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

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.

arXiv comment15 pages, 2 figures, accepted for publication in PLB

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• Cosmological scenario based on the first and second laws of thermodynamics: Thermodynamic constraints on a generalized cosmological model