On Brane World Cosmological Perturbations

TL;DR

This paper analyzes scalar cosmological perturbations in 3-brane world models with a 5D bulk, providing a framework to relate bulk and brane perturbations and simplifying the boundary conditions for numerical solutions.

Contribution

It explicitly connects the effective Einstein equations with Mukohyama's master equation and derives boundary conditions for perturbations on RS and DGP branes.

Findings

Derived boundary condition for the master variable on the brane.

Established relations between Weyl fluid perturbations and master variable.

Facilitated numerical evolution of perturbations in brane world models.

Abstract

We discuss the scalar cosmological perturbations in a 3-brane world with a 5D bulk. We first show explicitly how the effective perturbed Einstein's equations on the brane (involving the Weyl fluid) are encoded into Mukohyama's master equation. We give the relation between Mukohyama's master variable and the perturbations of the Weyl fluid, we also discuss the relation between the former and the perturbations of matter and induced metric on the brane. We show that one can obtain a boundary condition on the brane for the master equation solely expressible in term of the master variable, in the case of a perfect fluid with adiabatic perturbations on a Randall-Sundrum (RS) or Dvali-Gabadadze-Porrati (DGP) brane. This provides an easy way to solve numerically for the evolution of the perturbations as well as should shed light on the various approximations done in the literature to deal with the Weyl degrees of freedom.