Holographic Dark Energy Like in $f(R)$ Gravity

TL;DR

This paper explores the connection between $f(R)$ gravity and holographic dark energy, deriving evolution equations and the equation of state with varying gravitational constant, contributing to understanding dark energy models.

Contribution

It introduces a new energy density from $f(R)$ gravity that mimics holographic dark energy and derives its evolution considering a varying gravitational constant.

Findings

Derived a differential equation for the energy density parameter.

Established a relation for the equation of state at low redshifts with $G$ variation.

Provided insights into dark energy behavior in $f(R)$ gravity frameworks.

Abstract

We investigate the corresponding relation between $f(R)$ gravity and holographic dark energy. We introduce a kind of energy density from $f(R)$ which has role of the same as holographic dark energy. We obtain the differential equation that specify the evolution of the introduced energy density parameter based on varying gravitational constant. We find out a relation for the equation of state parameter to low redshifts which containing varying $G$ correction.