Axions and high-energy cosmic rays: Can the relic axion density be measured?

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.