Stephani-Schutz quantum cosmology

TL;DR

This paper investigates a quantum cosmological model with a cosmological constant and radiation, using Schutz's formalism to derive Schrödinger-like equations, and finds that the universe avoids singularities at the quantum level.

Contribution

It applies Schutz's formalism to the Stephani universe, deriving and solving Wheeler-DeWitt equations to analyze quantum behavior and singularity avoidance.

Findings

Wave packets oscillate between finite bounds

Expectation value of scale factor avoids zero

Model suggests quantum singularity resolution

Abstract

We study the Stephani quantum cosmological model in the presence of a cosmological constant in radiation dominated Universe. In the present work the Schutz's variational formalism which recovers the notion of time is applied. This gives rise to Wheeler-DeWitt equations which can be cast in the form of Schr\"odinger equations for the scale factor. We find their eigenvalues and eigenfunctions by using the Spectral Method. Then we use the eigenfunctions in order to construct wave packets and evaluate the time-dependent expectation value of the scale factor, which is found to oscillate between non-zero finite maximum and minimum values. Since the expectation value of the scale factor never tends to the singular point, we have an initial indication that this model may not have singularities at the quantum level.