Photon Gas Thermodynamics in Doubly Special Relativity

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 $10^{-3}{E}_{\mathrm{P}}$. Thus, DSR can have considerable influence on the early universe in cosmological study.

17 pages, 7 figures, final version for publication in APP

References in corpus (5)

• Lorentz violation effects on astrophysical propagation of very high energy photons
• Thermodynamics of Photon Gas with an Invariant Energy Scale
• Thermodynamics of a photon gas and deformed dispersion relations
• Eikonal equation of the Lorentz-violating Maxwell theory
• Black hole evaporation within a momentum-dependent metric

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• Photon gas thermodynamics in dS and AdS momentum spaces
• Ideal Quantum Gases with Planck Scale Limitations