Universal Aspects of Gravity Localized on Thick Branes

TL;DR

This paper investigates the universality of gravity localization on thick branes in higher-dimensional models, analyzing graviton modes, corrections to Newton's law, and scalar field configurations, extending the Randall-Sundrum framework.

Contribution

It establishes a universal equation for gravitational fluctuations in generalized brane backgrounds and explores conditions for localized gravity and scalar field sources.

Findings

Localized four-dimensional gravity occurs when continuum modes decouple at large distances.

Universal corrections to Newton's Law are derived based on metric behavior.

Single scalar fields can generate certain brane configurations but not all intersecting or higher-dimensional branes.

Abstract

We study gravity in backgrounds that are smooth generalizations of the Randall-Sundrum model, with and without scalar fields. These generalizations include three-branes in higher dimensional spaces which are not necessarily Anti-de Sitter far from the branes, intersecting brane configurations and configurations involving negative tension branes. We show that under certain mild assumptions there is a universal equation for the gravitational fluctuations. We study both the graviton ground state and the continuum of Kaluza-Klein modes and we find that the four-dimensional gravitational mode is localized precisely when the effects of the continuum modes decouple at distances larger than the fundamental Planck scale. The decoupling is contingent only on the long-range behaviour of the metric from the brane and we find a universal form for the corrections to Newton's Law. We also comment on the possible contribution of resonant modes. Given this, we find general classes of metrics which maintain localized four-dimensional gravity. We find that three-brane metrics in five dimensions can arise from a single scalar field source, and we rederive the BPS type conditions without any a priori assumptions regarding the form of the scalar potential. We also show that a single scalar field cannot produce conformally-flat locally intersecting brane configurations or a p-brane in greater than (p+2)-dimensions.