Thermodynamic analysis of universes with the initial and final de Sitter eras

Abstract

Our aim is studying the thermodynamics of cosmological models including initial and final de Sitter eras. For this propose, bearing Cai–Kim temperature in mind, we investigate the thermodynamic properties of a dark energy (DE) candidate with variable energy density, and show that the state parameter of this dark energy candidate [Formula: see text] should obey the [Formula: see text] constraint, whiles there is no interaction between the fluids filled the universe, and the universe is not in the de Sitter eras. Additionally, based on the thermal fluctuation theory, we study the possibility of inducing fluctuations to the entropy of the DE candidate due to a mutual interaction between the cosmos sectors. Therefore, we find a relation between the thermal fluctuations and the mutual interaction between the cosmos sectors, whiles the DE candidate has a varying energy density. Finally, bearing the coincidence problem in mind, we derive a constraint on the vacuum energy, and investigate its relation with the entropy evolution of the DE candidate. We also point to a model with initial and final de Sitter eras in which a gravitationally induced particle production process leads to change the expansion eras, whiles the corresponding pressure is considered as the cause of current accelerated phase. We study its thermodynamics, and show that such processes may also leave thermal fluctuations into the system. We also find an expression between the thermal fluctuations and the particle production rate. Finally, we use Hayward–Kodama temperature to get a relation for the horizon entropy in models including the gravitationally induced particle production process. Our study shows that the first law of thermodynamics is available on the apparent horizon whiles, the gravitationally induced particle production process, as the DE candidate, may add an additional term to the Bekenstein limit of the horizon. The relation between the validity of the second law of thermodynamics and the gravitationally particle production process is also studied.