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arXiv · 2011.03927

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

Jing Chen·Wen-Di Guo·Yu-Xiao Liu
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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.

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Jing Chen, Wen-Di Guo, Yu-Xiao Liu. 2020-11-08. Thick branes with inner structure in mimetic $f(R)$ gravity. https://doi.org/10.1140/epjc%2Fs10052-021-09504-y

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