Asymptotic states in brane cosmology with a nonlocal anisotropic stress

TL;DR

This paper studies the evolution of anisotropy in brane cosmology models with nonlocal stresses, showing conditions for isotropization and describing asymptotic behaviors.

Contribution

It introduces an ansatz for nonlocal anisotropic stress proportional to dark energy and analyzes the isotropization conditions in brane-world models.

Findings

Models with b3 a3 4/3 isotropize over time.

For b3 > 4/3, anisotropic future states occur.

Past asymptotic regimes are characterized for these models.

Abstract

We investigate the dynamics of a Bianchi I brane Universe in the presence of a nonlocal anisotropic stress ${\cal P}_{\mu\nu}$ proportional to a "dark energy" ${\cal U}$. Using this ansatz for the case ${\cal U} > 0$ we prove that if a matter on a brane satisfies the equation of state $p=(\gamma-1)\rho$ with $\gamma \le 4/3$ then all such models isotropize. For $\gamma > 4/3$ anisotropic future asymptotic states are found. We also describe the past asymptotic regimes for this model.