Constraints on Lorentz Invariance Violating Quantum Gravity and Large Extra Dimensions Models using High Energy Gamma Ray Observations

Observations of the multi-TeV spectra of the nearby BL objects Mkn 421 and Mkn 501 exhibit the high energy cutoffs predicted to be the result of intergalactic annihilation interactions, primarily with infrared photons having a flux level as determined by various astronomical observations. After correction for this absorption effect, the derived intrinsic spectra of these multi-TeV sources can be explained within the framework of simple synchrotron self-Compton emission models. Stecker and Glashow have shown that the existence of such annihilations via electron-positron pair production interactions up to an energy of 20 TeV puts strong constraints on Lorentz invariance violation. Such constraints have important implications for Lorentz invariance violating (LIV) quantum gravity models as well as LIV models involving large extra dimensions. We also discuss the implications of observations of high energy γ-rays from the Crab Nebula on constraining quantum gravity models.