Thermal analysis of photon-like particles in rainbow gravity

This work is devoted to study the thermodynamic behavior of photon–like particles within the $\mathit{\text{rainbow}}$ gravity formalism. To to do this, we chose two particular ansatzs to accomplish our calculations. First, we consider a dispersion relation which avoids UV divergences, getting a positive effective cosmological constant. We provide $\mathit{\text{numerical}}$ analysis for the thermodynamic functions of the system and bounds are estimated. Furthermore, a phase transition is also expected for this model. Second, we consider a dispersion relation employed in the context of $\mathit{\text{Gamma}}\mathit{\text{Ray}}\mathit{\text{Bursts}}$. Remarkably, for this latter case, the thermodynamic properties are calculated in an $\mathit{\text{analytical}}$ manner and they turn out to depend on the harmonic series $H_n$, gamma $\mathrm{\Gamma }(z)$, polygamma ${\psi }_n(z)$ and zeta Riemann functions $\zeta (z)$.