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A cold relic axion condensate resulting from vacuum misalignment in the earlyuniverse oscillates with a frequency m, where m is the axion mass. We determinethe properties of photons propagating in a simplified version of such abackground where the sinusoidal variation is replaced by a square wave profile.We prove that previous results that indicated that charged particles movingfast in such a background radiate, originally derived assuming that all momentainvolved were much larger than m, hold for long wavelengths too. We alsoanalyze in detail how the introduction of a magnetic field changes theproperties of photon propagation in such a medium. We briefly comment onpossible astrophysical implications of these results.

Photon propagation in a cold axion background with and without magnetic field