Photon Gas Thermodynamics in Doubly Special Relativity

TL;DR

This paper investigates how doubly special relativity modifies photon gas thermodynamics, revealing significant effects at high temperatures relevant to early universe cosmology.

Contribution

It provides a detailed analysis of thermodynamic properties of photon gases within DSR, incorporating modified dispersion relations and bounded energy-momentum space.

Findings

Positive λ reduces energy density and entropy compared to SR

Photon velocity and pressure-to-energy ratio increase with positive λ

Effects become significant at temperatures above 10^{-3} E_P

Abstract

Doubly special relativity (DSR), with both an invariant velocity and an invariant length scale, elegantly preserves the principle of relativity between moving observers, and appears as a promising candidate of the quantum theory of gravity. We study the modifications of photon gas thermodynamics in the framework of DSR with an invariant length $|\lambda|$, after properly taking into account the effects of modified dispersion relation, upper bounded energy-momentum space, and deformed integration measure. We show that with a positive $\lambda$, the grand partition function, the energy density, the specific heat, the entropy, and the pressure are smaller than those of special relativity (SR), while the velocity of photons and the ratio of pressure to energy are larger. In contrast, with a negative $\lambda$, the quantum gravity effects show up in the opposite direction. However, these effects only manifest themselves significantly when the temperature is larger than $10^{-3} E_{\rm P}$. Thus, DSR can have considerable influence on the early universe in cosmological study.