Thermodynamic behavior of cosmological models with fractional entropy

TL;DR

This paper explores a cosmological model based on fractional entropy, deriving generalized Friedmann equations, analyzing thermodynamic stability, and fitting the model to observational data, showing the fractional parameter influences cosmic expansion.

Contribution

It introduces a fractional entropy-based cosmological model, derives its thermodynamic properties, and constrains it using observational data, highlighting the impact of the fractional parameter on cosmic evolution.

Findings

The fractional model is thermodynamically stable during late-time acceleration.

Data favors the fractional parameter close to the General Relativity limit, $oxed{ ext{α} o 2}$.

Decreasing $ ext{α}$ increases $H_0$ and decreases $ ext{Ω}_{m0}$, affecting expansion dynamics.

Abstract

We investigate the thermodynamic and phenomenological implications of a cosmological model governed by fractional entropy applied to the apparent horizon of a flat Friedmann-Lema\^{i}tre-Robertson-Walker (FLRW) universe. By utilizing the unified first law of thermodynamics alongside the Kodama-Hayward temperature, we derive a generalized set of Friedmann equations characterized by a fractional parameter $\alpha \in (1,2]$. The thermodynamic analysis reveals that the specific heats $C_V$ and $C_p$ share the same sign and depend solely on the deceleration parameter, demonstrating that the fractional model is thermodynamically stable during the late-time accelerated expansion and does not exhibit phase transitions. To constrain the background dynamics, we confront the truncated fractional model with a joint sample of late-time observational data, including Cosmic Chronometers, Pantheon+SH0ES supernovae, and the latest DESI DR2 Baryon Acoustic Oscillations. Exploring the physically motivated range $ 1 < \alpha \leq 2 $, we find that the fit quality degrades monotonically as $\alpha$ decreases from the General Relativity limit, with the data favoring $\alpha$ close to $2$ while yielding $H_0 = 69.50 \pm 0.42$ km/s/Mpc and $\Omega_{m0} = 0.292 \pm 0.008 $ at $\alpha = 2$. Decreasing $\alpha$ coherently shifts $H_0$ upward and $\Omega_{m0} $ downward, revealing that the fractional parameter modulates the background expansion in a physically nontrivial and observationally distinguishable way.