Doubly-gauge-invariant formalism of brane-world cosmological perturbations

TL;DR

This paper reviews a formalism for analyzing cosmological perturbations in brane-world models, emphasizing gauge invariance and non-local effects from bulk gravitational waves, with implications for early universe cosmology.

Contribution

It introduces a doubly gauge invariant formalism that captures the evolution of scalar perturbations, including non-local effects, in brane-world cosmology.

Findings

Four independent equations describe scalar perturbations.

Non-local effects from bulk gravitational waves influence perturbation evolution.

At low energy, deviations from standard cosmology are due to non-local bulk effects.

Abstract

We review the doubly gauge invariant formalism of cosmological perturbations in the Randall-Sundrum brane world. This formalism leads to four independent equations describing the evolution of scalar perturbations. Three of these equations are differential equations written in terms of gauge invariant variables on the brane only, and the other is an integro-differential equation describing non-locality due to bulk gravitational waves. At low energy the evolution of the scalar-type cosmological perturbations in the brane-world cosmology differs from that in the standard cosmology only by non-local effects due to bulk gravitational waves.