Photon propagation in a cold axion background with and without magnetic
  field
  A cold relic axion condensate resulting from vacuum misalignment in the early
universe oscillates with a frequency m, where m is the axion mass. We determine
the properties of photons propagating in a simplified version of such a
background where the sinusoidal variation is replaced by a square wave profile.
We prove that previous results that indicated that charged particles moving
fast in such a background radiate, originally derived assuming that all momenta
involved were much larger than m, hold for long wavelengths too. We also
analyze in detail how the introduction of a magnetic field changes the
properties of photon propagation in such a medium. We briefly comment on
possible astrophysical implications of these results.
