The Mixmaster Model as a Cosmological Framework and Aspects of its Quantum Dynamics

TL;DR

This paper reviews the stochastic features of Mixmaster cosmological models, explores their geometric and chaotic properties, and discusses how quantum dynamics in the early universe relate to classical chaos.

Contribution

It provides a comprehensive review of Mixmaster dynamics, including their geometric structure, chaos covariance, and connection to quantum mechanics in the early universe.

Findings

Mixmaster chaos exhibits stochastic features and geometric complexity.

Chaos in Mixmaster models is analyzed in relation to time covariance.

Quantum dynamics in the Planck era relate to classical chaos through a semiclassical limit.

Abstract

This paper provides a review of some recent issues on the Mixmaster dynamics concerning the features of its stochasticity. After a description of the geometrical structure characterizing the homogeneous cosmological models in the Bianchi classification and the Belinsky-Khalatnikov-Lifshitz piecewise representation of the types VIII and IX oscillatory regime, we face the question regarding the time covariance of the resulting chaos as viewed in terms of continuous Misner-Chitr\'e like variables. Finally we show how in the statistical mechanics framework the Mixmaster chaos raises as semiclassical limit of the quantum dynamics in the Planckian era.