Higher-derivative Lorentz-breaking dispersion relations: a thermal description

Abstract

This paper is devoted to study the thermal aspects of a photon gas within the context of Planck-scale-modified dispersion relations. We study the spectrum of radiation and the correction to the \textit{Stefan$-$Boltzmann} law in different cases when the Lorentz symmetry is no longer preserved. Explicitly, we examine two models within the context of CPT$-$even and CPT$-$odd sectors respectively. To do so, three distinct scenarios of the Universe are considered: the Cosmic Microwave Background (CMB), the electroweak epoch, and the inflationary era. Moreover, the equations of state in these cases turn out to display a dependence on Lorentz-breaking parameters. Finally, we also provide for both theories the analyses of the Helmholtz free energy, the mean energy, the entropy and the heat capacity.