Brane Cosmology in an Arbitrary Number of Dimensions

TL;DR

This paper derives generalized cosmological equations for branes in arbitrary dimensions, extending previous models and addressing curvature divergence issues, with applications to symmetric and compactified bulk geometries.

Contribution

It provides a unified framework for brane cosmology in any number of dimensions, including non-$\mathbb{Z}_2$ symmetric cases and regularized branes.

Findings

Derived effective cosmological equations for arbitrary D-dimensional bulk.

Extended previous 5 and 6-dimensional models to general dimensions.

Applied results to symmetric and compactified AdS-Schwarzschild bulks.

Abstract

We derive the effective cosmological equations for a non-$\mathbb{Z}_2$ symmetric codimension one brane embedded in an arbitrary D-dimensional bulk spacetime, generalizing the $D=5,6$ cases much studied previously. As a particular case, this may be considered as a regularized codimension (D-4) brane avoiding the problem of curvature divergence on the brane. We apply our results to the case of spherical symmetry around the brane and to partly compactified AdS-Schwarzschild bulks.