Generalized second law of thermodynamics for FRW cosmology with logarithmic correction

¹ Department of Physics, University of Tehran - P.O.B. 14395-547, Tehran 14399-55961, Iran
² Center for Advanced Mathematics and Physics, National University of Sciences and Technology (NUST) Islamabad, Pakistan

^a mohsenisad@ut.ac.ir
^b mjamil@camp.nust.edu.pk

Received: 29 September 2010
Accepted: 30 November 2010

Abstract

In the previous analyses in the literature about the generalized second law (GSL) in an accelerated expanding universe the usual relation for the entropy, i.e. , 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/4+πα ln(A/4)+γ, where α and γ 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 universe and assume that it 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 the GSL is valid whenever α(<)>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 than or equal to the Hawking temperature.