Thermodynamics of massless particles in curved spacetime

A. A. Araújo Filho

doi:10.1142/S0219887823502262

paper

Thermodynamics of massless particles in curved spacetime

arXiv:2201.00066 · doi:10.1142/S0219887823502262

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 $C (η)$ 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 provide. Particularly, we separate our study within three distinct cases, i.e., $s = 0, p = 0$ ; $s = 1, p = 1$ ; $s = 2, p = 1$ . 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 $C (η)$ and the Riemann zeta function $ξ (s)$ . Furthermore, our analyses are accomplished in general taking into account three different regimes of temperature of the universe, i.e., the inflationary era ( $T = 1 0^{13}$ GeV), the electroweak epoch ( $T = 1 0^{3}$ GeV) and the cosmic microwave background ( $T = 1 0^{- 13}$ GeV).

arXiv comment50 pages, and 18 figures

Thermodynamics of massless particles in curved spacetime

Abstract

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