Quantum Stephani Universe in vicinity of the symmetry center

We study a class of spherically symmetric Stephani cosmological models in the presence of a self-interacting scalar field in both classical and quantum domains. We discuss the construction of 'canonical' wavepackets resulting from the solutions of a class of Wheeler–DeWitt equations in the Stephani Universe. We suggest appropriate initial conditions which result in wavepackets containing some desirable properties, most importantly good classical and quantum correspondence. We also study the situation from the de Broglie–Bohm interpretation of quantum mechanics viewpoint to recover the notion of time and compare the classical and Bohmian results. We show the usage of the canonical prescription and appropriate choices of expansion coefficients to result in the suppression of the quantum potential and coincidence of classical and Bohmian results. We show that, in some cases, contrary to the Friedmann–Robertson–Walker case, the bound state solutions also exist for all positive values of the cosmological constant.We study a class of spherically symmetric Stephani cosmological models in the presence of a self-interacting scalar field in both classical and quantum domains. We discuss the construction of 'canonical' wavepackets resulting from the solutions of a class of Wheeler–DeWitt equations in the Stephani Universe. We suggest appropriate initial conditions which result in wavepackets containing some desirable properties, most importantly good classical and quantum correspondence. We also study the situation from the de Broglie–Bohm interpretation of quantum mechanics viewpoint to recover the notion of time and compare the classical and Bohmian results. We show the usage of the canonical prescription and appropriate choices of expansion coefficients to result in the suppression of the quantum potential and coincidence of classical and Bohmian results. We show that, in some cases, contrary to the Friedmann–Robertson–Walker case, the bound state solutions also exist for all positive values of the cosmological constant.

arXiv:0806.1913Journal of Cosmology and Astroparticle PhysicsJul 4, 20089 citations

Canonical wave packets in quantum cosmology

S S Gousheh, H R Sepangi, P Pedram +1 more

We discuss the construction of wave packets resulting from solutions of a class of Wheeler–DeWitt equations in Robertson–Walker-type cosmologies, for arbitrary curvature. We show that there always exists a 'canonical initial slope' for a given initial wavefunction, which optimizes some desirable properties of the resulting wave packet, most importantly a good classical-quantum correspondence. This can be properly denoted as a canonical wave packet. We introduce a general method for finding these canonical initial slopes which is a generalization of our earlier work.We discuss the construction of wave packets resulting from solutions of a class of Wheeler–DeWitt equations in Robertson–Walker-type cosmologies, for arbitrary curvature. We show that there always exists a 'canonical initial slope' for a given initial wavefunction, which optimizes some desirable properties of the resulting wave packet, most importantly a good classical-quantum correspondence. This can be properly denoted as a canonical wave packet. We introduce a general method for finding these canonical initial slopes which is a generalization of our earlier work.

arXiv:gr-qc/0701035Classical and Quantum GravityAug 16, 200712 citations

Canonical wave packets in quantum cosmology

Siamak Sadat Gousheh, Hamid Reza Sepangi, Pouria Pedram +1 more

We discuss the construction of wave packets resulting from the solutions of a class of Wheeler-DeWitt equations in Robertson-Walker type cosmologies, for arbitrary curvature. We show that there always exists a “canonical initial slope ” for a given initial wave function, which optimizes some desirable properties of the resulting wave packet, most importantly good classical-quantum correspondence. This can be properly denoted as a canonical wave packet. We introduce a general method for finding these canonical initial slopes which is generalization of our earlier work. PACS numbers: 04.20.Ex, 04.60.Kz, 04.25.-g 1We discuss the construction of wave packets resulting from the solutions of a class of Wheeler-DeWitt equations in Robertson-Walker type cosmologies, for arbitrary curvature. We show that there always exists a “canonical initial slope ” for a given initial wave function, which optimizes some desirable properties of the resulting wave packet, most importantly good classical-quantum correspondence. This can be properly denoted as a canonical wave packet. We introduce a general method for finding these canonical initial slopes which is generalization of our earlier work. PACS numbers: 04.20.Ex, 04.60.Kz, 04.25.-g 1

Jan 1, 200813 citations

QUANTUM COSMOLOGY AND THE ACCELERATED UNIVERSE

Eduardo Sergio Santini

The quantized Friedmann-Lema\^ıtre-Robertson-Walker (FLRW) model minimally coupled to a free massless scalar field is studied and interpreted in the Bohm-de Broglie framework. We analyze the quantum bohmian trajectories corresponding to a certain class of gaussian packets, solutions of the Wheeler-DeWitt equation. We show that these bohmian trajectories undergo an accelerated expansion in the middle of its evolution due to the presence of quantum cosmological effects in this period. It is shown that the luminosity-redshift relation in the quantum cosmological model can be made close to the corresponding relation coming from the classical model suplemented by a cosmological constant, for $z<1$ . In this way we have the posibility of interpreting the present observations of high redshift supernovae as the consequence of a quantum cosmological effect.The quantized Friedmann-Lema\^ıtre-Robertson-Walker (FLRW) model minimally coupled to a free massless scalar field is studied and interpreted in the Bohm-de Broglie framework. We analyze the quantum bohmian trajectories corresponding to a certain class of gaussian packets, solutions of the Wheeler-DeWitt equation. We show that these bohmian trajectories undergo an accelerated expansion in the middle of its evolution due to the presence of quantum cosmological effects in this period. It is shown that the luminosity-redshift relation in the quantum cosmological model can be made close to the corresponding relation coming from the classical model suplemented by a cosmological constant, for $z<1$. In this way we have the posibility of interpreting the present observations of high redshift supernovae as the consequence of a quantum cosmological effect.

arXiv:gr-qc/0410112The Ninth Marcel Grossmann MeetingFeb 1, 20060 citations

Bohmian quantum cosmology from the Wheeler-DeWitt equation

Spyros Basilakos, Gerasimos Kouniatalis, Emmanuel N. Saridakis +1 more

We construct a Bohmian quantum cosmological model for a spatially flat Friedmann-Robertson-Walker universe filled with a single scalar field whose potential provides a unified description of cold dark matter and dark energy at the background level. Starting from the Einstein-Hilbert action supplemented by a scalar field, we derive the minisuperspace Lagrangian and the associated canonical Hamiltonian formulation. By means of a nontrivial canonical transformation, the minisuperspace dynamics is mapped into that of a two-dimensional hyperbolic oscillator with a fixed frequency ratio, rendering the Wheeler-DeWitt equation exactly solvable by separation of variables. The resulting Wheeler-DeWitt solutions are expressed in terms of parabolic cylinder functions and are parametrised by a continuous separation constant, reflecting the constrained nature of the theory and the absence of a standard Schrödinger time parameter. Adopting the de Broglie-Bohm formulation, we derive deterministic guidance equations in minisuperspace and construct a well-defined Bohmian Hubble parameter directly in terms of the pilot-wave phase. Finally, we present a Wheeler-DeWitt-derived toy wave function for which the Bohmian trajectories and the associated cosmological expansion history can be obtained analytically, reproducing the late-time ΛCDM behaviour while exhibiting quantum modifications at earlier epochs.We construct a Bohmian quantum cosmological model for a spatially flat Friedmann-Robertson-Walker universe filled with a single scalar field whose potential provides a unified description of cold dark matter and dark energy at the background level. Starting from the Einstein-Hilbert action supplemented by a scalar field, we derive the minisuperspace Lagrangian and the associated canonical Hamiltonian formulation. By means of a nontrivial canonical transformation, the minisuperspace dynamics is mapped into that of a two-dimensional hyperbolic oscillator with a fixed frequency ratio, rendering the Wheeler-DeWitt equation exactly solvable by separation of variables. The resulting Wheeler-DeWitt solutions are expressed in terms of parabolic cylinder functions and are parametrised by a continuous separation constant, reflecting the constrained nature of the theory and the absence of a standard Schrödinger time parameter. Adopting the de Broglie-Bohm formulation, we derive deterministic guidance equations in minisuperspace and construct a well-defined Bohmian Hubble parameter directly in terms of the pilot-wave phase. Finally, we present a Wheeler-DeWitt-derived toy wave function for which the Bohmian trajectories and the associated cosmological expansion history can be obtained analytically, reproducing the late-time ΛCDM behaviour while exhibiting quantum modifications at earlier epochs.

arXiv:2512.18818Physics Letters BMar 7, 20262 citations

Consistent probabilities in perfect fluid quantum universes

Clécio R. Bom, Nelson Pinto-Neto, Grasiele Batista dos Santos

Recently it has been claimed that the Wheeler--DeWitt quantization of gravity is unable to avoid cosmological singularities. However, in order to make this assertion, one must specify the underlying interpretation of quantum mechanics which has been adopted. For instance, several nonsingular models were obtained in Wheeler--DeWitt quantum cosmology in the framework of the de Broglie--Bohm quantum theory. Conversely, there are specific situations where the singularity cannot be avoided in the framework of the consistent histories approach to quantum mechanics. In these specific situations, the matter content is described by a scalar field, and the Wheeler--DeWitt equation looks like a Klein--Gordon equation. The aim of this work is to study a possible singular behavior of quantum cosmological models in which the matter content is described by a hydrodynamical perfect fluid, where the resulting wave equation is a genuine Schr\"odinger equation. In this case, it is shown that the conclusions of the consistent histories and the de Broglie--Bohm approaches coincide in the quantum cosmological models where the curvature of the spatial sections is not positive definite, namely, that the cosmological singularities are eliminated. In the case of positive spatial curvature, the family of histories is no longer consistent, and no conclusion can be given in this framework.Recently it has been claimed that the Wheeler--DeWitt quantization of gravity is unable to avoid cosmological singularities. However, in order to make this assertion, one must specify the underlying interpretation of quantum mechanics which has been adopted. For instance, several nonsingular models were obtained in Wheeler--DeWitt quantum cosmology in the framework of the de Broglie--Bohm quantum theory. Conversely, there are specific situations where the singularity cannot be avoided in the framework of the consistent histories approach to quantum mechanics. In these specific situations, the matter content is described by a scalar field, and the Wheeler--DeWitt equation looks like a Klein--Gordon equation. The aim of this work is to study a possible singular behavior of quantum cosmological models in which the matter content is described by a hydrodynamical perfect fluid, where the resulting wave equation is a genuine Schr\"odinger equation. In this case, it is shown that the conclusions of the consistent histories and the de Broglie--Bohm approaches coincide in the quantum cosmological models where the curvature of the spatial sections is not positive definite, namely, that the cosmological singularities are eliminated. In the case of positive spatial curvature, the family of histories is no longer consistent, and no conclusion can be given in this framework.

arXiv:1308.5210Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fieldsJan 21, 20141 citation

z<1

. In this way we have the posibility of interpreting the present observations of high redshift supernovae as the consequence of a quantum cosmological effect.