Cherenkov radiation in a photon gas

It is well known that a charged particle moving with constant velocity in vacuum does not radiate. In a medium, the situation can be different. If the so-called Cherenkov condition is satisfied, i.e. the particle velocity exceeds the phase speed in the medium, the particle will radiate. We show that a charge moving with a constant velocity in a gas of photons emits Cherenkov radiation, even in the γ-ray regime, due to nonlinear quantum electrodynamical effects. Our result is evaluated with respect to the radiation background in the early universe, and it is argued that the effect can be significant