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, 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.

arXiv comment30 pages, 10 figures; Sec IV updated; Appendix C added; minor other changes made; matches the published version

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• Spinor Walls in Five-Dimensional Warped Spacetime
• Spontaneous branes formation
• Formation and evolution of a 2-brane structure in multidimensional $f(R)$ gravity
• Thick branes in the scalar-tensor representation of $f(R,T)$ gravity
• New brane-like solutions in modified four-dimensional Einstein-Gauss-Bonnet gravity