Braneworld cosmological solutions and their stability

TL;DR

This paper analyzes the stability of cosmological solutions in a braneworld model with a scalar-curvature term, revealing conditions for static solutions and their stability, and comparing results with the Randall-Sundrum model.

Contribution

It extends previous work by including the scalar-curvature term in the brane action, exploring static solutions with various geometries and their stability properties.

Findings

Expanding de Sitter solution is an attractor.

Expanding Friedmann solution is a repeller.

Static solutions with matter can be stable across different geometries.

Abstract

We consider cosmological solutions and their stability with respect to homogeneous and isotropic perturbations in the braneworld model with the scalar-curvature term in the action for the brane. Part of the results are similar to those obtained by Campos and Sopuerta for the Randall-Sundrum braneworld model. Specifically, the expanding de Sitter solution is an attractor, while the expanding Friedmann solution is a repeller. In the braneworld theory with the scalar-curvature term in the action for the brane, static solutions with matter satisfying the strong energy condition exist not only with closed spatial geometry but also with open and flat ones even in the case where the dark-radiation contribution is absent. In a certain range of parameters, static solutions are stable with respect to homogeneous and isotropic perturbations.