Reconstructing f(R) theory according to holographic dark energy

TL;DR

This paper establishes a link between holographic dark energy and $f(R)$ gravity, reconstructing the $f(R)$ function for different parameter regimes to analyze their future cosmological evolution.

Contribution

It introduces a method to reconstruct $f(R)$ gravity models based on holographic dark energy parameters, highlighting their distinct future behaviors.

Findings

Different $f(R)$ models correspond to different holographic parameter regimes.

Reconstructed $f(R)$ functions exhibit unique future evolution patterns.

The approach provides a unified framework for connecting dark energy models with modified gravity.

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.