant
Brodsky, Stanley J.; Shrock, Robert
2011-01-01
Casher and Susskind [Casher A, Susskind L (1974) Phys Rev 9:436–460] have noted that in the light-front description, spontaneous chiral symmetry breaking is a property of hadronic wavefunctions and not of the vacuum. Here we show from several physical perspectives that, because of color confinement, quark and gluon condensates in quantum chromodynamics (QCD) are associated with the internal dynamics of hadrons. We discuss condensates using condensed matter analogues, the Anti de Sitter/conformal field theory correspondence, and the Bethe–Salpeter–Dyson–Schwinger approach for bound states. Our analysis is in agreement with the Casher and Susskind model and the explicit demonstration of “in-hadron” condensates by Roberts and coworkers [Maris P, Roberts CD, Tandy PC (1998) Phys Lett B 420:267–273], using the Bethe–Salpeter–Dyson–Schwinger formalism for QCD-bound states. These results imply that QCD condensates give zero contribution to the cosmological constant, because all of the gravitational effects of the in-hadron condensates are already included in the normal contribution from hadron masses.
Viability of the matter bounce scenario in Loop Quantum Cosmology from BICEP2 last data
De Haro, Jaume; Amorós, Jaume E-mail: jaume.amoros@upc.edu
2014-08-01
The CMB map provided by the Planck project constrains the value of the ratio of tensor-to-scalar perturbations, namely r, to be smaller than 0.11 (95 % CL). This bound rules out the simplest models of inflation. However, recent data from BICEP2 is in strong tension with this constrain, as it finds a value r=0.20{sup +0.07}{sub -0.05} with 0r= disfavored at 7.0 σ, which allows these simplest inflationary models to survive. The remarkable fact is that, even though the BICEP2 experiment was conceived to search for evidence of inflation, its experimental data matches correctly theoretical results coming from the matter bounce scenario (the alternative model to the inflationary paradigm). More precisely, most bouncing cosmologies do not pass Planck's constrains due to the smallness of the value of the tensor/scalar ratio r≤ 0.11, but with new BICEP2 data some of them fit well with experimental data. This is the case with the matter bounce scenario in the teleparallel version of Loop Quantum Cosmology.
Viability of the matter bounce scenario in Loop Quantum Cosmology from BICEP2 last data
NASA Astrophysics Data System (ADS)
de Haro, Jaume; Amorós, Jaume
2014-08-01
The CMB map provided by the Planck project constrains the value of the ratio of tensor-to-scalar perturbations, namely r, to be smaller than 0.11 (95 % CL). This bound rules out the simplest models of inflation. However, recent data from BICEP2 is in strong tension with this constrain, as it finds a value r=0.20+0.07-0.05 with 0r= disfavored at 7.0 σ, which allows these simplest inflationary models to survive. The remarkable fact is that, even though the BICEP2 experiment was conceived to search for evidence of inflation, its experimental data matches correctly theoretical results coming from the matter bounce scenario (the alternative model to the inflationary paradigm). More precisely, most bouncing cosmologies do not pass Planck's constrains due to the smallness of the value of the tensor/scalar ratio r<= 0.11, but with new BICEP2 data some of them fit well with experimental data. This is the case with the matter bounce scenario in the teleparallel version of Loop Quantum Cosmology.
Logarithmic corrected polynomial f(R) inflation mimicking a cosmological constant
NASA Astrophysics Data System (ADS)
Sadeghi, J.; Pourhassan, B.; Kubeka, A. S.; Rostami, M.
2016-05-01
In this paper, we consider an inflationary model of f(R) gravity with polynomial form plus logarithmic term. We calculate some cosmological parameters and compare our results with the Planck 2015 data. We find that presence of both logarithmic and polynomial corrections is necessary to yield slow-roll condition. Also, we study critical points and stability of the model to find that it is a viable model.
NASA Astrophysics Data System (ADS)
Chakraborty, Shuvendu; Debnath, Ujjal; Jamil, Mubasher; Myrzakulov, Ratbay
2012-07-01
In this work, we have calculated the deceleration parameter, statefinder parameters and EoS parameters for different dark energy models with variable G correction in homogeneous, isotropic and non-flat universe for Kaluza-Klein Cosmology. The statefinder parameters have been obtained in terms of some observable parameters like dimensionless density parameter, EoS parameter and Hubble parameter for holographic dark energy, new agegraphic dark energy and generalized Chaplygin gas models.
Teleparallel loop quantum cosmology in a system of intersecting branes
NASA Astrophysics Data System (ADS)
Sepehri, Alireza; Pradhan, Anirudh; Beesham, Aroonkumar; de Haro, Jaume
2016-09-01
Recently, some authors have removed the big bang singularity in teleparallel Loop Quantum Cosmology (LQC) and have shown that the universe may undergo a number of oscillations. We investigate the origin of this type of teleparallel theory in a system of intersecting branes in M-theory in which the angle between them changes with time. This system is constructed by two intersecting anti-D8-branes, one compacted D4-brane and a D3-brane. These branes are built by joining M0-branes which develop in decaying fundamental strings. The compacted D4-brane is located between two intersecting anti-D8 branes and glues to one of them. Our universe is located on the D3 brane which wraps around the D4 brane from one end and sticks to one of the anti-D8 branes from the other one. In this system, there are three types of fields, corresponding to compacted D4 branes, intersecting branes and D3-branes. These fields interact with each other and make the angle between branes oscillate. By decreasing this angle, the intersecting anti-D8 branes approach each other, the D4 brane rolls, the D3 brane wraps around the D4 brane, and the universe contracts. By separating the intersecting branes and increasing the angle, the D4 brane rolls in the opposite direction, the D3 brane separates from it and the expansion branch begins. Also, the interaction between branes in this system gives us the exact form of the relevant Lagrangian for teleparallel LQC.
Classical and Quantum Wormholes in a Flat Λ-Decaying Cosmology
NASA Astrophysics Data System (ADS)
Darabi, F.
2009-04-01
We study the classical and quantum wormholes for a flat Euclidean Friedmann-Robertson-Walker metric with a perfect fluid including an ordinary matter source plus a source playing the role of dark energy (decaying cosmological term). It is shown that classical wormholes exist for this model and the quantum version of such wormholes are consistent with the Hawking-Page conjecture for quantum wormholes as solutions of the Wheeler-DeWitt equation.
Entanglement and Quantum Error Correction with Superconducting Qubits
NASA Astrophysics Data System (ADS)
Reed, Matthew
2015-03-01
Quantum information science seeks to take advantage of the properties of quantum mechanics to manipulate information in ways that are not otherwise possible. Quantum computation, for example, promises to solve certain problems in days that would take a conventional supercomputer the age of the universe to decipher. This power does not come without a cost however, as quantum bits are inherently more susceptible to errors than their classical counterparts. Fortunately, it is possible to redundantly encode information in several entangled qubits, making it robust to decoherence and control imprecision with quantum error correction. I studied one possible physical implementation for quantum computing, employing the ground and first excited quantum states of a superconducting electrical circuit as a quantum bit. These ``transmon'' qubits are dispersively coupled to a superconducting resonator used for readout, control, and qubit-qubit coupling in the cavity quantum electrodynamics (cQED) architecture. In this talk I will give an general introduction to quantum computation and the superconducting technology that seeks to achieve it before explaining some of the specific results reported in my thesis. One major component is that of the first realization of three-qubit quantum error correction in a solid state device, where we encode one logical quantum bit in three entangled physical qubits and detect and correct phase- or bit-flip errors using a three-qubit Toffoli gate. My thesis is available at arXiv:1311.6759.
NP-hardness of decoding quantum error-correction codes
Hsieh, Min-Hsiu; Le Gall, Francois
2011-05-15
Although the theory of quantum error correction is intimately related to classical coding theory and, in particular, one can construct quantum error-correction codes (QECCs) from classical codes with the dual-containing property, this does not necessarily imply that the computational complexity of decoding QECCs is the same as their classical counterparts. Instead, decoding QECCs can be very much different from decoding classical codes due to the degeneracy property. Intuitively, one expects degeneracy would simplify the decoding since two different errors might not and need not be distinguished in order to correct them. However, we show that general quantum decoding problem is NP-hard regardless of the quantum codes being degenerate or nondegenerate. This finding implies that no considerably fast decoding algorithm exists for the general quantum decoding problems and suggests the existence of a quantum cryptosystem based on the hardness of decoding QECCs.
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.
Quantum Newtonian cosmology and the biconfluent Heun functions
Vieira, H. S.; Bezerra, V. B.
2015-09-15
We obtain the exact solution of the Schrödinger equation for a particle (galaxy) moving in a Newtonian universe with a cosmological constant, which is given in terms of the biconfluent Heun functions. The first six Heun polynomials of the biconfluent function are written explicitly. The energy spectrum which resembles the one corresponding to the isotropic harmonic oscillator is also obtained. The wave functions as well as the energy levels codify the role played by the cosmological constant.
Nuclear Quantum Gravitation - The Correct Theory
NASA Astrophysics Data System (ADS)
Kotas, Ronald
2016-03-01
Nuclear Quantum Gravitation provides a clear, definitive Scientific explanation of Gravity and Gravitation. It is harmonious with Newtonian and Quantum Mechanics, and with distinct Scientific Logic. Nuclear Quantum Gravitation has 10 certain, Scientific proofs and 21 more good indications. With this theory the Physical Forces are obviously Unified. See: OBSCURANTISM ON EINSTEIN GRAVITATION? http://www.santilli- Foundation.org/inconsistencies-gravitation.php and Einstein's Theory of Relativity versus Classical Mechanics http://www.newtonphysics.on.ca/einstein/
Stochastic background of relic gravitons in a bouncing quantum cosmological model
Bessada, Dennis; Pinto-Neto, Nelson; Siffert, Beatriz B.; Miranda, Oswaldo D. E-mail: beatriz@if.ufrj.br E-mail: oswaldo@das.inpe.br
2012-11-01
The spectrum and amplitude of the stochastic background of relic gravitons produced in a bouncing universe is calculated. The matter content of the model consists of dust and radiation fluids, and the bounce occurs due to quantum cosmological effects when the universe approaches the classical singularity in the contracting phase. The resulting amplitude is very small and it cannot be observed by any present and near future gravitational wave detector. Hence, as in the ekpyrotic model, any observation of these relic gravitons will rule out this type of quantum cosmological bouncing model.
Universe’s memory and spontaneous coherence in loop quantum cosmology
NASA Astrophysics Data System (ADS)
Pawłowski, Tomasz
2016-07-01
The quantum bounce a priori connects several (semi)classical epochs of universe evolution, however determining if and how well the semiclassicality is preserved in this transition is highly nontrivial. We review the present state of knowledge in that regards in the isotropic sector of loop quantum cosmology (LQC). This knowledge is next extended by studies of an isotropic universe admitting positive cosmological constant (featuring an infinite chain of large universe epochs). It is also shown, that such universe always admits a semiclassical epoch thanks to spontaneous coherence, provided it is semiclassical in certain constant of motion playing the role of energy.
NASA Astrophysics Data System (ADS)
Umeh, Obinna; Clarkson, Chris; Maartens, Roy
2014-10-01
The next generation of telescopes will usher in an era of precision cosmology, capable of determining the cosmological model to beyond the percent level. For this to be effective, the theoretical model must be understood to at least the same level of precision. A range of subtle relativistic effects remain to be explored theoretically, and offer the potential for probing general relativity in this new regime. We present the distance-redshift relation to second order in cosmological perturbation theory for a general dark energy model. This relation determines the magnification of sources at high precision, as well as redshift space distortions in the mildly non-linear regime. We identify a range of new lensing effects, including: double-integrated and nonlinear-integrated Sachs-Wolfe contributions, transverse Doppler effects, lensing from the induced vector mode and gravitational wave backgrounds, in addition to lensing from the second-order potential. Modifications to Doppler lensing from redshift space distortions are identified. Finally, we find a new double-coupling between the density fluctuations integrated along the line of sight, and gradients in the density fluctuations coupled to transverse velocities along the line of sight. These can be large and thus offer important new probes of gravitational lensing and general relativity. This paper accompanies paper II (Umeh, Clarkson and Maartens 2014 Class. Quantum Grav. 31 205001) , where a comprehensive derivation is given.
Emergence of the product of constant curvature spaces in loop quantum cosmology
NASA Astrophysics Data System (ADS)
Dadhich, Naresh; Joe, Anton; Singh, Parampreet
2015-09-01
The loop quantum dynamics of Kantowski-Sachs spacetime and the interior of higher genus black hole spacetimes with a cosmological constant has some peculiar features not shared by various other spacetimes in loop quantum cosmology. As in the other cases, though the quantum geometric effects resolve the physical singularity and result in a non-singular bounce, after the bounce a spacetime with small spacetime curvature does not emerge in either the subsequent backward or the forward evolution. Rather, in the asymptotic limit the spacetime manifold is a product of two constant curvature spaces. Interestingly, though the spacetime curvature of these asymptotic spacetimes is very high, their effective metric is a solution to Einstein’s field equations. Analysis of the components of the Ricci tensor shows that after the singularity resolution, the Kantowski-Sachs spacetime leads to an effective metric which can be interpreted as the ‘charged’ Nariai, while the higher genus black hole interior can similarly be interpreted as an anti Bertotti-Robinson spacetime with a cosmological constant. These spacetimes are ‘charged’ in the sense that the energy-momentum tensor that satisfies Einstein’s field equations is formally the same as the one for the uniform electromagnetic field, albeit it has a purely quantum geometric origin. The asymptotic spacetimes also have an emergent cosmological constant which is different in magnitude, and sometimes even its sign, from the cosmological constant in the Kantowski-Sachs and the interior of higher genus black hole metrics. With a fine tuning of the latter cosmological constant, we show that ‘uncharged’ Nariai, and anti Bertotti-Robinson spacetimes with a vanishing emergent cosmological constant can also be obtained.
NASA Astrophysics Data System (ADS)
Paranjape, Aseem; Singh, T. P.
2007-08-01
It is known that any explicit averaging scheme of the type essential for describing the large scale behavior of the Universe must necessarily yield corrections to the Einstein equations applied in the cosmological setting. The question of whether or not the resulting corrections to the Einstein equations are significant is still a subject of debate, partly due to possible ambiguities in the averaging schemes available. In particular, it has been argued in the literature that the effects of averaging could be gauge artifacts. We apply the formalism of Zalaletdinov’s macroscopic gravity (MG), which is a fully covariant and nonperturbative averaging scheme, in an attempt to construct gauge independent corrections to the standard Friedmann-Lemaître-Robertson-Walker (FLRW) equations. We find that whereas one cannot escape the problem of dependence on one gauge choice—which is inherent in the assumption of large scale homogeneity and isotropy—it is however possible to construct space-time scalar corrections to the standard FLRW equations. This partially removes the criticism concerning the corrections being gauge artifacts. For a particular initial choice of gauge which simplifies the formalism, we explicitly construct these scalars in terms of the underlying inhomogeneous geometry, and incidentally demonstrate that the formal structure of the corrections with this gauge choice is identical to that of analogous corrections derived by Buchert in the context of spatial averaging of scalars.
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.
Less Interpretation and More Decoherence in Quantum Gravity and Inflationary Cosmology
NASA Astrophysics Data System (ADS)
Crull, Elise M.
2015-09-01
I argue that quantum decoherence—understood as a dynamical process entailed by the standard formalism alone—carries us beyond conceptual aspects of non-relativistic quantum mechanics deemed insurmountable by many contributors to the recent quantum gravity and cosmology literature. These aspects include various incarnations of the measurement problem and of the quantum-to-classical puzzle. Not only can such problems be largely bypassed or dissolved without default to a particular interpretation, but theoretical work in relativistic arenas stands to gain substantial physical and philosophical insight by incorporating decoherence phenomena.
Single-Shot Fault-Tolerant Quantum Error Correction
NASA Astrophysics Data System (ADS)
Bombín, Héctor
2015-07-01
Conventional quantum error correcting codes require multiple rounds of measurements to detect errors with enough confidence in fault-tolerant scenarios. Here, I show that for suitable topological codes, a single round of local measurements is enough. This feature is generic and is related to self-correction and confinement phenomena in the corresponding quantum Hamiltonian model. Three-dimensional gauge color codes exhibit this single-shot feature, which also applies to initialization and gauge fixing. Assuming the time for efficient classical computations to be negligible, this yields a topological fault-tolerant quantum computing scheme where all elementary logical operations can be performed in constant time.
Inequivalence of unitarity and self-adjointness: An example in quantum cosmology
Lemos, N.A. )
1990-02-15
An example of a quantum cosmological model is presented whose dynamics is unitary although the time-dependent Hamiltonian operator fails to be self-adjoint (because it is not defined) for a particular value of {ital t}. The model is shown to be singular, and this disproves a conjecture put forward by Gotay and Demaret to the effect that unitary quantum dynamics in a slow-time'' gauge is always nonsingular.
Quantum error correction assisted by two-way noisy communication
Wang, Zhuo; Yu, Sixia; Fan, Heng; Oh, C. H.
2014-01-01
Pre-shared non-local entanglement dramatically simplifies and improves the performance of quantum error correction via entanglement-assisted quantum error-correcting codes (EAQECCs). However, even considering the noise in quantum communication only, the non-local sharing of a perfectly entangled pair is technically impossible unless additional resources are consumed, such as entanglement distillation, which actually compromises the efficiency of the codes. Here we propose an error-correcting protocol assisted by two-way noisy communication that is more easily realisable: all quantum communication is subjected to general noise and all entanglement is created locally without additional resources consumed. In our protocol the pre-shared noisy entangled pairs are purified simultaneously by the decoding process. For demonstration, we first present an easier implementation of the well-known EAQECC [[4, 1, 3; 1
Quantum error correction assisted by two-way noisy communication
NASA Astrophysics Data System (ADS)
Wang, Zhuo; Yu, Sixia; Fan, Heng; Oh, C. H.
2014-11-01
Pre-shared non-local entanglement dramatically simplifies and improves the performance of quantum error correction via entanglement-assisted quantum error-correcting codes (EAQECCs). However, even considering the noise in quantum communication only, the non-local sharing of a perfectly entangled pair is technically impossible unless additional resources are consumed, such as entanglement distillation, which actually compromises the efficiency of the codes. Here we propose an error-correcting protocol assisted by two-way noisy communication that is more easily realisable: all quantum communication is subjected to general noise and all entanglement is created locally without additional resources consumed. In our protocol the pre-shared noisy entangled pairs are purified simultaneously by the decoding process. For demonstration, we first present an easier implementation of the well-known EAQECC [[4, 1, 3; 1
Quantum error correction assisted by two-way noisy communication.
Wang, Zhuo; Yu, Sixia; Fan, Heng; Oh, C H
2014-01-01
Pre-shared non-local entanglement dramatically simplifies and improves the performance of quantum error correction via entanglement-assisted quantum error-correcting codes (EAQECCs). However, even considering the noise in quantum communication only, the non-local sharing of a perfectly entangled pair is technically impossible unless additional resources are consumed, such as entanglement distillation, which actually compromises the efficiency of the codes. Here we propose an error-correcting protocol assisted by two-way noisy communication that is more easily realisable: all quantum communication is subjected to general noise and all entanglement is created locally without additional resources consumed. In our protocol the pre-shared noisy entangled pairs are purified simultaneously by the decoding process. For demonstration, we first present an easier implementation of the well-known EAQECC [[4, 1, 3; 1
Quantum corrections during inflation and conservation of adiabatic perturbations
Campo, David
2010-02-15
The possibility that quantum corrections break the conservation of superhorizon adiabatic perturbations in single field inflation is examined. I consider the lowest order corrections from massless matter fields in the Hamiltonian formalism. Particular emphasis is therefore laid on the renormalization. The counterterms are the same as in the Lagrangian formalism. The renormalized value of the tadpole is zero. I find a possible secular dependence of the power spectrum at one loop due to the trace anomaly, but this result depends on the approximation of the modes and is inconclusive. The symmetry (not) violated by the quantum corrections is the invariance by dilatation. Perspectives on the backreaction problem are briefly discussed.
Quantum Gravity Corrections to the Tunneling Radiation of Scalar Particles
NASA Astrophysics Data System (ADS)
Wang, Peng; Yang, Haitang; Ying, Shuxuan
2016-05-01
The original derivation of Hawking radiation shows the complete evaporation of black holes. However, theories of quantum gravity predict the existence of the minimal observable length. In this paper, we investigate the tunneling radiation of the scalar particles by introducing the quantum gravity effects influenced by the generalized uncertainty principle. The Hawking temperatures are not only determined by the properties of the black holes, but also affected by the quantum numbers of the emitted particles. The quantum gravity corrections slow down the increase of the temperatures. The remnants are found during the evaporation.
Serialized Quantum Error Correction Protocol for High-Bandwidth Quantum Repeaters
NASA Astrophysics Data System (ADS)
Glaudell, Andrew; Waks, Edo; Taylor, Jacob
Advances in single-photon creation, transmission, and detection suggest that sending quantum information over optical fibers may have low enough losses to be overcome using quantum error correction. Such error-corrected communication is equivalent to a novel quantum repeater scheme, but crucial questions regarding implementation and system requirements remain open. In this talk, I will show that long-range entangled bit generation with rates approaching 108 entangled bits per second may be possible using a completely serialized protocol, in which photons are generated, entangled, and error corrected via sequential, one-way interactions with as few matter qubits as possible. Provided loss and error rates of the required elements are below the threshold for quantum error correction, this scheme demonstrates improved performance over transmission of single photons. We find improvement in entangled bit rates at large distances using this serial protocol and various quantum error correcting codes.
NASA Astrophysics Data System (ADS)
Lucky Chang, Wen-Hsuan; Proty Wu, Jiun-Huei
2016-06-01
We aim to use the observations of B-mode polarization in the Cosmic Microwave Background (CMB) to probe the ‘parent universe’ under the context of Loop Quantum Cosmology (LQC). In particular, we investigate the possibility for the gravitational waves (GW) such as those from the stellar binary systems in the parent universe to survive the big bounce and thus to be still observable today. Our study is based on the background dynamics with the zeroth-order holonomy correction using the Arnowitt-Deser-Misner (ADM) formalism. We propose a new framework in which transfer functions are invoked to bring the GWs in the parent universe through the big bounce, inflation, and big bang to reach today. This transparent and intuitive formalism allows us to accurately discuss the influence of the GWs from the parent universe on the B-mode polarization in the CMB today under backgrounds of different LQC parameters. These features can soon be tested by the forth-coming CMB observations and we note that the LQC backgrounds with symmetric bouncing scenarios are ruled out by the latest observational results from Planck and BICEP2/Keck experiments.
Correctable noise of quantum-error-correcting codes under adaptive concatenation
NASA Astrophysics Data System (ADS)
Fern, Jesse
2008-01-01
We examine the transformation of noise under a quantum-error-correcting code (QECC) concatenated repeatedly with itself, by analyzing the effects of a quantum channel after each level of concatenation using recovery operators that are optimally adapted to use error syndrome information from the previous levels of the code. We use the Shannon entropy of these channels to estimate the thresholds of correctable noise for QECCs and find considerable improvements under this adaptive concatenation. Similar methods could be used to increase quantum-fault-tolerant thresholds.
Quantum corrections to nonlinear ion acoustic wave with Landau damping
Mukherjee, Abhik; Janaki, M. S.; Bose, Anirban
2014-07-15
Quantum corrections to nonlinear ion acoustic wave with Landau damping have been computed using Wigner equation approach. The dynamical equation governing the time development of nonlinear ion acoustic wave with semiclassical quantum corrections is shown to have the form of higher KdV equation which has higher order nonlinear terms coming from quantum corrections, with the usual classical and quantum corrected Landau damping integral terms. The conservation of total number of ions is shown from the evolution equation. The decay rate of KdV solitary wave amplitude due to the presence of Landau damping terms has been calculated assuming the Landau damping parameter α{sub 1}=√(m{sub e}/m{sub i}) to be of the same order of the quantum parameter Q=ℏ{sup 2}/(24m{sup 2}c{sub s}{sup 2}L{sup 2}). The amplitude is shown to decay very slowly with time as determined by the quantum factor Q.
Quantum Bohm correction to polarization spectrum of graphene
Akbari-Moghanjoughi, M.
2013-10-15
In this paper, by using a quantum hydrodynamic plasma model which incorporates the important quantum statistical pressure and electron diffraction force, we present the corrected plasmon dispersion relation for graphene which includes a k{sup 4} quantum term arising from the collective electron density wave interference effects. This correction may well describe the shortcoming of the previous results based on the classical hydrodynamics and confirms that the quantum hydrodynamic model may be as effective as the random phase approximation in successful description of the collective density excitations in quantum plasmas. It is clearly observed that the quantum correction due to the collective interaction of electron waves gives rise to significant contribution in the dispersion behavior of the collective plasmon density waves in a wide range of wavelength, as a fundamental property of the monolayer atom-thick graphene. It is revealed that the plasmon density-perturbation linear phase-speed in graphene possesses some universal minimum characteristic value, in the absence of an external magnetic field. It is further remarked that such correction also has important effect on the dielectric function, hence on the impurity screening, in graphene.
Quantization ambiguities and bounds on geometric scalars in anisotropic loop quantum cosmology
NASA Astrophysics Data System (ADS)
Singh, Parampreet; Wilson-Ewing, Edward
2014-02-01
We study quantization ambiguities in loop quantum cosmology that arise for space-times with non-zero spatial curvature and anisotropies. Motivated by lessons from different possible loop quantizations of the closed Friedmann-Lemaître-Robertson-Walker cosmology, we find that using open holonomies of the extrinsic curvature, which due to gauge-fixing can be treated as a connection, leads to the same quantum geometry effects that are found in spatially flat cosmologies. More specifically, in contrast to the quantization based on open holonomies of the Ashtekar-Barbero connection, the expansion and shear scalars in the effective theories of the Bianchi type II and Bianchi type IX models have upper bounds, and these are in exact agreement with the bounds found in the effective theories of the Friedmann-Lemaître-Robertson-Walker and Bianchi type I models in loop quantum cosmology. We also comment on some ambiguities present in the definition of inverse triad operators and their role.
Quantum gravity stability of isotropy in homogeneous cosmology
NASA Astrophysics Data System (ADS)
Broda, Bogusław
2011-10-01
It has been shown that anisotropy of homogeneous spacetime described by the general Kasner metric can be damped by quantum fluctuations coming from perturbative quantum gravity in one-loop approximation. Also, a formal argument, not limited to one-loop approximation, is put forward in favor of stability of isotropy in the exactly isotropic case.
Quantum error-correcting codes over mixed alphabets
NASA Astrophysics Data System (ADS)
Wang, Zhuo; Yu, Sixia; Fan, Heng; Oh, C. H.
2013-08-01
We study the quantum error-correcting codes over mixed alphabets to deal with a more complicated and practical situation in which the physical systems for encoding may have different numbers of energy levels. In particular we investigate their constructions and propose the theory of quantum Singleton bound. Two kinds of code constructions are presented: a projection-based construction for general case and a graphical construction based on a graph-theoretical object composite coding clique dealing with the case of reducible alphabets. We find out some optimal one-error correcting or detecting codes over two alphabets. Our method of composite coding clique also sheds light on constructing standard quantum error-correcting codes, and other families of optimal codes are found.
Ground state of the universe in quantum cosmology
NASA Astrophysics Data System (ADS)
Gorobey, Natalia; Lukyanenko, Alexander
2016-01-01
We find a physical state of a closed universe with the minimal excitation of the universe expansion energy in quantum gravity. It is an analog of the vacuum state of the ordinary quantum field theory in the Minkowsky space, but in our approach an energy of space of a closed universe together with the energy of its matter content are minimized. This ground state is chosen among an enlarged set of physical states, compared with the ordinary covariant quantum gravity. In our approach, physical states are determined by weak constraints: quantum mechanical averages of gravitational constraint operators equal zero. As a result, they appear to be non-static in such a modification of quantum gravity. Quantum dynamics of the universe is described by Schrödinger equation with a cosmic time determined by weak gravitational constraints. In order to obtain the observed megascopic universe with the inflation stage just after its quantum beginning, a lot of the energy in the form of the inflaton scalar field condensate is prescribed to the initial state. Parameters of the initial state for a homogeneous model of the universe are calculated.
Effect of Quantum Correction in the Bose-Hubbard Model
Matsumoto, Hideki; Takahashi, Kiyoshi; Ohashi, Yoji
2006-09-07
Effects of quantum correction in the Bose-Hubbard model at finite temperature are investigated for a homogeneous atomic Bose gas in an optical lattice near its superfluid-insulator transition. Starting from a strong coupling limit, higher order quantum corrections due to the hopping interaction is included in a local approximation (a dynamical mean field approximation) of the non-crossing approximation. When the upper or lower Hubbard band approaches zero energy, there appears a shallow band in the middle of the Hubbard gap due to a strong correlation in the system.
Quantum error correcting codes and 4-dimensional arithmetic hyperbolic manifolds
Guth, Larry; Lubotzky, Alexander
2014-08-15
Using 4-dimensional arithmetic hyperbolic manifolds, we construct some new homological quantum error correcting codes. They are low density parity check codes with linear rate and distance n{sup ε}. Their rate is evaluated via Euler characteristic arguments and their distance using Z{sub 2}-systolic geometry. This construction answers a question of Zémor [“On Cayley graphs, surface codes, and the limits of homological coding for quantum error correction,” in Proceedings of Second International Workshop on Coding and Cryptology (IWCC), Lecture Notes in Computer Science Vol. 5557 (2009), pp. 259–273], who asked whether homological codes with such parameters could exist at all.
Quantum error correcting codes and 4-dimensional arithmetic hyperbolic manifolds
NASA Astrophysics Data System (ADS)
Guth, Larry; Lubotzky, Alexander
2014-08-01
Using 4-dimensional arithmetic hyperbolic manifolds, we construct some new homological quantum error correcting codes. They are low density parity check codes with linear rate and distance nɛ. Their rate is evaluated via Euler characteristic arguments and their distance using {Z}_2-systolic geometry. This construction answers a question of Zémor ["On Cayley graphs, surface codes, and the limits of homological coding for quantum error correction," in Proceedings of Second International Workshop on Coding and Cryptology (IWCC),
Quantum error correction for state transfer in noisy spin chains
NASA Astrophysics Data System (ADS)
Kay, Alastair
2016-04-01
Can robustness against experimental imperfections and noise be embedded into a quantum simulation? In this paper, we report on a special case in which this is possible. A spin chain can be engineered such that, in the absence of imperfections and noise, an unknown quantum state is transported from one end of the chain to the other, due only to the intrinsic dynamics of the system. We show that an encoding into a standard error-correcting code (a Calderbank-Shor-Steane code) can be embedded into this simulation task such that a modified error-correction procedure on readout can recover from sufficiently low rates of noise during transport.
New class of photonic quantum error correction codes
NASA Astrophysics Data System (ADS)
Silveri, Matti; Michael, Marios; Brierley, R. T.; Salmilehto, Juha; Albert, Victor V.; Jiang, Liang; Girvin, S. M.
We present a new class of quantum error correction codes for applications in quantum memories, communication and scalable computation. These codes are constructed from a finite superposition of Fock states and can exactly correct errors that are polynomial up to a specified degree in creation and destruction operators. Equivalently, they can perform approximate quantum error correction to any given order in time step for the continuous-time dissipative evolution under these errors. The codes are related to two-mode photonic codes but offer the advantage of requiring only a single photon mode to correct loss (amplitude damping), as well as the ability to correct other errors, e.g. dephasing. Our codes are also similar in spirit to photonic ''cat codes'' but have several advantages including smaller mean occupation number and exact rather than approximate orthogonality of the code words. We analyze how the rate of uncorrectable errors scales with the code complexity and discuss the unitary control for the recovery process. These codes are realizable with current superconducting qubit technology and can increase the fidelity of photonic quantum communication and memories.
Classical and quantum dynamics of a perfect fluid scalar-metric cosmology
NASA Astrophysics Data System (ADS)
Vakili, Babak
2010-05-01
We study the classical and quantum models of a Friedmann-Robertson-Walker (FRW) cosmology, coupled to a perfect fluid, in the context of the scalar-metric gravity. Using the Schutz' representation for the perfect fluid, we show that, under a particular gauge choice, it may lead to the identification of a time parameter for the corresponding dynamical system. It is shown that the evolution of the universe based on the classical cosmology represents a late time power law expansion coming from a big-bang singularity in which the scale factor goes to zero while the scalar field blows up. Moreover, this formalism gives rise to a Schrödinger-Wheeler-DeWitt (SWD) equation for the quantum-mechanical description of the model under consideration, the eigenfunctions of which can be used to construct the wave function of the universe. We use the resulting wave function in order to investigate the possibility of the avoidance of classical singularities due to quantum effects by means of the many-worlds and ontological interpretation of quantum cosmology.
Non-singular bounce scenarios in loop quantum cosmology and the effective field description
Cai, Yi-Fu; Wilson-Ewing, Edward E-mail: wilson-ewing@phys.lsu.edu
2014-03-01
A non-singular bouncing cosmology is generically obtained in loop quantum cosmology due to non-perturbative quantum gravity effects. A similar picture can be achieved in standard general relativity in the presence of a scalar field with a non-standard kinetic term such that at high energy densities the field evolves into a ghost condensate and causes a non-singular bounce. During the bouncing phase, the perturbations can be stabilized by introducing a Horndeski operator. Taking the matter content to be a dust field and an ekpyrotic scalar field, we compare the dynamics in loop quantum cosmology and in a non-singular bouncing effective field model with a non-standard kinetic term at both the background and perturbative levels. We find that these two settings share many important properties, including the result that they both generate scale-invariant scalar perturbations. This shows that some quantum gravity effects of the very early universe may be mimicked by effective field models.
Cosmological matter-antimatter asymmetry as a quantum fluctuation
NASA Astrophysics Data System (ADS)
Kobakhidze, Archil; Manning, Adrian
2015-06-01
We entertain a new paradigm according to which the observed matter-antimatter asymmetry is generated as a large-scale quantum fluctuation over the baryon-symmetric state that occurred during the cosmic inflation.
Creation of particles in a cyclic universe driven by loop quantum cosmology
NASA Astrophysics Data System (ADS)
Tavakoli, Yaser; Fabris, Júlio C.
2015-05-01
We consider an isotropic and homogeneous universe in loop quantum cosmology (LQC). We assume that the matter content of the universe is dominated by dust matter in early time and a phantom matter at late time which constitutes the dark energy component. The quantum gravity modifications to the Friedmann equation in this model indicate that the classical big bang singularity and the future big rip singularity are resolved and are replaced by quantum bounce. It turns out that the big bounce and recollapse in the herein model contribute to a cyclic scenario for the universe. We then study the quantum theory of a massive, nonminimally coupled scalar field undergoing cosmological evolution from primordial bounce towards the late time bounce. In particular, we solve the Klein-Gordon equation for the scalar field in the primordial and late time regions, in order to investigate particle production phenomena at late time. By computing the energy density of created particles at late time, we show that this density is negligible in comparison to the quantum background density at Planck era. This indicates that the effects of quantum particle production do not influence the future bounce.
Vergeles, S. N.
2008-01-15
The problem of the doubling of states is investigated in the framework of the theory of discrete quantum gravity under the assumption that the theory has a continuum (macroscopic) limit. It is demonstrated that irregular (in some sense) modes of fields (i.e., modes that change abruptly on scales of a lattice step and have a finite energy when the lattice step tends to zero) are separated from the normal modes. Some cosmological consequences of this finding are discussed.
Bond additivity corrections for quantum chemistry methods
Melius, C.F.; Allendorf, M.D.
2000-03-23
New bond additivity correction (BAC) methods have been developed for the G2 method, BAC-G2, as well as for a hybrid density functional theory (DFT) Moller-Plesset (MP)2 method, BAC-hybrid. These BAC methods use a new form of BAC corrections, involving atomic, molecular, and bond-wise additive terms. These terms enable one to treat positive and negative ions as well as neutrals. The BAC-G2 method reduces errors in the G2 method due to nearest-neighbor bonds. The parameters within the BAC-G2 method only depend on atom types. Thus the BAC-G2 method can be used to determine the parameters needed by BAC methods involving lower levels of theory, such as BAC-hybrid and BAC-MP4. The BAC-hybrid method is expected to scale well for large molecules. The BAC-hybrid method uses the differences between the DFT and MP2 predictions as an indication of the method's accuracy, whereas the BAC-G2 method uses its internal methods (G1 and G2MP2) to accomplish this. A statistical analysis of the error in each of the methods is presented on the basis of calculations performed for large sets (more than 120) of molecules.