Future limits on isotropic Lorentz violation in the photon sector from   UHECRs and TeV gamma rays
  Present and future ultra-high-energy-cosmic-ray facilities (e.g., the Pierre Auger Observatory with South and North components) and TeV-gamma-ray telescope arrays (e.g., HESS or VERITAS and CTA) have the potential to set stringent indirect bounds on the nine Lorentz-violating parameters of nonbirefringent modified Maxwell theory minimally coupled to standard Dirac theory. Theoretically, the most interesting case is isotropic Lorentz violation, which is described by a single parameter [taken to vanish for the standard Lorentz-invariant theory]. It appears possible to obtain in the future an upper (lower) indirect bound on this single isotropic Lorentz-violating parameter at the +10^{-21} (-10^{-17}) level. Comparison is made with existing and future direct bounds from laboratory experiments. The possible physics implications of upper bounds at the 10^{-21} level are discussed. 
F.R. Klinkhamer
hep-ph astro-ph.HE