Randall-Sundrum limit of f(R) brane-world models

TL;DR

This paper derives junction conditions for five-dimensional f(R) gravity that reduce to Randall-Sundrum conditions in the Einstein limit, and demonstrates their application to cosmological models on the brane.

Contribution

It introduces a method to obtain junction conditions for f(R) brane-world models that smoothly transition to the Randall-Sundrum case in the Einstein limit.

Findings

The junction conditions reduce to standard Randall-Sundrum conditions as f(R) approaches R.

Application to a Friedmann universe shows the derived equations recover the Randall-Sundrum Friedmann equation.

The approach provides a consistent way to study f(R) modifications in brane-world cosmology.

Abstract

By setting some special boundary conditions in the variational principle we obtain junction conditions for the five-dimensional $f(R)$ gravity which in the Einstein limit $f(R)\rightarrow R$ transform into the standard Randall-Sundrum junction conditions. We apply these junction conditions to a particular model of a Friedmann universe on the brane and show explicitly that the limit gives the standard Randall-Sundrum model Friedmann equation.