Thick branes with inner structure in mimetic $f(R)$ gravity

Abstract

In this paper, we study the structure and gravitational resonances of thick branes generated by a mimetic scalar field in $f(R)$ gravity. We obtain several typical thick brane solutions for $f(R)=R+\alpha R^2$. To study their stability, we analyze the tensor perturbation of the metric. It is shown that any thick brane model with $df/dR>0$ is stable and the graviton zero mode can be localized on the brane for each solution, which indicates that the four-dimensional Newtonian gravity can be restored. The effect of the parameter $\alpha$ on the gravitational resonances is studied. As a brane splits into multi sub-branes, the effective potential of the tensor perturbation will have an abundant inner structure with multi-wells, and this will lead to new phenomena of the gravitational resonances.

16 pages, 26 figures

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• Consistency between black hole and mimetic gravity -- Case of $(2+1)$-dimensional gravity
• Structure formation in mimetic gravity
• Multi-kink brane in Gauss-Bonnet gravity and its stability
• Scalar perturbation of gravitating double-kink solutions
• Characteristic modes of thick brane model: resonances and quasinormal modes
• Evolution of scalar field resonances in a braneworld
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• Isotropic stellar model in mimetic theory
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• Pure geometric $f(R)$ branes
• Thick brane models in generalized mimetic gravity