Pure geometric $f(R)$ branes

TL;DR

This paper explores pure geometric $f(R)$ brane models in five-dimensional spacetime, classifying solutions based on the cosmological constant, analyzing their stability, and localizing gravity modes in different cosmological scenarios.

Contribution

It provides explicit solutions for $f(R)$ branes with constant scalar curvature and analyzes their stability and gravity localization properties across different cosmological constants.

Findings

Stable solutions for Minkowski, de Sitter, and anti-de Sitter branes.

Localization of gravity zero modes and Kaluza-Klein modes depending on brane type.

Tensor fluctuation analysis consistent in Einstein and Jordan frames.

Abstract

In this paper, we investigate pure geometric $f(R)$ cosmology branes embedded in five-dimensional spacetime. The form of $f(R)$ is chosen as a polynomial. The Five-dimensional scalar curvature $R$ is assumed to be constant. Based on the value of the four-dimensional cosmological constant $\lambda_4$, the branes can be classified into Minkowski, de Sitter, and de anti-de Sitter cases. Solutions for each case can be calculated. These solutions are stable against linear tensor perturbations in all cases. In the Minkowski brane case, the zero mode of gravity can be localized on the brane. In the de Sitter brane case, the zero mode and one massive Kaluza-Klein mode can be localized on the brane. In the anti-de Sitter brane case, all massive Kaluza-Klein modes can be localized on the brane. The results of the analysis of tensor fluctuations are the same in both the Einstein frame and the Jordan frame.