Cosmological FLRW phase transitions under exponential corrected entropy

TL;DR

The paper investigates how exponential corrections to horizon entropy modify the thermodynamics and dynamics of a flat FLRW universe. By integrating the exponential entropy into the unified first law and employing the Hayward–Kodama surface gravity, it derives a modified Friedmann equation and an effective horizon equation of state, revealing new thermodynamic features such as heat-capacity divergences and phase transitions controlled by the deformation parameter $\alpha$. Phase-structure analysis shows a single critical point with $T<0$ for $\alpha>0$ and a more intricate, reentrant behavior for $\alpha<0$, though only certain branches remain physically viable under horizon-causality constraints. When confronting cosmological data (Pantheon+ SH0ES and cosmic chronometers), the model yields a background expansion nearly indistinguishable from ΛCDM, with a best-fit $\alpha$ near zero; nonetheless small negative $\alpha$ can mildly raise $H_0$, offering a potential, albeit modest, alleviation of the $H_0$ tension. The results indicate that horizon thermodynamics with exponential corrections can coexist with standard cosmology while imprinting nontrivial thermodynamic structure that may reflect quantum-gravitational microphysics.

Abstract

This work considers how exponential corrections to the Bekenstein-Hawking entropy formula affect the thermodynamic behavior of the FLRW cosmological model. These corrections drastically change the form of the Friedman field equations inducing non-trivial phase transition behavior. For negative values of the trace parameter $α$, the system presents first-order phase transitions above the critical temperature, and for positive $α$, the system undergoes a reentrant phase transition. As these corrections are presumably relevant at the early Universe stage, to corroborate the presence of some potential vestige of this contribution in the current era, a study has been carried out comparing observational data and current values of the Hubble parameter.

Figures (6)

• Figure 1: Heat capacity $C_P$ as a function of the reduced volume $v$ for two representative values of the deformation parameter, $\alpha = 1$ and $\alpha = -1$. The sign of $\alpha$ controls the thermodynamic behavior of the system: positive $\alpha$ leads to a stable branch with positive heat capacity, while a negative $\alpha$ from one side introduces regions of negative heat capacity, signaling possible thermodynamic instabilities. Besides, at points where the heat capacity diverges, a phase transition occurs.
• Figure 2: The trend of the pressure versus the reduced volume for different values of the temperature, considering $\alpha=1$ (left panel) and $\alpha=-1$ (right panel).
• Figure 3: The behavior of the Gibbs free energy versus the pressure for increasing values of the temperature $T$.
• Figure 4: The behavior of the Gibbs free energy versus the pressure for increasing values of the temperature $T$.
• Figure 5: This plot show a comparison of the modified Friedmann equation (\ref{['H(z)']}) in our model with $\alpha=\pm 2$ (solid line) and the standard $\Lambda$CDM prediction from Planck 2018 parameters (black dashed line) against observational data from cosmic chronometers (black point) Jimenez2003Simon2005Stern2010Moresco2012Zhang2014Moresco2015Moresco2016Ratsimbazafy2017. The positive $\alpha$ case leads to a faster growth of $H(z)$ at high redshifts, while negative $\alpha$ case predicts lower expansion rates