Quantum Stephani exact cosmological solutions and the selection of time variable

TL;DR

This paper investigates quantum cosmological models with perfect fluid Stephani solutions, applying Schutz's formalism to recover time, and analyzes the evolution of the universe's scale factor using quantum interpretations.

Contribution

It introduces a method to incorporate time into Stephani quantum cosmology and constructs wave packets to study the universe's quantum behavior.

Findings

Expectation value of the scale factor evolves over time.

Wave packets exhibit quantum effects on cosmological dynamics.

Different quantum interpretations provide consistent results.

Abstract

We study perfect fluid Stephani quantum cosmological model. In the present work the Schutz's variational formalism which recovers the notion of time is applied. This gives rise to Wheeler-DeWitt equation for the scale factor. We use the eigenfunctions in order to construct wave packets for each case. We study the time-dependent behavior of the expectation value of the scale factor, using many-worlds and deBroglie-Bohm interpretations of quantum mechanics.