Classical and quantum dynamics of a perfect fluid scalar-energy dependent metric cosmology

TL;DR

This paper explores classical and quantum models of a flat energy-dependent FRW cosmology with a perfect fluid, revealing conditions for a bouncing universe and analyzing quantum effects that may prevent singularities.

Contribution

It introduces a novel energy-dependent scalar-rainbow metric framework and derives a Schrödinger-Wheeler-DeWitt equation for quantum cosmology.

Findings

Classical universe models can exhibit a bounce instead of a big bang.

Quantum wave functions suggest possible avoidance of singularities.

Energy-dependent gauge fixing helps identify a time parameter in the model.

Abstract

Inspired from the idea of minimally coupling of a real scalar field to geometry, we investigate the classical and quantum models of a flat energy-dependent FRW cosmology coupled to a perfect fluid in the framework of the scalar-rainbow metric gravity. We use the standard Schutz' representation for the perfect fluid and show that under a particular energy-dependent gauge fixing, it may lead to the identification of a time parameter for the corresponding dynamical system. It is shown that, under some circumstances on the minisuperspace prob energy, the classical evolution of the of the universe represents a late time expansion coming from a bounce instead of the big-bang singularity. Then we go forward by showing that this formalism gives rise to a Schr\"{o}dinger-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 Bohmian interpretation of quantum cosmology.