Tensor perturbations of Palatini $f(\mathcal{R})$-branes

TL;DR

This paper explores thick brane solutions in Palatini $f( ext{R})$ gravity, analyzing tensor perturbations, stability, and graviton localization, demonstrating the recovery of 4D gravity and discussing KK modes and Newtonian corrections.

Contribution

It provides analytical solutions for $f( ext{R})= ext{R}+ ext{α R}^2$ branes in Palatini gravity, analyzing stability, graviton localization, and KK mode spectra.

Findings

Tensor perturbations are stable for $df/d\mathcal{R}>0$.

Graviton zero mode can be localized, enabling 4D gravity.

KK modes contribute corrections to Newtonian potential.

Abstract

We investigate the thick brane model in Palatini $f(\mathcal{R})$ gravity. The brane is generated by a real scalar field with a scalar potential. We solve the system analytically and obtain a series of thick brane solutions for the $f(\mathcal{R})=\mathcal{R}+\alpha \mathcal{R}^2$-brane model. It is shown that tensor perturbations of the metric are stable for $df({\mathcal{R}})/d{\mathcal{R}}>0$. For nonconstant curvature solutions, the graviton zero mode can be localized on the brane, which indicates that the four-dimensional gravity can be recovered on the brane. Mass spectrum of graviton KK modes and their corrections to the Newtonian potential are also discussed.