Thick branes with inner structure in mimetic f(R) gravity

In this paper, we study the structure and gravitational resonances of thick branes generated by a mimetic scalar field in f ( R ) gravity. We obtain several typical thick brane solutions for f ( R ) = R + α R 2 . To study their stability, we analyze the tensor perturbation of the metric. It is shown that any thick brane model with d f / d R > 0 is stable and the graviton zero mode can be localized on the brane for each solution, which indicates that the four-dimensional Newtonian gravity can be restored. The effect of the parameter α on the gravitational resonances is studied. As a brane splits into multi sub-branes, the effective potential of the tensor perturbation will have an abundant inner structure with multi-wells, and this will lead to new phenomena of the gravitational resonances.