Generalized second law of thermodynamics for FRW cosmology with logarithmic correction

TL;DR

This paper examines how quantum and thermal corrections to the entropy of cosmological horizons influence the validity of the generalized second law in an accelerating universe, constraining parameters and dark energy temperature.

Contribution

It introduces a modified entropy relation with logarithmic corrections into the GSL analysis for FRW cosmology, exploring constraints on correction parameters and dark energy temperature.

Findings

GSL holds for positive logarithmic correction coefficient in accelerated universe.

In super-accelerated expansion, dark energy temperature is constrained to be below or equal to Hawking temperature.

Logarithmic corrections impact the thermodynamic behavior of the universe.

Abstract

In the previous analyses in the literature about the generalized second law (GSL) in an accelerated expanding universe the usual area relation for the entropy, i.e. $S={A\over 4G}$, was used for the cosmological horizon entropy. But this entropy relation may be modified due to thermal and quantum fluctuations or corrections motivated by loop quantum gravity giving rise to S={A\over 4}+\pi\alpha \ln({A\over 4})+\gamma, where $\alpha$ and $\gamma$ are some constants whose the values are still in debate in the literature. Our aim is to study the constraints that GSL puts on these parameters. Besides, we investigate the conditions that the presence of such modified terms in the entropy puts on other physical parameters the system such as the temperature of dark energy via requiring the validity of GSL. In our study we consider a spatially flat Friedman-Robertson-Walker and assume that the universe is composed of several interacting components (including dark energy). The model is investigated in the context of thermal equilibrium and non-equilibrium situations. We show that in a (super) accelerated universe GSL is valid whenever $\alpha (<)>0$ leading to a (negative) positive contribution from logarithmic correction to the entropy. In the case of super acceleration the temperature of the dark energy is obtained to be less or equal to the Hawking temperature.