Bohmian Quantum Cosmology from the Wheeler-DeWitt Equation

Fuente: arXiv
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Auteurs principaux: Basilakos, Spyros, Kouniatalis, Gerasimos, Saridakis, Emmanuel N., Tzerefos, Charalampos
Format: Preprint
Publié: 2025
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author Basilakos, Spyros
Kouniatalis, Gerasimos
Saridakis, Emmanuel N.
Tzerefos, Charalampos
author_facet Basilakos, Spyros
Kouniatalis, Gerasimos
Saridakis, Emmanuel N.
Tzerefos, Charalampos
contents 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 Schrodinger 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 $Λ$CDM behaviour while exhibiting quantum modifications at earlier epochs.
format Preprint
id arxiv_https___arxiv_org_abs_2512_18818
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Bohmian Quantum Cosmology from the Wheeler-DeWitt Equation
Basilakos, Spyros
Kouniatalis, Gerasimos
Saridakis, Emmanuel N.
Tzerefos, Charalampos
General Relativity and Quantum Cosmology
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 Schrodinger 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 $Λ$CDM behaviour while exhibiting quantum modifications at earlier epochs.
title Bohmian Quantum Cosmology from the Wheeler-DeWitt Equation
topic General Relativity and Quantum Cosmology
url https://arxiv.org/abs/2512.18818