Wave Function of the Radion in the dS and AdS Brane Worlds

TL;DR

This paper analyzes the radion's wave function in five-dimensional brane world models with non-zero curvature, revealing its mass properties and couplings, and constructing the low-energy effective theory for different brane geometries.

Contribution

It extends the analysis of the radion in brane worlds to cases with non-zero brane curvature, providing explicit wave functions, mass characteristics, and effective theory formulations.

Findings

Radion has negative mass^2 in de Sitter branes and positive in anti-de Sitter branes.

Radion wave function is normalizable in AdS space, ensuring finite effects at large brane separations.

Constructed the low-energy effective theory for the radion in curved brane scenarios.

Abstract

We study the linearized metric perturbation corresponding to the radion for the generalization of the five dimensional two brane setup of Randall and Sundrum to the case when the curvature of each brane is locally constant but non-zero. We find the wave fuction of the radion in a coordinate system where each brane is sitting at a fixed value of the extra coordinate. We find that the radion now has a mass$^2$, which is negative for the case of de Sitter branes but positive for anti de Sitter branes. We also determine the couplings of the radion to matter on the branes, and construct the four dimensional effective theory for the radion valid at low energies. In particular we find that in AdS space the wave function of the radion is always normalizable and hence its effects, though small, remain finite at arbitrarily large brane separations.