Mixmaster Chaos via the Invariant Measure

TL;DR

This paper analyzes the chaotic behavior of the Mixmaster universe using statistical mechanics, demonstrating that its invariant measure is uniform and independent of the temporal gauge choice.

Contribution

It introduces a microcanonical ensemble description of the Mixmaster dynamics with a uniform invariant measure derived from Liouville measure.

Findings

The invariant measure is uniform across the phase space.

The measure's covariance is independent of the temporal gauge.

The system's chaoticity is characterized within a statistical mechanics framework.

Abstract

The chaoticity of the Mixmaster is discussed in the framework of Statistical Mechanics by using Misner--Chitre-like variables and an ADM reduction of its dynamics. We show that such a system is well described by a microcanonical ensemble whose invariant measure is induced by the corresponding Liouville one and is uniform. The covariance with respect to the choice of the temporal gauge of the obtained invariant measure is outlined.