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.

15 pages, 2 figures, accepted for publication in PLB

References in corpus (7)

• The Confrontation between General Relativity and Experiment
• f(R,T) gravity
• Thermodynamic Behavior of Friedmann Equation at Apparent Horizon of FRW Universe
• Friedmann Equations of FRW Universe in Scalar-tensor Gravity, f(R) Gravity and First Law of Thermodynamics
• Thermodynamical Properties of Apparent Horizon in Warped DGP Braneworld
• Barrow entropic dark energy: A member of generalized holographic dark energy family
• Gravity and Scalar Fields