A dynamical system approach to the holographic dark energy in a modified theory of gravity

Abstract

In this paper, we carry a dynamical system analysis of a holographic dark energy model of a modified theory of gravity based on braneworld scenario. The infra-red cutoff of the holographic dark energy is considered to be the Hubble scale in a first approach and the Ricci scalar curvature scale in a second approach. We present a detailed analysis of the critical points, their stability and the late-time cosmological viability of the solutions in the phase space. For both holographic dark energy models, we investigate the case of a noninteracting braneworld and extend our analysis to the interacting case between dark energy and cold dark matter by considering some specific forms of interaction.