Cosmological FLRW phase transitions under exponential corrected entropy

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 $\alpha$, the system presents first-order phase transitions above the critical temperature, and for positive $\alpha$, 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.