Perfect Fluid Quantum Anisotropic Universe: Merits and Challenges

TL;DR

This paper explores the quantization of anisotropic cosmological models with perfect fluids, addressing issues like singularity avoidance and non-unitarity, and proposes operator ordering as a solution.

Contribution

It introduces a method for quantizing Bianchi type V and IX models using Schutz's potentials, and demonstrates how operator ordering can improve unitarity.

Findings

Complete wave packet formation in some models

Singularity avoidance in specific cases

Operator ordering alleviates non-unitarity

Abstract

The present paper deals with quantization of perfect fluid anisotropic cosmological models. Bianchi type V and IX models are discussed following Schutz's method of expressing fluid velocities in terms of six potentials. The wave functions are found for several examples of equations of state. In one case a complete wave packet could be formed analytically. The initial singularity of a zero proper volume can be avoided in this case, but it is plagued by the usual problem of non-unitarity of anisotropic quantum cosmological models. It is seen that a particular operator ordering alleviates this problem.