Tensor Perturbations and Thick Branes in Higher-dimensional \(f(R)\) Gravity

Abstract

We study brane worlds in an anisotropic higher-dimensional spacetime within the context of \(f(R)\) gravity. Firstly, with a concrete metric ansatz, we demonstrate that this spacetime is stable against linear tensor perturbations under certain conditions. We provide a conclusion for higher-dimensional \(f(R)\) gravity in this particular metric. Moreover, the Kaluza-Klein modes of the graviton are analyzed. Secondly, we investigate thick brane solutions in six dimensions and their properties. We further exhibit two sets of solutions for thick branes. At last, the effective potential of the Kaluza-Klein modes of the graviton is discussed for the two solvable \(f(R)\) models in higher dimensions.