The structure of $f(R)$-brane model

TL;DR

This paper explores how the parameter in $f(R)$-brane models influences graviton localization and resonance phenomena, revealing conditions under which resonant modes appear or are absent, affecting gravity's behavior on the brane.

Contribution

It analyzes the impact of the parameter $eta$ in $f(R)$ gravity on graviton resonance and localization, providing new insights into the structure of $f(R)$-brane models.

Findings

Inner brane structure can be tuned by $eta$

No graviton resonance in some parameter ranges

Resonant modes can exist without internal brane structure

Abstract

Recently, a family of interesting analytical brane solutions were found in $f(R)$ gravity with $f(R)=R+\alpha R^2$ in Ref. [Phys. Lett. B 729, 127 (2014)]. In these solutions, inner brane structure can be turned on by tuning the value of the parameter $\alpha$. In this paper, we investigate how the parameter $\alpha$ affects the localization and the quasilocalization of the tensorial gravitons around these solutions. It is found that, in a range of $\alpha$, despite the brane has an inner structure, there is no graviton resonance. However, in some other regions of the parameter space, although the brane has no internal structure, the effective potential for the graviton KK modes has a singular structure, and there exists a series of graviton resonant modes. The contribution of the massive graviton KK modes to the Newton's law of gravity is discussed shortly.