Classical and Quantum Features of the Mixmaster Singularity

TL;DR

This review comprehensively examines the classical and quantum properties of the Mixmaster cosmological model, highlighting recent advances in understanding its singularity behavior in both homogeneous and inhomogeneous contexts.

Contribution

It provides a detailed synthesis of forty years of research on the Mixmaster model, including classical chaos, quantization methods, and inhomogeneous extensions.

Findings

Classical Mixmaster exhibits chaotic behavior near singularity.

Quantum analysis reveals modified dynamics and potential singularity resolution.

Inhomogeneous models extend classical and quantum features to more realistic cosmologies.

Abstract

This review article is devoted to analyze the main properties characterizing the cosmological singularity associated to the homogeneous and inhomogeneous Mixmaster model. After the introduction of the main tools required to treat the cosmological issue, we review in details the main results got along the last forty years on the Mixmaster topic. We firstly assess the classical picture of the homogeneous chaotic cosmologies and, after a presentation of the canonical method for the quantization, we develop the quantum Mixmaster behavior. Finally, we extend both the classical and quantum features to the fully inhomogeneous case. Our survey analyzes the fundamental framework of the Mixmaster picture and completes it by accounting for recent and peculiar outstanding results.