Classical and Quantum Features of the Mixmaster Singularity

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.

170 pages, 14 figures, ~500 references. Invited review paper to appear on Int. J. Mod. Phys. A. v2: minor changes, references added. v3: Conclusions added

References in corpus (11)

• The behavior of non-linear anisotropies in bouncing Bianchi I models of loop quantum cosmology
• The Big-Bang Singularity in the framework of a Generalized Uncertainty Principle
• Singularities and Quantum Gravity
• Bianchi Model CMB Polarization and its Implications for CMB Anomalies
• The Bianchi IX model in Loop Quantum Cosmology
• Quantum suppression of the generic chaotic behavior close to cosmological singularities
• Relativistic chaos is coordinate invariant
• Quantum Dynamics of the Taub Universe in a Generalized Uncertainty Principle framework
• Bianchi spacetimes in noncommutative phase-space
• Generalized uncertainty principle in Bianchi type I quantum cosmology
• Semiclassical States in Quantum Cosmology: Bianchi I Coherent States