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

TL;DR

This paper explores thick brane models with internal structure in mimetic $f(R)$ gravity, analyzing their stability, gravitational resonances, and the effects of parameters on their inner structure and localization properties.

Contribution

It introduces new thick brane solutions in mimetic $f(R)$ gravity with $f(R)=R+eta R^2$, and studies their stability, resonance behavior, and the impact of parameters on their internal structure.

Findings

All models with $df/dR>0$ are stable.

Graviton zero mode can be localized on the brane.

Inner structure affects gravitational resonances and multi-brane configurations.

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.