UHECR bounds on Lorentz violation in the photon sector
  The aim of this brief review is to present a case study of how astrophysics data can be used to get bounds on Lorentz-violating parameters. For this purpose, a particularly simple Lorentz-violating modification of the Maxwell theory of photons is considered, which maintains gauge invariance, CPT, and renormalization. With a standard spin-one-half Dirac particle minimally coupled to this nonstandard photon, the resulting modified-quantum-electrodynamics model involves nineteen dimensionless "deformation parameters." Ten of these parameters lead to birefringence and are already tightly constrained by astrophysics. New bounds on the remaining nine nonbirefringent parameters have been obtained from the inferred absence of vacuum Cherenkov radiation in ultrahigh-energy-cosmic-ray (UHECR) events. The resulting astrophysics bounds improve considerably upon current laboratory bounds and the implications of this "null experiment" may be profound, both for elementary particle physics and cosmology. 
F.R. Klinkhamer