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

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 Painlevé sense. We prove that they are unstable in the vicinity of the cosmological singularity. The regularity of the dynamics is also examined with the dynamical systems method. Our results confirm the BKL conjecture that the dynamics near the singularity becomes generically chaotic.

Quantum dynamics corresponding to chaotic BKL scenario

“…We have verified that prototype's dynamics leads to the gravitational singularity [6,7]. That dynamics is generically unstable turning into chaotic process near the singularity [8].…”

“…It has been shown [8] that the perturbed classical solution near the gravitational singularity exhibits some elements of the chaotic behaviour. Our results present the quantum dynamics corresponding to the BKL scenario.…”

“…To have the paper self-contained, we recall in this section the main results of Ref. [8] to be used later.…”

“…c(0) = −120 t −5 0 , ċ(0) = −600 t −6 0 . The stability analyses carried out in [8] have shown that the solution (4) is unstable against small perturbation. More precisely, substituting the following functions…”

“…The paper is organized as follows: In Sec. II we recall the main results of the paper [8] to have our paper self-contained. Sec.…”