Pure geometric thick f(R)-branes: stability and localization of gravity

We study two exactly solvable five-dimensional thick brane worldmodels in puremetric f (R) gravity. Working in the Einstein frame, we show that these solutions are stable against small linear perturbations, including the tensor, vector, and scalar modes. For both models, the corresponding gravitational zero mode is localized on the brane, which leads to the four-dimensional Newton law; while the massive modes are non-localized and only contribute a small correction to the Newton law at a large distance.