Generic instability of the dynamics underlying the Belinski-Khalatnikov-Lifshitz scenario

TL;DR

This paper derives and tests a class of solutions to the BKL cosmological scenario, demonstrating their instability and confirming the chaotic nature of dynamics near singularities.

Contribution

It introduces a new class of exact solutions to the BKL scenario and proves their instability, supporting the conjecture of chaotic behavior near singularities.

Findings

Derived a class of exact solutions to BKL scenario

Proved these solutions are unstable near singularity

Confirmed the chaotic nature of dynamics close to singularities

Abstract

A class of exact solutions to the Belinski-Khalatnikov-Lifshitz (BKL) scenario is derived and tested for their stability against small perturbations. These are the only regular solutions in the Painlev\'{e} sense. We prove that they are unstable in the vicinity of the cosmological singularity. Regularity of the dynamics is also examined with the dynamical systems method. Our results confirm the conjecture of BKL that the dynamics near the singularity becomes generically chaotic.