BKL oscillations in 2+1 space-time dimensions

TL;DR

This paper explores whether 2+1 dimensional cosmological models can exhibit BKL-like oscillations near singularities, using a toy model and phase space analysis within the cosmological billiards framework.

Contribution

It introduces a toy model demonstrating BKL oscillations in 2+1 dimensions and interprets these dynamics through topological degrees of freedom of gravity.

Findings

The singularity corresponds to a separatrix in phase space.

The toy model exhibits oscillatory dynamics similar to BKL behavior.

A physical interpretation relates models to topological gravity in 2+1 dimensions.

Abstract

We investigate the question whether there are cosmological models in 2+1 space-time dimensions which exhibit dynamics similar to BKL oscillations, as the cosmological singularity is approached. Based on intuition, we conceive a toy model which displays such oscillatory dynamics. We show that in the phase space of this model, the cosmological singularity is represented by a separatrix curve and discuss the model's dynamics within the cosmological billiards picture. Finally, we offer a physical interpretation for a family of similar cosmological models in terms of the topological degrees of freedom of gravity in 2+1 dimensions.