Localization Issues for Robertson-Walker Branes

TL;DR

This paper investigates the localization of gravity in Randall-Sundrum branes embedded in AdS_5, revealing how different brane geometries affect warping and demonstrating a scalar field mechanism for gravity localization.

Contribution

It analyzes the warping behavior of various Robertson-Walker branes in AdS_5 and introduces a scalar field approach to naturally localize gravity without fine-tuning.

Findings

Warping varies with brane geometry, warping for M_4 and dS_4, antiwarping for AdS_4 and RW.

Gravitational fluctuations are affected by a delta function at the brane.

A sine-Gordon scalar field can localize gravity around an M_4 brane naturally.

Abstract

We discuss some of the localization issues associated with the embedding of Robertson-Walker type Randall-Sundrum branes in a bulk $AdS_5$. Specifically, we show that of the branes which are embeddable in $AdS_5$ the geometry associated with $M_4$ and $dS_4$ branes warps away from the brane while that associated with $AdS_4$ and $RW$ branes of any spatial 3-curvature antiwarps away from the brane. We discuss the gravitational fluctuations around an $M_4$ brane and analyze the specific role played by a delta function singularity at the brane. We show how a bulk sine-Gordon scalar field can without any fine-tuning naturally lead to localization of gravity around an $M_4$ brane.