Pure geometric thick $f(R)$-branes: stability and localization of gravity

TL;DR

This paper presents two stable five-dimensional thick brane models in pure metric $f(R)$ gravity, demonstrating the localization of gravity and minimal corrections to Newton's law from massive modes.

Contribution

The study introduces two exactly solvable $f(R)$ thick brane models, analyzing their stability and gravity localization in the Einstein frame.

Findings

Both models are stable against linear perturbations.

The gravitational zero mode is localized on the brane.

Massive modes are nonlocalized, causing small corrections to Newton's law.

Abstract

We study two exactly solvable five-dimensional thick brane world models in pure metric $f(R)$ gravity. Working in the Einstein frame, we show that these solutions are stable against small linear perturbations, including the tensor, vector, and scalar modes. For both models, the corresponding gravitational zero mode is localized on the brane, which leads to the four-dimensional Newton's law; while the massive modes are nonlocalized and only contribute a small correction to the Newton's law at a large distance.