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
$p\to p \gamma$ or $e\to e \gamma$ 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.
