Axions and Cosmic Rays

We investigate the propagation of a charged particle in a spatially constant but time dependent pseudoscalar background. Physically this pseudoscalar background could be provided by a relic axion density. The background leads to an explicit breaking of Lorentz invariance; as a consequence processes such as $p\to p γ$ or $e\to e γ$ are possible within some kinematical constraints. The phenomenon is described by the QED lagrangian extended with a Chern-Simons term that contains a 4-vector which characterizes the breaking of Lorentz invariance induced by the time-dependent background. While the radiation induced (similar to the Cherenkov effect) is too small to influence the propagation of cosmic rays in a significant way, the hypothetical detection of the photons radiated by high energy cosmic rays via this mechanism would provide an indirect way of verifying the cosmological relevance of axions. We discuss on the order of magnitude of the effect.