Quantum Cosmological Model Research Articles

Reply to “Comment on ‘Quantization of Friedmann-Robertson-Walker spacetimes in the presence of a negative cosmological constant and radiation”’

The previous Comment contains a valid criticism of the numerical precision of the results reported in a recent paper of ours, as well as fresh ideas on how to characterize a quantum cosmological singularity. However, we argue that, contrary to what is suggested in the Comment, the quantum cosmological models we studied show hardly any sign of singular behavior.

Die präsentistische Auffassung der Zeit im Kontext der Relativitätstheorien und der Quantenkosmologie von James Hartle und Stephen Hawking: Ein Vergleich (Teil II) Präsentismus und Quantenkosmologie

This article explores the compatibility of a presentistic account of time with both the theories of relativity and the quantum cosmology of James Hartle and Stephen Hawking. The aim of this article is to show that while it is still possible to try a defence of presentism in the relativistic frame, the defence of such a position jointly with the quantum cosmological model of Hartle and Hawking is untenable. The article is divided in two parts. The aim of this second part is twofold: first to summarize the main features of the quantum cosmological model of Hartle and Hawking, and second to show that the strategies to make the presentistic account of time compatible with the theories of the relativitiy do not work in the context of this quantum cosmological model. The possible consequences of the incompatibility of presentism with quantum cosmology are outlined.

Does the Big Rip survive quantization?

It is known that certain quantum cosmological models present quantum behavior for large scale factors. Since quantization can suppress past singularities, it is natural to inquire whether quantum effects can prevent future singularities. To this end, a Friedmann–Robertson–Walker quantum cosmological model dominated by a phantom energy fluid is investigated. The classical model displays accelerated expansion ending in a Big Rip. The quantization is performed in three different ways, which turn out to lead to the same result, namely there is a possibility that quantum gravitational effects could not remove the Big Rip.

Topological string in harmonic space and correlation functions in [formula omitted] stringy cosmology

We develop the harmonic space method for conifold and use it to study local complex deformations of T * S 3 preserving manifestly SL ( 2 , C ) isometry. We derive the perturbative manifestly SL ( 2 , C ) invariant partition function Z top of topological string B model on locally deformed conifold. Generic n momentum and winding modes of 2D c = 1 noncritical theory are described by highest υ ( n , 0 ) and lowest components υ ( 0 , n ) of SL ( 2 , C ) spin s = n 2 multiplets ( υ ( n − k , k ) ) , 0 ⩽ k ⩽ n and are shown to be naturally captured by harmonic monomials. Isodoublets ( n = 1 ) describe uncoupled units of momentum and winding modes and are exactly realized as the SL ( 2 , C ) harmonic variables U α + and V α − . We also derive a dictionary giving the passage from Laurent (Fourier) analysis on T * S 1 ( S 1 ) to the harmonic method on T * S 3 ( S 3 ). The manifestly SU ( 2 , C ) covariant correlation functions of the S 3 quantum cosmology model of Gukov–Saraikin–Vafa are also studied.

Perturbative degrees of freedom in loop quantum gravity: anisotropies

The relation between an isotropic model and an anisotropic model in loop quantum cosmology is discussed in detail, comparing the strict symmetry reduction with a perturbative implementation of symmetry. While the latter cannot be done in a canonical manner, it allows one to consider the dynamics including the role of small non-symmetric degrees of freedom for the symmetric evolution. This serves as a model for the general situation of perturbative degrees of freedom in a background-independent quantization such as loop quantum gravity, and for the more complicated addition of perturbative inhomogeneities. While being crucial for cosmological phenomenology, it is shown that perturbative non-symmetric degrees of freedom do not allow definitive conclusions for the singularity issue and in such a situation could even lead to wrong claims.

Tomography of quantum states of the universe and cosmological dynamics

It has been proven that conventional quantum mechanics can be reformulated without using the concept of wave function or matrix density. Quantum states can be described in terms of a standard positive probability distribution. Such probability distributions (tomograms) satisfy classical-like equations, which substitute the Schrödinger equation. We consider quantum cosmology in the probability distribution approach. We derive the tomogram corresponding to theWheeler-de Witt equation. We also use the circumstance that cosmological evolution equations for a homogeneous and isotropic universe can be converted into very simple classical equations to derive a quantum cosmological model which links the tomogram reconstructed from observations to the initial conditions of the universe.

Hamiltonian formulation of curvature squared action

It has been observed earlier that, in principle, it is possible to obtain a quantum mechanical interpretation of higher order quantum cosmological models in the spatially homogeneous and isotropic background, if auxiliary variable required for the Hamiltonian formulation of the theory is chosen properly. It was suggested that for such a choice, it is required to get rid of all the total derivative terms from the action containing higher order curvature invariant terms, prior to the introduction of auxiliary variable. Here, the earlier work has been modified and it is shown that the action, $A=\beta\int \sqrt{-g} R^2 d^4 x$ should be supplemented by a boundary term in the form $\sigma=4\beta\int ^{3}R K \sqrt{h} d^{3}x$, where, $^3 R$, $K$ and $h$ are the Ricci scalar for three-space, trace of the extrinsic curvature and determinant of the metric on the three space respectively. The result has been tested in the background of homogeneous and anisotropic models and thus confirmed.

On the physical Hilbert space of loop quantum cosmology

In this paper we present a model of Riemannian loop quantum cosmology with a self-adjoint quantum scalar constraint. The physical Hilbert space is constructed using refined algebraic quantization. When matter is included in the form of a cosmological constant, the model is exactly solvable and we show explicitly that the physical Hilbert space is separable, consisting of a single physical state. We extend the model to the Lorentzian sector and discuss important implications for standard loop quantum cosmology.

Mass quantization in quantum and susy cosmological models with matter content

We present the study of the quantum closed Friedmann-Robertson-Walker (FRW) cosmological model with a matter content given by a perfect fluid with barotropic state equation p = γρ The Wheeler-DeWitt equation is viewed as the Schrödinger equation for the linear harmonic oscillator with energy E. Such type of Universe has quantized masses of the order of the Planck mass and harmonic oscillator wave functions. Then, we consider the n = 2 supersymmetric superfield approach for the same model and obtain a normalizable wave function (at zero energy) of the universe. Besides, the mass parameter spectrum is found in the Schrödinger picture, being similar to those obtained by other methods, using a black hole system.

Lorentz Invariance on Trial

Precision experiments and astrophysical observations provide complementary tests of Lorentz invariance and may soon open a window onto new physics. They have already constrained models of quantum gravity and cosmology.

The Bianchi IX model in loop quantum cosmology

The Bianchi IX model has been used often to investigate the structure close to singularities of general relativity. Its classical chaos is expected to have, via the BKL scenario, implications even for the approach to general inhomogeneous singularities. Thus, it is a popular model to test consequences of modifications to general relativity suggested by quantum theories of gravity. This paper presents a detailed proof that modifications coming from loop quantum gravity lead to a non-chaotic effective behaviour. The way this is realized, independently of quantization ambiguities, suggests a new look at initial and final singularities.

Tensorial perturbations in the bulk of inflating brane worlds

In this paper we consider the stability of some inflating brane-world models in quantum cosmology. It is shown that whereas the singular model based on the construction of inflating branes from Euclidean five-dimensional anti-de Sitter space is unstable to tensorial cosmological perturbations in the bulk, the nonsingular model which uses a five-dimensional asymptotically anti-de Sitter wormhole to construct the inflating branes is stable to these perturbations.

The accelerated expansion of the Universe as a quantum cosmological effect

We study the quantized Friedmann–Lemaı̂tre–Robertson–Walker (FLRW) model minimally coupled to a free massless scalar field. In a previous paper, [Phys. Rev. D 62 (2000) 83507], solutions of this model were constructed as Gaussian superpositions of negative and positive modes solutions of the Wheeler–DeWitt equation, and quantum Bohmian trajectories were obtained in the framework of the Bohm–de Broglie (BdB) interpretation of quantum cosmology. In the present Letter, we analyze the quantum Bohmian trajectories of a different class of Gaussian packets. We are able to show that this new class generates Bohmian trajectories which begin classical (with decelerated expansion), undergo an accelerated expansion in the middle of its evolution due to the presence of quantum cosmological effects in this period, and return to its classical decelerated expansion in the far future. We also show that the relation between luminosity distance and redshift in the quantum cosmological model can be made close to the corresponding relation coming from the classical model supplemented by a cosmological constant, for z<1. These results suggest the possibility of interpreting the present observations of high redshift supernovae as the manifestation of a quantum cosmological effect.

A Quantum Cosmological Model with Static and Dynamic Wormholes

Quantization is performed of a Friedmann-Robertson-Walker universe filled with a conformally invariant scalar field and a perfect fluid with equation of state $p=\alpha \rho$. A well-known discrete set of static quantum wormholes is shown to exist for radiation ($\alpha =1/3$), and a novel continuous set is found for cosmic strings ($\alpha = -1/3$), the latter states having throat radii of any size. In both cases wave-packet solutions to the Wheeler-DeWitt equation are obtained with all the properties of evolving quantum wormholes. In the case of a radiation fluid, a detailed analysis of the quantum dynamics is made in the context of the Bohm-de Broglie interpretation. It is shown that a repulsive quantum force inversely proportional to the cube of the scale factor prevents singularities in the quantum domain. For the states considered, there are no particle horizons either.

Pseudo-Hermiticity for a class of nondiagonalizable Hamiltonians

We give two characterization theorems for pseudo-Hermitian (possibly nondiagonalizable) Hamiltonians with a discrete spectrum that admit a block-diagonalization with finite-dimensional diagonal blocks. In particular, we prove that for such an operator H the following statements are equivalent: (1) H is pseudo-Hermitian; (2) the spectrum of H consists of real and/or complex-conjugate pairs of eigenvalues and the geometric multiplicity and the dimension of the diagonal blocks for the complex-conjugate eigenvalues are identical; (3) H is Hermitian with respect to a positive-semidefinite inner product. We further discuss the relevance of our findings for the merging of a complex-conjugate pair of eigenvalues of diagonalizable pseudo-Hermitian Hamiltonians in general, and the PT-symmetric Hamiltonians and the effective Hamiltonian for a certain closed FRW minisuperspace quantum cosmological model in particular.

TIMELESS PROPERTIES FOR QUANTUM COSMOLOGICAL MODELS

Inspired by the central equation of canonical quantum gravity, the timeless Wheeler-DeWitt equation, we investigate timeless properties for quantum cosmological models. In particular we are interested in the following question: What is the probability of the system entering certain regions of its configuration space without reference to time at all? For the classical case this is a property of the entire system trajectories and can be formulated using a phase space probability distribution 1. In the quantum case we propose and investigate a probability which we obtain by adapting the decoherent histories approach to quantum theory 2 to the timeless case and by using the induced inner product on the physical state space of quantum cosmological models 3. For the example of the Klein-Gordon equation we have investigated the case of space–like surfaces and our results agree with the standard operator methods 4. For a more general model we consider a semiclassical approximation as well as the effect of an environment 1. When the histories are decoherent, the probabilities approximately coincide with the classical case, with the phase space probability distribution replaced by the Wigner function of the quantum state. The influence functional of the environment respects the reparametrization invariance of the quantum cosmological Wheeler-DeWitt equation.

QUANTUM PERFECT FLUID COSMOLOGICAL MODEL AND ITS CLASSICAL ANALOGUE

The quantization of gravity coupled to a perfect fluid model leads to a Schrödinger-like equation, where the matter variable plays the role of time. The wave function can be determined, in the flat case, for an arbitrary barotropic equation of state p = α ρ; solutions can also be found for the radiative non-flat case. The wave packets are constructed, from which the expectation value for the scale factor is determined. The quantum scenarios reveal a bouncing Universe, free from singularity. Such quantum cosmological perfect fluid models admit a universal classical analogue, represented by the addition, to the ordinary classical model, of a repulsive stiff matter fluid1,2. The existence of this universal classical analogue may imply that this perfect fluid coupled to gravity model is not a real quantum system. The quantum cosmological perfect fluid model is, for a flat spatial section, formally equivalent to a free particle in ordinary quantum mechanics, for any value of α, while the radiative non-flat case is equivalent to the harmonic oscillator. The repulsive fluid needed to reproduce the quantum results is the same in both cases.

Quantum Cosmological Perfect Fluid Models

Perfect fluid Friedmann-Robertson-Walker quantum cosmological models for an arbitrary barotropic equation of state $p = \alpha\rho$ are constructed using Schutz's variational formalism. In this approach the notion of time can be recovered. By superposition of stationary states, finite-norm wave-packet solutions to the Wheeler-DeWitt equation are found. The behaviour of the scale factor is studied by applying the many-worlds and the ontological interpretations of quantum mechanics. Singularity-free models are obtained for $\alpha < 1$. Accelerated expansion at present requires $- 1/3 > \alpha > - 1$.

Isotropic loop quantum cosmology

Isotropic models in loop quantum cosmology allow explicit calculations, thanks largely to a completely known volume spectrum, which is exploited in order to write down the evolution equation in a discrete internal time. Because of genuinely quantum geometrical effects, the classical singularity is absent in those models in the sense that the evolution does not break down there, contrary to the classical situation where spacetime is inextendible. This effect is generic and does not depend on matter violating energy conditions, but it does depend on the factor ordering of the Hamiltonian constraint. Furthermore, it is shown that loop quantum cosmology reproduces standard quantum cosmology and hence (e.g., via WKB approximation) classical behaviour in the large volume regime where the discreteness of space is insignificant. Finally, an explicit solution to the Euclidean vacuum constraint is discussed which is the unique solution with semiclassical behaviour representing quantum Euclidean space.

Quantum cosmological perfect fluid model and its classical analogue

The quantization of gravity coupled to a perfect fluid model leads to a Schr\"odinger-like equation, where the matter variable plays the role of time. The wave function can be determined, in the flat case, for an arbitrary barotropic equation of state $p = \alpha\rho$; solutions can also be found for the radiative non-flat case. The wave packets are constructed, from which the expectation value for the scale factor is determined. The quantum scenarios reveal a bouncing Universe, free from singularity. We show that such quantum cosmological perfect fluid models admit a universal classical analogue, represented by the addition, to the ordinary classical model, of a repulsive stiff matter fluid. The meaning of the existence of this universal classical analogue is discussed. The quantum cosmological perfect fluid model is, for a flat spatial section, formally equivalent to a free particle in ordinary quantum mechanics, for any value of $\alpha$, while the radiative non-flat case is equivalent to the harmonic oscillator. The repulsive fluid needed to reproduce the quantum results is the same in both cases.