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

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Cited by in corpus (6)

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• Gravitational wave probes of Barrow cosmology with LISA standard sirens
• Entropy as logarithmic term of the central charge and modified Friedmann equation in AdS/CFT correspondence
• The $D$-dimensional charged AdS black holes solutions in polytropic dark energy from Barrow entropy
• Holographic thermodynamic relation for dissipative and non-dissipative universes in a flat FLRW cosmology
• Cosmological scenario based on the first and second laws of thermodynamics: Thermodynamic constraints on a generalized cosmological model