A quantum gravity extension to the Mixmaster dynamics

TL;DR

This paper extends Mixmaster dynamics by incorporating loop quantum cosmology effects, replacing classical singularities with non-singular bounces, and providing a simplified transition rule in terms of Misner variables.

Contribution

It introduces a quantum gravity extension to Mixmaster dynamics, modeling bounces as transitions between classical solutions with simple rules in Misner variables.

Findings

Non-singular bounce replaces classical singularity.

Transition rules are simple in Misner variables.

Quantum effects modify classical Mixmaster behavior.

Abstract

In the loop quantum cosmology effective dynamics for the vacuum Bianchi type I and type IX space-times, a non-singular bounce replaces the classical singularity. The bounce can be approximated as an instantaneous transition between two classical vacuum Bianchi I solutions, with simple transition rules relating the solutions before and after the bounce. These transition rules are especially simple when expressed in terms of the Misner variables: the evolution of the mean logarithmic scale factor is reversed, while the shape parameters are unaffected. As a result, the loop quantum cosmology effective dynamics for the vacuum Bianchi IX space-time can be approximated by a sequence of classical vacuum Bianchi I solutions, following the usual Mixmaster transition maps in the classical regime, and undergoing a bounce with this new transition rule in the Planck regime.