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

TL;DR

This paper explores classical and quantum models of a scalar-metric cosmology with a perfect fluid, revealing how quantum effects might prevent classical singularities and providing a framework for the universe's wave function.

Contribution

It introduces a novel approach using Schutz' representation to identify a time parameter and derives a Schrödinger-Wheeler-DeWitt equation for quantum cosmology.

Findings

Classical universe exhibits late-time power-law expansion from a big bang singularity.

Quantum wave function suggests potential avoidance of singularities.

The formalism links classical dynamics with quantum cosmological descriptions.

Abstract

We study the classical and quantum models of a Friedmann-Robertson-Walker (FRW) cosmology, coupled to a perfect fluid, in the context of the scalar-metric gravity. Using the Schutz' representation for the perfect fluid, we show that, under a particular gauge choice, it may lead to the identification of a time parameter for the corresponding dynamical system. It is shown that the evolution of the universe based on the classical cosmology represents a late time power law expansion coming from a big-bang singularity in which the scale factor goes to zero while the scalar field blows up. Moreover, 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 ontological interpretation of quantum cosmology.