  In this work, we use Lorentz invariance violation (LIV) introduced as a
generic modification to particle dispersion relations to study some
consequences of single photon emission, known as vacuum Cherenkov radiation,
and photon decay processes in cosmic and gamma rays. These processes are
forbidden in a Lorentz invariant theory but allowed under the hypothesis of
LIV. We show that the emission rate have a dependency on the cosmic ray primary
mass and the electric charge that could modify the UHECR spectrum. Furthermore,
LIV dramatically enhances photon decay into an electro-positron pair above
certain energy threshold. This last effect can then be used to set limits to
the LIV energy scale from the direct observation of very high energy cosmic
photon events by telescopes of gamma-rays.
