Linear stability of f(R, φ, X) thick branes: tensor perturbations

We explore thick branes in f (R, phi, X) gravity. We obtain the linear tensor perturbation equation of f (R, phi, X) branes and show that the branes are stable against the tensor perturbations under the condition of In order to obtain thick brane solutions of the fourth-order field equations in this theory, we employ the reconstruction technique. We get exact solutions of the specific f (R, phi, X) thick brane generated by a noncanonical scalar field. It is shown that the zero mode of the graviton for the thick brane is localized under certain conditions. This implies that the four-dimensional Newtonian potential is recovered on the brane. The effects of the Kaluza-Klein modes of the graviton for the f (R, phi, X) thick brane are also discussed.