Entropy evolution of universes with initial and final de Sitter eras

TL;DR

This paper examines the entropy evolution in two cosmological models with initial and final de Sitter phases, demonstrating that both tend toward thermodynamic equilibrium, aligning with the second law of thermodynamics.

Contribution

It compares two recent cosmological models with de Sitter phases, analyzing their entropy behavior and thermodynamic consistency during cosmic evolution.

Findings

Both models approach thermodynamic equilibrium in the final de Sitter phase.

Entropy of the apparent horizon plus matter and radiation increases and is concave.

Models not approaching equilibrium conflict with the second law of thermodynamics.

Abstract

This brief report studies the behavior of entropy in two recent models of cosmic evolution by J.A.S. Lima, S. Basilakos, and F.E.M. Costa [Phys. Rev. D \underline{86}, 103534 (2012)], and J. A. S. Lima, S. Basilakos, and J. Sol\'{a} [arXiv:1209.2802]. Both start with an initial de Sitter expansion, go through the conventional radiation and matter dominated eras to be followed by a final and everlasting de Sitter expansion. In spite of their outward similarities (from the observational viewpoint they are arbitrary close to the conventional $\Lambda$CDM model), they deeply differ in the physics behind them. Our study reveals that in both cases the universe approaches thermodynamic equilibrium in the last de Sitter era in the sense that the entropy of the apparent horizon plus that of matter and radiation inside it increases and is concave. Accordingly, they are consistent with thermodynamics. Cosmological models that do not approach equilibrium at the last phase of their evolution appear in conflict with the second law of thermodynamics.