Thick brane in $f(R)$ gravity with Palatini dynamics

TL;DR

This paper explores a five-dimensional thick brane model in Palatini $f(R)$ gravity, providing exact solutions and analyzing deviations from standard models through a perturbative approach with a small parameter.

Contribution

It introduces a novel thick brane scenario in Palatini $f(R)$ gravity with exact solutions and a perturbative analysis of deviations from Einstein gravity.

Findings

Exact solutions for scalar field and warp factor in Palatini $f(R)$ gravity.

Perturbative analysis with $f(R)=R+\epsilon R^n$ showing deviations from standard brane models.

Insights into the effects of Palatini modifications on brane structure.

Abstract

This work deals with modified gravity in five dimensional spacetime. We study a thick Palatini $f(R)$ brane, that is, a braneworld scenario described by an anti-de Sitter warped geometry with a single extra dimension of infinite extent, sourced by real scalar field under the Palatini approach, where the metric and the connection are regarded as independent degrees of freedom. We consider a first-order framework which we use to provide exact solutions for the scalar field and warp factor. We also investigate a perturbative scenario such that the Palatini approach is implemented through a Lagrangian $f(R)=R+\epsilon R^n$, where the small parameter $\epsilon$ controls the deviation from the standard thick brane case.