Tensor perturbations of $f(R)$-branes

TL;DR

This paper studies how tensor perturbations behave in $f(R)$ gravity models with flat thick branes, showing conditions for decoupling, localization of gravity, and stability considerations.

Contribution

It provides a detailed analysis of tensor perturbations in $f(R)$-brane models, including conditions for decoupling and localization of gravity, extending previous work in standard gravity.

Findings

Tensor perturbations decouple from scalar field perturbations under certain gauges.

The perturbed equation simplifies to Klein-Gordon form only for constant curvature or $f(R)=R$.

Gravity localization is possible on some flat thick branes under specific conditions.

Abstract

We analyze the tensor perturbations of flat thick domain wall branes in $f(R)$ gravity. Our results indicate that under the transverse and traceless gauge, the metric perturbations decouple from the perturbation of the scalar field. Besides, the perturbed equation reduces to the familiar Klein-Gordon equation for massless spin-2 particles only when the bulk curvature is a constant or when $f(R)=R$. As an application of our results, we consider the possibility of localizing gravity on some flat thick branes. The stability of these brane solutions is also shortly discussed.