Bouncing universe in a heat bath

TL;DR

This paper develops a thermal model for photon modes in a bouncing universe with Lorentz-breaking dispersion, analyzing thermodynamic properties across different cosmic epochs and revealing conditions for potential instability.

Contribution

It introduces an analytical thermal description of photon modes in a bouncing universe with Lorentz violation, exploring thermodynamics during various cosmic eras.

Findings

Spectral radiance, entropy, and Helmholtz free energy are derived analytically.

Thermodynamic behavior generally aligns with the second law of thermodynamics.

Certain configurations suggest possible thermodynamic instability.

Abstract

We develop a thermal description for photon modes within the context of bouncing universe. Within this study, we start with a Lorentz-breaking dispersion relation which accounts for modified Friedmann equations with a bounce solution. We calculate the spectral radiance, the entropy, the Helmholtz free energy, the heat capacity, and the mean energy. Nevertheless, the latter two ones turn out to contribute only in a trivial manner. Furthermore, one intriguing aspect gives rise to: for some configurations of $\eta$, $l_{P}$, and $T$, the thermodynamical behavior of the system seems to indicate instability. However, despite of showing this particularity, the solutions of the thermodynamic functions in general turn out to agree with the literature, e.g., the second law of thermodynamics is maintained. More so, all the results are derived \textit{analytically} and three different regimes of temperature of the universe are also considered, i.e., the inflationary era, the electroweak epoch and the cosmic microwave background.