  In a previous work we investigated the propagation of fast moving charged
particles in a spatially constant but slowly time dependent pseudoscalar
background, such as the one provided by cold relic axions. The background
induces cosmic rays to radiate in the low-energy spectrum. While the energy
loss caused by this mechanism on the primary cosmic rays is negligible, we
investigate the hypothetical detection of the photons radiated and how they
could provide an indirect way of verifying the cosmological relevance of
axions. Assuming that the cosmic ray flux is of the form J(E)~ E^-g we find
that the energy radiated follows a distribution k^-((g-1)/2) for proton
primaries, identical to the Galaxy synchrotron radiation that is the main
background, and k^-(g/2) for electron primaries, which in spite of this sharper
decay provide the dominant contribution in the low-energy spectrum. We discuss
possible ways to detect this small diffuse contribution. Local detection in the
vicinity of powerful cosmic rays emitters might also be possible.
