Thermodynamics of massless particles in curved spacetime

Abstract

This work is devoted to study the behavior of massless particles within the context of curved spacetime. In essence, we investigate the consequences of the scale factor [Formula: see text] of the Friedmann–Robertson–Walker metric in the Einstein–aether formalism to study photon-like particles. To do so, we consider the system within the canonical ensemble formalism in order to derive the following thermodynamic state quantities: spectral radiance, Helmholtz free energy, pressure, entropy, mean energy and the heat capacity. Moreover, the correction to the Stefan–Boltzmann law and the equation of states are also provided. Particularly, we separate our study within three distinct cases, i.e. [Formula: see text] [Formula: see text]; [Formula: see text] [Formula: see text]; [Formula: see text] [Formula: see text]. In the first one, the results are derived numerically. Nevertheless, for the rest of the cases, all the calculations are accomplished analytically showing explicitly the dependence of the scale factor [Formula: see text] and the Riemann zeta function [Formula: see text]. Furthermore, our analyses are accomplished in general taking into account three different regimes of temperature of the universe, i.e. the inflationary era ([Formula: see text][Formula: see text]GeV), the electroweak epoch ([Formula: see text][Formula: see text]GeV) and the cosmic microwave background ([Formula: see text][Formula: see text]GeV).