Quantum FRW cosmological solutions in the presence of Chaplygin gas and perfect fluid

TL;DR

This paper develops a quantum cosmological model with Chaplygin gas and perfect fluid, showing that quantum effects prevent singularities and predict late-time accelerated expansion of the universe.

Contribution

It introduces a Schr"odinger-Wheeler-DeWitt equation approach with Schutz's formalism, providing a quantum perspective on cosmological evolution with Chaplygin gas.

Findings

Quantum expectation value of the scale factor avoids singularity.

The universe's expansion accelerates at late times.

Quantum effects differ from classical predictions.

Abstract

We present a Friedmann-Robertson-Walker quantum cosmological model in the presence of Chaplygin gas and perfect fluid for early and late time epoches. In this work, we consider perfect fluid as an effective potential and apply Schutz's variational formalism to the Chaplygin gas which recovers the notion of time. These give rise to Schr\"odinger-Wheeler-DeWitt equation for the scale factor. We use the eigenfunctions in order to construct wave packets and study the time dependent behavior of the expectation value of the scale factor using the many-worlds interpretation of quantum mechanics. We show that contrary to the classical case, the expectation value of the scale factor avoids singularity at quantum level. Moreover, this model predicts that the expansion of Universe is accelerating for the late times.