Stefan-Boltzmann law in rainbow space-time

We investigate the modification of the Stefan-Boltzmann law in the space-time whose geometry is energy-dependent. From the energy-momentum tensor of the electromagnetic field in rainbow space-time, we obtain the energy density of the isotropic radiation, valid up to the first order in the rainbow parameters. Using this in the first law of thermodynamics, we find the change in entropy of the radiation, and from this, the Stefan-Boltzmann relation is derived. We show that for two choices of the rainbow functions, the temperature dependence of the energy of the radiation is different from the $T^4$ law. We have also derived the corrections to Wien's displacement law in the rainbow space-time.