Thick brane in f (R) gravity with Palatini dynamics

This work deals with modified gravity in five-dimensional space-time. 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 a 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 + is an element of R-n, where the small parameter is an element of controls the deviation from the standard thick brane case. In both cases it is found that the warp factor tends to localize the extra dimension due to the nonlinear corrections.