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

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 $f(R)=R+ϵR^n$, where the small parameter $ϵ$ controls the deviation from the standard thick brane case.