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

A bstract We explore thick branes in f ( R, ϕ, X ) gravity. We obtain the linear tensor perturbation equation of f ( R, ϕ, X ) branes and show that the branes are stable against the tensor perturbations under the condition of ∂ f R ϕ X ∂ R > 0 . 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, ϕ, 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, ϕ, X ) thick brane are also discussed.