Photon Gas Thermodynamics in Doubly Special Relativity
  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.
