Quantum cosmological perfect fluid models

TL;DR

This paper constructs quantum cosmological models with perfect fluids using Schutz's formalism, recovering time and finding singularity-free solutions that can explain accelerated expansion under certain conditions.

Contribution

It introduces a method to build quantum cosmological models with arbitrary barotropic fluids and analyzes their behavior using different quantum interpretations.

Findings

Singularity-free models are achieved for $ ext{\alpha} < 1$.

Accelerated expansion occurs for $-1/3 > \alpha > -1$.

Finite-norm wave-packet solutions to the Wheeler-DeWitt equation are found.

Abstract

Perfect fluid Friedmann-Robertson-Walker quantum cosmological models for an arbitrary barotropic equation of state $p = \alpha\rho$ are constructed using Schutz's variational formalism. In this approach the notion of time can be recovered. By superposition of stationary states, finite-norm wave-packet solutions to the Wheeler-DeWitt equation are found. The behaviour of the scale factor is studied by applying the many-worlds and the ontological interpretations of quantum mechanics. Singularity-free models are obtained for $\alpha < 1$. Accelerated expansion at present requires $- 1/3 > \alpha > - 1$.