Evolution of Cosmological Perturbations in the Brane World

TL;DR

This paper develops a formalism to analyze cosmological perturbations in the Randall-Sundrum brane world scenario, showing that late-time scalar perturbation evolution matches 4D cosmology if heavy graviton effects are negligible.

Contribution

The paper introduces a new formalism for coupled brane and bulk perturbation dynamics and demonstrates conditions under which 4D cosmological results are recovered in the brane world.

Findings

Late-time scalar perturbations match 4D cosmology when heavy graviton effects are ignored.

Scalar temperature anisotropies can be computed using the Bardeen parameter's constancy under certain conditions.

Massive gravitons with specific masses have negligible effects on perturbation evolution.

Abstract

The evolution of the cosmological perturbations is studied in the context of the Randall-Sundrum brane world scenario, in which our universe is realized on a three-brane in the five dimensional Anti-de Sitter(AdS) spacetime. We develop a formalism to solve the coupled dynamics of the cosmological perturbations in the brane world and the gravitational wave in the AdS bulk. Using our formalism, the late time evolution of the cosmological scalar perturbations at any scales larger than the AdS curvature scale $l$ is shown to be identical with the one obtained in the conventional 4D cosmology, provided the effect of heavy graviton modes may be neglected. Here the late time means the epoch when the Hubble horizon $H^{-1}$ in the 4D brane world is sufficiently larger than the AdS curvature scale $l$. If the inflation occurs sufficiently lower than $l^{-1}$, the scalar temperature anisotropies in the Cosmic Microwave Background at large scales can be calculated using the constancy of the Bardeen parameter as is done in the 4D cosmology. The assumption of the result is that the effect of the massive graviton with mass $m e^{-\alpha_0}>l^{-1}$ in the brane world is negligible, where $e^{\alpha_0}$ is the scale factor of the brane world. We also discuss the effect of these massive gravitons on the evolution of the perturbations.