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.
Highlights
Appearance of higher derivatives in equations of motion, investigation on junction conditions of f (R) gravity in the brane world scenarios opens the possibility of a new class of thin brane solutions [5,6,7,8,9,10,11]
Nontrivial analytical thick brane solutions with nonconstant curvature in f (R) theory were first investigated in ref. [21] and further considered in refs. [16, 22,23,24,25,26,27,28,29,30,31,32]
A localized massless graviton KK mode contributes to the four-dimensional Newtonian potential and the massive ones lead to corrections to the Newtonian potential
Summary
The perturbations of the metric couple to the perturbations of bulk fields Each type of these perturbation modes obeys independent equations of motion at the linearized level [35, 37, 38, 40, 41]. The perturbations of a scalar field in the bulk does not appear in the equation of motion of the tensor mode. We examine the following linear tensor perturbations in the context of f (R) gravity: ds2 = a2(y)(ημν + hμν )dxμdxν + dy2 + b2(y)δijdxidxj ,. The case m2 − l2 0 and m2 < 0 will result in some apparent tachyon states of the graviton in the M4;. There is the possibility of the existence of other linear instabilities in the spacetime considered here
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