The Bianchi classification of the three-dimensional Lie algebras and of the spatially homogeneous universes is presented in a rather pedagogical manner. The dynamics of the Bianchi-I, Bianchi-II and Bianchi-IX universes are discussed in detail. A special attention is paid to the phenomenon of the oscillatory approach to the cosmological singularity (BKL) known also as the Mixmaster universe. The stochasticity in cosmology and the connection between cosmological billiards and infinite-dimensional Lie algebras are briefly illustrated.

The Bianchi Classification of the Three-Dimensional Lie Algebras and Homogeneous Cosmologies and the Mixmaster Universe

A. Kamenchtchik
2019

Abstract

The Bianchi classification of the three-dimensional Lie algebras and of the spatially homogeneous universes is presented in a rather pedagogical manner. The dynamics of the Bianchi-I, Bianchi-II and Bianchi-IX universes are discussed in detail. A special attention is paid to the phenomenon of the oscillatory approach to the cosmological singularity (BKL) known also as the Mixmaster universe. The stochasticity in cosmology and the connection between cosmological billiards and infinite-dimensional Lie algebras are briefly illustrated.
2019
Proceedings, Domoschool - the International Alpine School in Mathematics and Physics: Einstein Equations: Physical and Mathematical aspects of General Relativity : Domodossola, Italy, July 16-20, 2018
93
137
A. Kamenchtchik
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11585/713976
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