Second order perturbations in the radius stabilized Randall-Sundrum two branes model II -- Effect of relaxing strong coupling approximation --

TL;DR

This paper analyzes second-order gravitational perturbations in the Randall-Sundrum two-brane model with radius stabilization, examining effects of relaxing the strong coupling approximation and its impact on deviations from 4D Einstein gravity.

Contribution

It extends previous work by relaxing the strong coupling limit, revealing new corrections that affect metric perturbations and radion mass in stabilized brane models.

Findings

Relaxing the strong coupling limit introduces corrections that can enhance deviations from 4D gravity.

In some cases, corrections significantly reduce the stabilized radion mass.

The effect is prominent when matter resides on the negative tension brane.

Abstract

We discuss gravitational perturbations in the Randall-Sundrum two branes model with radius stabilization. Following the idea by Goldberger and Wise for the radius stabilization, we introduce a scalar field which has potentials localized on the branes in addition to a bulk potential. In our previous paper we discussed gravitational perturbations induced by static, spherically symmetric and nonrelativistic matter distribution on the branes under the condition that the values of the scalar field on the respective branes cannot fluctuate due to its extremely narrow brane potentials. We call this case the strong coupling limit. Our concern in this paper is to generalize our previous analysis relaxing the limitation of taking the strong coupling limit. We find that new corrections in metric perturbations due to relaxing the strong coupling limit enhance the deviation from the 4D Einstein gravity only in some exceptional cases. In the case that matter fields reside on the negative tension brane, the stabilized radion mass becomes very small when the new correction becomes large.