Cosmological dynamics of brane f(R) gravity

TL;DR

This paper investigates the cosmological behavior of brane world models with a general f(R) gravity in the bulk, relaxing symmetry conditions, and analyzes their solutions and stability properties.

Contribution

It introduces a framework for brane f(R) gravity without Z2 symmetry, deriving new cosmological solutions and analyzing their stability and evolution.

Findings

Existence of exponential and power-law solutions for vacuum brane space-times.

Matter-dominated epoch requires ordinary matter in the bulk.

Universe transitions from unstable matter epoch to stable accelerated expansion.

Abstract

The cosmological dynamics of a brane world scenario where the bulk action is taken as a generic function of the Ricci scalar is considered in a framework where the use of the $\mathbb{Z}_2$ symmetry and Israel junction conditions are relaxed. The corresponding cosmological solutions for some specific forms of $f(\mc{R})$ are obtained and shown to be in the form of exponential as well as power law for a vacuum brane space-time. It is shown that the existence of matter dominated epoch for a bulk action in the form of a power law for $\cal R$ can only be obtained in the presence of ordinary matter. Using phase space analysis, we show that the universe must start from an unstable matter dominated epoch and eventually falls into a stable accelerated expanding phase.