Reconstructing f(R) theory according to holographic dark energy

Abstract

In this paper a connection between the holographic dark energy model and the $f(R)$ theory is established. We treat the $f(R)$ theory as an effective description for the holographic dark energy and reconstruct the function $f(R)$ with the parameter $c>1$, $c=1$ and $c<1$, respectively. We show the distinctive behavior of each cases realized in $f(R)$ theory, especially for the future evolution.