WKB Approximation for the Polymer Quantization of the Taub Model

TL;DR

This paper introduces a novel WKB approximation method within polymer quantum mechanics to analyze the Taub cosmological model, revealing a cyclical universe with finite anisotropy.

Contribution

It develops a new algorithm for separating classical and quantum variables in polymer quantum cosmology, applied specifically to the Taub universe with scalar field.

Findings

The universe oscillates between minimum and maximum volumes.

Anisotropy remains finite throughout the evolution.

The model predicts a cyclical universe behavior.

Abstract

We develop a suitable technical algorithm to implement a separation of the Minisuperspace configurational variables into quasi-classical and purely quantum degrees of freedom, in the framework of a Polymer quantum Mechanics reformulation of the canonical dynamics. We then implement the obtained general scheme to the specific case of a Taub Universe, in the presence of a free massless scalar field. In particular, we identify the quasi-classical variables in the Universe volume and a suitable function of the scalar field, while the purely quantum degree of freedom corresponds to the Universe anisotropy. We demonstrate that the Taub cosmology is associated to a cyclical Universe, oscillating between a minimum and maximum volume turning points, respectively. The pure quantum Universe anisotropy has always a finite value.