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−γ we find that the energy radiated via this mechanism has a power spectrum k to the power of minus gamma minus 1 over 2 for proton primaries and k to the power of minus gamma over 2 for electron primaries, which dominate for low values of k where the effect is maximized. Unfortunately this radiation is shadowed by the synchrotron radiation background making the observation of this effect very difficult. Yet its detection would constitute direct evidence of the presence of a cold axion background