Modified Friedmann equations from fractional entropy

TL;DR

This paper derives modified Friedmann equations using fractional entropy in two frameworks, showing that fractional effects influence the initial singularity and the evolution of the universe, with potential constraints on the equation of state.

Contribution

It introduces fractional entropy into Friedmann equations via thermodynamics and entropic gravity, revealing new effects on cosmic evolution and singularity accessibility.

Findings

Generalized second law always holds within the apparent horizon.

Fractional effects modify the deceleration parameter in flat universe.

Initial singularity remains accessible despite fractional corrections.

Abstract

Based on the fractional black hole entropy (Jalalzadeh S. et al., Eur. Phys. J. C, 81 (2021) 632), we derive the modified Friedmann equations from two different frameworks. First, we consider the modifications of Friedmann equations from the first law of thermodynamics at the apparent horizon. We show that the generalized second law (GSL) of thermodynamics always holds in a region bounded by the apparent horizon. Then, we obtain Friedmann equations from Verlinde's entropic gravity framework. We also compute the fractional corrections to the deceleration parameter $q$ in the flat case $k=0$ for both frameworks. Furthermore, we consider the time to reach the initial singularity for the two frameworks. The results indicate that the initial singularity is accessible for both frameworks. However, fractional effects may provide a constraint on the equation of state parameter in the entropic gravity scenario since the time is imaginary for $-2/3\alpha<\omega<-1/3$.