Stability of the Anisotropic Brane Cosmology

TL;DR

This paper investigates the stability of anisotropic Bianchi type I brane cosmology, showing that it becomes isotropic over time and remains stable against perturbations, contrasting with conventional Einstein's theory.

Contribution

It demonstrates the stability and isotropization of anisotropic brane cosmology models, highlighting differences from traditional Einstein models in initial conditions and long-term behavior.

Findings

Anisotropic expansion diminishes over time in brane models.

Initial anisotropy can grow in Einstein's theory, unlike in brane models.

Brane cosmology is stable against anisotropic perturbations at large times.

Abstract

The stability of the Bianchi type I anisotropic brane cosmology is analyzed in this paper. We also study the effect of the brane solution by comparing the models on the 3-brane and the models in the conventional Einstein's space. Analysis is presented for two different models: one with a perfect fluid and the other one with a dilaton field. It is shown that the anisotropic expansion is smeared out dynamically for both theories in the large time limit independent of the models with different types of matter. The initial states are, however, dramatically different. A primordial anisotropic expansion will grow for the conventional Einstein's theory. On the other hand, it is shown that the initial state is highly isotropic for the brane universe except for a very particular case. Moreover, it is also shown that the Bianchi type I anisotropic cosmology is stable against any anisotropic perturbation for both theories in the large time limit.