A class of 5D inhomogeneous models with a cosmological constant

TL;DR

This paper explores a class of five-dimensional inhomogeneous brane models with a cosmological constant, analyzing how bulk matter influences the evolution of a spatially inhomogeneous universe while maintaining conformal flatness.

Contribution

It introduces a new class of 5D inhomogeneous brane models with a cosmological constant, extending previous SII spacetimes to higher dimensions.

Findings

Model generalizes SII spacetimes to 5D

Shows bulk matter affects brane cosmology

Maintains conformal flatness of the induced geometry

Abstract

In this work we would like to address the problem of the effect of bulk matter on the brane cosmological evolution in a general way. We assume that the spatial part of the brane metric is not maximally symmetric, therefore spatially inhomogeneous. However we retain the conformal flatness property of the standard cosmological model (FRW) i.e. the Weyl tensor of the induced 4D geometry is zero. We refer to it as Spatially Inhomogeneous Irrotational (SII) brane. It is shown that the model can be regarded as the 5D generalization of the SII spacetimes found recently [1].