Brane $f(\cal R)$ gravity

TL;DR

This paper explores a brane world model with a bulk action as a general function of Ricci scalar, deriving Einstein equations and showing potential explanations for cosmic acceleration and galaxy rotation curves.

Contribution

It derives Einstein equations for a brane with a general $f(\ ext{R})$ bulk action and presents solutions explaining acceleration and galaxy dynamics.

Findings

Cosmological solutions suggest accelerated expansion.

Spherically symmetric solutions can explain galaxy rotation curves.

A conserved geometric quantity acts like matter in the equations.

Abstract

We consider a brane world scenario in which the bulk action is assumed to have the form of a generic function of the Ricci scalar $f(\mathcal{R})$ and derive the resulting Einstein field equations on the brane. In a constant curvature bulk a conserved geometric quantity appears in the field equations which can be associated with matter. We present cosmological and spherically symmetric solutions by assuming specific forms for $f(\mathcal{R})$ and show that the former can explain an accelerated expanding universe while the latter may account for galaxy rotation curves.