Bohmian Quantum Cosmology from the Wheeler-DeWitt Equation

Abstract

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 $\Lambda$CDM behaviour while exhibiting quantum modifications at earlier epochs.

10 pages, 3 figures

References in corpus (14)

• The Complete Light-curve Sample of Spectroscopically Confirmed Type Ia Supernovae from Pan-STARRS1 and Cosmological Constraints from The Combined Pantheon Sample
• Purely kinetic k-essence as unified dark matter
• New Schwarzschild-like solutions in f(T) gravity through Noether symmetries
• Quantum cosmology from the de Broglie-Bohm perspective
• Unified Dark Matter in Scalar Field Cosmologies
• Dark Fluid: a complex scalar field to unify dark energy and dark matter
• General Analytic Solutions of Scalar Field Cosmology with Arbitrary Potential
• $f(R)$-gravity from Killing Tensors
• The Bohm Interpretation of Quantum Cosmology
• An Inflationary Non-singular Quantum Cosmological Model
• Consistent Scalar and Tensor Perturbation Power Spectra in Single Fluid Matter Bounce with Dark Energy Era
• Quantum matter bounce with a dark energy expanding phase
• Classical and Quantum Limits in Bohmian Quantum Cosmology
• Elimination of cosmological singularities in quantum cosmology by suitable operator orderings