Lev Landau and the problem of singularities in cosmology

TL;DR

This paper explores various aspects of cosmological singularities, including classical and modern models, mathematical structures, and recent developments related to cosmic acceleration, providing a comprehensive overview of singularity issues in cosmology.

Contribution

It offers an integrated analysis of classical and modern singularity models, connecting cosmological dynamics with advanced mathematical frameworks like infinite-dimensional Lie algebras.

Findings

Analysis of BKL oscillatory approach to singularity

Discussion of singularities in multidimensional and superstring models

Introduction of new types of cosmological singularities related to cosmic acceleration

Abstract

We consider different aspects of the problem of cosmological singularity such as the BKL oscillatory approach to singularity, the new features of the cosmological dynamics in the neighbourhood of the singularity in multidimensional and superstring cosmological models and their connections with such a modern branch of mathematics as infinite-dimensional Lie algebras. Besides, we consider some new types of cosmological singularities which were widely discussed during last decade after the discovery of the phenomenon of cosmic acceleration.