Braneworld cosmological models with anisotropy

TL;DR

This paper constructs anisotropic braneworld cosmological models by solving five-dimensional bulk equations, analyzing how anisotropy relates to bulk Weyl curvature, and showing models can isotropize over time.

Contribution

It provides explicit solutions for anisotropic braneworlds with a detailed analysis of Weyl curvature and anisotropy evolution, addressing a gap in previous ad hoc approaches.

Findings

Models can isotropize and approach Friedmann branes.

Anisotropic stress is required for anisotropy on the brane.

Explicit bulk solutions relate brane anisotropy to Weyl curvature.

Abstract

For a cosmological Randall-Sundrum braneworld with anisotropy, i.e., of Bianchi type, the modified Einstein equations on the brane include components of the five-dimensional Weyl tensor for which there are no evolution equations on the brane. If the bulk field equations are not solved, this Weyl term remains unknown, and many previous studies have simply prescribed it ad hoc. We construct a family of Bianchi braneworlds with anisotropy by solving the five-dimensional field equations in the bulk. We analyze the cosmological dynamics on the brane, including the Weyl term, and shed light on the relation between anisotropy on the brane and Weyl curvature in the bulk. In these models, it is not possible to achieve geometric anisotropy for a perfect fluid or scalar field -- the junction conditions require anisotropic stress on the brane. But the solutions can isotropize and approach a Friedmann brane in an anti-de Sitter bulk.