Entropy and its conservation in expanding Universe

TL;DR

This paper explores a conserved charge in general relativity across different cosmic eras, showing it corresponds to entropy in inflation, matter, and radiation-dominated periods, supported by numerical analysis.

Contribution

It demonstrates that a recently proposed conserved charge in general relativity aligns with entropy in various expanding universe phases, providing new insights into gravitational thermodynamics.

Findings

Conserved charge equals Bekenstein-Hawking entropy in de Sitter space.

Charge corresponds to matter and radiation entropy in respective eras.

Numerical analysis supports the interpretation of the conserved charge as entropy.

Abstract

We investigate properties of the conserved charge in general relativity, recently proposed by one of the present authors with his collaborators, in the inflation era, the matter dominated era and the radiation dominated era of the expanding Universe. We show that the conserved charge in the inflation era becomes the Bekenstein-Hawking entropy for de Sitter space, and it becomes the matter entropy and the radiation entropy in the matter and radiation dominated eras, respectively, while the charge itself is always conserved. These properties are qualitatively confirmed by a numerical analysis of a model with a scalar field and radiations. Results in this paper provide more evidences on the interpretation that the conserved charge in general relativity corresponds to entropy.