Gravity in the brane-world for two-branes model with stabilized modulus

TL;DR

This paper analyzes linear gravitational perturbations in a two-brane Randall-Sundrum model with a stabilization mechanism, confirming the recovery of 4D gravity and exploring the Kaluza-Klein spectrum.

Contribution

It provides a complete scheme for perturbation analysis, formulas for mass spectrum evaluation, and insights into stability conditions of the model.

Findings

Zero mode truncation reproduces 4D Einstein gravity

Formulas for Kaluza-Klein mode contributions are derived

Potential tachyonic modes depend on the bulk scalar field configuration

Abstract

We present a complete scheme to discuss linear perturbations in the two-branes model of the Randall and Sundrum scenario with the stabilization mechanism proposed by Goldberger and Wise. We confirm that under the approximation of zero mode truncation the induced metric on the branes reproduces that of the usual 4-dimensional Einstein gravity. We also present formulas to evaluate the mass spectrum and the contribution to the metric perturbations from all the Kaluza-Klein modes. We also conjecture that the model has tachyonic modes unless the background configuration for the bulk scalar field introduced to stabilize the distance between the two branes is monotonic in the fifth dimension.