Brane f(R) gravity cosmologies

TL;DR

This paper derives cosmological equations for $f(R)$ brane gravity using generalized Israel junction conditions, revealing conditions for static and non-static brane solutions in a five-dimensional bulk.

Contribution

It introduces a new framework for analyzing $f(R)$ brane cosmologies with generalized junction conditions, highlighting the role of Weyl tensor and bulk matter in brane dynamics.

Findings

Existence of non-static $dS_4$ brane in $AdS_5$ bulk with zero Weyl tensor.

Static brane solutions when Weyl tensor contribution is non-zero.

Need for dynamical bulk matter for more general non-static configurations.

Abstract

By the application of the generalized Israel junction conditions we derive cosmological equations for the fourth-order $f(R)$ brane gravity and study their cosmological solutions. We show that there exists a non-static solution which describes a four-dimensional de-Sitter $(dS_4)$ brane embedded in a five-dimensional anti-de-Sitter $(AdS_5)$ bulk for a vanishing Weyl tensor contribution. On the other hand, for the case of a non-vanishing Weyl tensor contribution, there exists a static brane only. We claim that in order to get some more general non-static $f(R)$ brane configurations, one needs to admit a dynamical matter energy-momentum tensor in the bulk rather than just a bulk cosmological constant.