Evolution of Cosmological Models in the Brane-world Scenario

TL;DR

This paper systematically analyzes the qualitative behavior of various cosmological models within Randall-Sundrum brane-world scenarios using dynamical systems techniques, revealing new critical points and bifurcations compared to general relativity.

Contribution

It provides a comprehensive dynamical systems analysis of cosmological models in brane-world scenarios, highlighting structural changes and new phenomena not present in standard general relativity.

Findings

Identification of new critical points in brane-world models

Analysis of bifurcations affecting cosmological dynamics

Differences in anisotropy evolution compared to GR

Abstract

In this work we consider Randall-Sundrum brane-world type scenarios, in which the spacetime is described by a five-dimensional manifold with matter fields confined in a domain wall or three-brane. We present the results of a systematic analysis, using dynamical systems techniques, of the qualitative behaviour of the Friedmann-Lemaitre-Robertson-Walker and the Bianchi I and V cosmological models in these scenarios. We construct the state spaces for these models and discuss how their structure changes with respect to the general-relativistic case, in particular, what new critical points appear and their nature, the occurrence of bifurcations and the dynamics of anisotropy.