Perturbations on and off de Sitter brane in anti-de Sitter bulk

TL;DR

This paper analyzes linearized metric perturbations in a two-brane setup within anti-de Sitter space, identifying light modes like the radion and graviton, and explores their implications for holographic cosmology and observable features.

Contribution

It provides a complete analysis of scalar, vector, and tensor perturbations in a time-dependent brane model, highlighting the properties of light modes relevant for holographic cosmology.

Findings

Radion has a red power spectrum at late times.

Radion persists in the single-brane limit.

Light modes include radion and transverse-traceless graviton.

Abstract

Motivated by holographic models of (pseudo)conformal Universe, we carry out complete analysis of linearized metric perturbations in the time-dependent two-brane setup of the Lykken-Randall type. We present the equations of motion for the scalar, vector and tensor perturbations and identify light modes in the spectrum, which are scalar radion and transverse-traceless graviton. We show that there are no other modes in the discrete part of the spectrum. We pay special attention to properties of light modes and show, in particular, that the radion has red power spectrum at late times, as anticipated on holographic grounds. Unlike the graviton, the radion survives in the single-brane limit, when one of the branes is sent to the adS boundary. These properties imply that potentially observable features characteristic of the 4d (pseudo)conformal cosmology, such as statistical anisotropy and specific shapes of non-Gaussianity, are inherent also in holographic conformal models as well as in brane world inflation.