Classical and Quantum Features of the Mixmaster Singularity

Details Classical and Quantum Features of the Mixmaster Singularity Classical and Quantum Features of the Mixmaster Singularity

2007-12-18

arxiv.org/abs/0712.3008v3

Int.J.Mod.Phys.A23:2353-2503,2008

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

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

Scientific paper

10.1142/S0217751X08040275

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.

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