Perfect fluid quantum Universe in the presence of negative cosmological constant

TL;DR

This paper develops quantum cosmological models with perfect fluids and negative cosmological constant, showing that quantum effects may prevent singularities in the universe's evolution.

Contribution

It introduces a method to solve Wheeler-DeWitt equations for various perfect fluid dominated universes with negative cosmological constant using spectral methods.

Findings

Expectation values of scale factors oscillate between finite bounds.

Quantum models suggest avoidance of classical singularities.

Wave packets constructed indicate non-singular quantum cosmology.

Abstract

We present perfect fluid Friedmann-Robertson-Walker quantum cosmological models in the presence of negative cosmological constant. In this work the Schutz's variational formalism is applied for radiation, dust, cosmic string, and domain wall dominated Universes with positive, negative, and zero constant spatial curvature. In this approach the notion of time can be recovered. These give rise to Wheeler-DeWitt equations for the scale factor. We find their igenvalues and eigenfunctions by using Spectral Method. After that, we use the eigenfunctions in order to construct wave packets for each case and evaluate the time-dependent expectation value of the scale factors, which are found to oscillate between finite maximum and minimum values. Since the expectation values of the scale factors never tends to the singular point, we have an initial indication that these models may not have singularities at the quantum level.