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

TL;DR

This paper explores the stability and properties of thick brane solutions in higher-dimensional $f(R)$ gravity, analyzing tensor perturbations and Kaluza-Klein modes to understand graviton behavior in such models.

Contribution

It provides new stable thick brane solutions in six-dimensional $f(R)$ gravity and examines their tensor perturbations and graviton spectra.

Findings

Spacetime with specific metric ansatz is stable against tensor perturbations.

Two sets of thick brane solutions are constructed in six dimensions.

Effective potentials for Kaluza-Klein modes are analyzed for the solutions.

Abstract

We study brane worlds in an anisotropic higher-dimensional spacetime within the context of $f(R)$ gravity. Firstly, we demonstrate that this spacetime with a concrete metric ansatz is stable against linear tensor perturbations under certain conditions. 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 solved $f(R)$ models in higher dimensions.