Modified Friedmann equations from fractional entropy

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 sh...

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Bibliographic Details
Published in:arXiv.org 2023-09
Main Authors: Çoker, Zeynep, Ökcü, Özgür, Aydiner, Ekrem
Format: Article
Language:English
Subjects:
Deceleration
Energy conservation law
Entropy
Equations of state
Horizon
Mathematical analysis
Parameters
Singularities
Thermodynamics
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Summary: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
ISSN:2331-8422
DOI:10.48550/arxiv.2308.10212