The Compton-Getting effect on ultra-high energy cosmic rays of   cosmological origin
  Deviations from isotropy have been a key tool to identify the origin and the primary type of cosmic rays at low energies. We suggest that the Compton-Getting effect can play a similar role at ultra-high energies: If at these energies the cosmic ray flux is dominated by sources at cosmological distances, then the movement of the Sun relative to the cosmic microwave background frame induces a dipole anisotropy at the 0.6% level. The energy dependence and the orientation of this anisotropy provide important information about the transition between galactic and extragalactic cosmic rays, the charge of the cosmic ray primaries, the galactic magnetic field and, at the highest energies, the energy-loss horizon of cosmic rays. A 3-sigma detection of this effect requires around 10^6 events in the considered energy range and is thus challenging but not impossible with present detectors. As a corollary we note that the Compton-Getting effect allows one also to constrain the fraction of the diffuse gamma-ray background emitted by sources at cosmological distance, with promising detection possibilities for the GLAST satellite. 
M. Kachelriess, P.D. Serpico