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

TL;DR

This work analyzes linear perturbations in the Randall–Sundrum two-brane setup with Goldberger–Wise stabilization, deriving the full mass spectrum and the KK contributions to metric perturbations. It shows that stabilization removes the massless scalar radion and, under zero-mode truncation, yields 4D Einstein gravity on both branes, while the lowest tensor and scalar masses depend on the brane separation $d$ and the bulk scalar dynamics, with explicit expressions and regimes studied. A Green’s-function, contact-interaction approach is developed to sum KK contributions and confirm the long-range gravity is governed by the zero mode and scalar sector, with KK modes providing short-range corrections. The findings establish a consistent linear perturbation framework and clarify the conditions under which tachyonic instabilities may arise, offering a basis for exploring nonlinear effects and phenomenology in stabilized brane-world scenarios.

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.