Brane cosmology with an anisotropic bulk

TL;DR

This paper explores anisotropic brane cosmologies within a five-dimensional bulk, deriving explicit vacuum solutions and analyzing conditions under which branes can support perfect fluids in such anisotropic settings.

Contribution

It provides explicit anisotropic bulk solutions and examines the constraints on brane matter content, highlighting conditions for perfect fluid support in anisotropic brane-world models.

Findings

Anisotropic vacuum bulk solutions with negative cosmological constant are obtained.

A static bulk cannot support a perfect fluid brane if the bulk is anisotropic.

Certain bulk geometries allow embedding a perfect fluid brane with determined energy density and pressure.

Abstract

In the context of brane cosmology, a scenario where our universe is a 3+1-dimensional surface (the ``brane'') embedded in a five-dimensional spacetime (the ``bulk''), we study geometries for which the brane is anisotropic - more specifically Bianchi I - though still homogeneous. We first obtain explicit vacuum bulk solutions with anisotropic three-dimensional spatial slices. The bulk is assumed to be empty but endowed with a negative cosmological constant. We then embed Z_2-symmetric branes in the anisotropic spacetimes and discuss the constraints on the brane energy-momentum tensor due to the five-dimensional anisotropic geometry. We show that if the bulk is static, an anisotropic brane cannot support a perfect fluid. However, we find that for some of our bulk solutions it is possible to embed a brane with a perfect fluid though its energy density and pressure are completely determined by the bulk geometry.