Thermodynamics of the universes admitting isotropic radiation

TL;DR

This paper explores the thermodynamic properties of Stephani Universes, especially those with isotropic radiation, deriving key expressions and analyzing models including an ultrarelativistic gas.

Contribution

It provides a detailed thermodynamic analysis of Stephani Universes with isotropic radiation, including new expressions for sound speed and solution constraints.

Findings

Derived general expressions for sound speed in these universes.

Identified constraints on solutions based on physical properties.

Analyzed a specific ultrarelativistic gas model.

Abstract

The thermodynamic interpretation of the Stephani Universes is studied in detail. The general expression of the speed of sound and of the thermodynamic schemes associated with a thermodynamic solution is obtained. The constraints imposed on the solutions by considering some significant physical properties are analyzed. We focus on the models where the cosmological observer measures isotropic radiation. We consider some examples, and a solution that models an ultrarelativistic gas is analyzed in detail.