Modified Gravity in the framework of holographic dark energy

Abstract: The modified gravity is considered in the framework of the holographic dark energy. An analysis of the autonomous system, the critical points and their stability is presented. Unlike the dark energy models based on $f(R)$, it is found that working in the holographic frame enriches the possibility of accelerated and matter type points for different cosmological scenarios, making viable trajectories of successful $f(R)$ models that are not allowed without the consideration of the holographic framework. The implications for the Hu-Sawicki model are analyzed.