A note on the relations between thermodynamics, energy definitions and Friedmann equations

TL;DR

This paper explores the relationship between thermodynamics and Friedmann equations in cosmology, revealing limitations of perfect fluids and proposing models that unify inflation and current acceleration, with implications for dark energy.

Contribution

It introduces a method to solve Friedmann and thermodynamic pressure equations simultaneously, analyzing various energy definitions and their cosmological implications.

Findings

Perfect fluid solutions cannot satisfy both equations simultaneously.

Some solutions may unify inflationary and current acceleration eras.

Constraints on cosmic fluids are discussed with observational considerations.

Abstract

In what follows, we investigate the relation between the Friedmann and thermodynamic pressure equations, through solving the Friedmann and thermodynamic pressure equations simultaneously. Our investigation shows that a perfect fluid, as a suitable solution for the Friedmann equations leading to the standard modelling of the universe expansion history, cannot simultaneously satisfy the thermodynamic pressure equation and those of Friedmann. Moreover, we consider various energy definitions, such as the Komar mass, and solve the Friedmann and thermodynamic pressure equations simultaneously to get some models for dark energy. The cosmological consequences of obtained solutions are also addressed. Our results indicate that some of obtained solutions may unify the dominated fluid in both the primary inflationary and current accelerating eras into one model. In addition, by taking into account a cosmic fluid of a known equation of state, and combining it with the Friedmann and thermodynamic pressure equations, we obtain the corresponding energy of these cosmic fluids and face their limitations. Finally, we point out the cosmological features of this cosmic fluid and also study its observational constraints.