Perturbations of brane worlds

TL;DR

This paper investigates how perturbations behave in brane world cosmological models with a five-dimensional anti-de Sitter bulk, focusing on bulk gravitons and brane matter perturbations.

Contribution

It provides a detailed analysis of bulk and brane perturbations, especially for scalar field matter, using conformally Minkowskian coordinates to clarify their interactions.

Findings

Restrictions on bulk gravitons with scalar field matter

Solutions to brane perturbation equations in this setup

Insights into the interplay between bulk gravitons and brane matter

Abstract

We consider cosmological models where the universe, governed by Einstein's equations, is a piece of a five dimensional double-sided anti-de Sitter spacetime (that is, a "$Z_2$-symmetric bulk") with matter confined to its four dimensional Robertson-Walker boundary or "brane". We study the perturbations of such models. We use conformally minkowskian coordinates to disentangle the contributions of the bulk gravitons and of the motion of the brane. We find the restrictions put on the bulk gravitons when matter on the brane is taken to be a scalar field and we solve in that case the brane perturbation equations.