Singularity avoidance in a quantum model of the Mixmaster universe

TL;DR

This paper develops a quantum model of the Mixmaster universe that employs advanced quantization and approximation techniques, demonstrating singularity avoidance through a repulsive potential and analyzing anisotropic energy behavior during contraction.

Contribution

It introduces a novel quantum approach combining affine and Weyl quantizations with adiabatic and harmonic approximations to model the Bianchi-IX universe.

Findings

Singularity is avoided due to a repulsive potential from affine quantization.

Quantum anisotropic energy grows slower than classical during contraction.

Classical recollapse is recovered far from the quantum bounce.

Abstract

We present a quantum model of the vacuum Bianchi-IX dynamics. It is based on four main elements. First, we use a compound quantization procedure: an affine coherent state quantization for isotropic variables and a Weyl quantization for anisotropic ones. Second, inspired by standard approaches in molecular physics, we make an adiabatic approximation (Born-Oppenheimer-like approximation). Third, we expand the anisotropy potential about its minimum in order to deal with its harmonic approximation. Fourth, we develop an analytical treatment on the semiclassical level. The resolution of the classical singularity occurs due to a repulsive potential generated by the affine quantization. This procedure shows that during contraction the quantum energy of anisotropic degrees of freedom grows much slower than the classical one. Furthermore, far from the quantum bounce, the classical recollapse is reproduced. Our treatment is put in the general context of methods of molecular physics, which can include both adiabatic and nonadiabatic approximations.