An attempt to add Barrow entropy in $f(R)$ gravity

TL;DR

This paper explores combining Barrow entropy with $f(R)$ gravity to modify Friedmann equations, analyzing the universe's evolution through a specific $f(R)$ model and thermodynamic principles.

Contribution

It introduces a novel approach to integrate Barrow entropy into $f(R)$ gravity, deriving modified cosmological equations and analyzing their implications.

Findings

Modified Friedmann equations incorporating Barrow entropy and $f(R)$ gravity.

Calculated cosmological parameters for a specific $f(R)$ model.

Discussed the universe's dynamic evolution under the combined framework.

Abstract

In this work, a way to consider together two originally different corrections to the Friedmann equations is presented. The first is the Barrow entropy, which imposes a fractal structure on the black hole horizon area. While the second is the well-known $f(R)$ gravity, which comes from a generalization of the Einstein-Hilbert action. Using the ideas of gravity-thermodynamics conjecture, these two models are combined. Then the modified Friedmann equation is obtained. Choosing a particular $f(R)$ model, an application is investigated. The state parameter and the density parameters for matter and dark energy are calculated. With these results, the dynamic evolution of the universe is discussed.