Lorentz Invariance Violation Effects on Gamma-Gamma Absorption and Compton Scattering

In this paper, we consider the impact of Lorentz Invariance Violation (LIV) on the $\gamma -\gamma$ opacity of the Universe to VHE-gamma rays, compared to the effect of local under-densities (voids) of the Extragalactic Background Light, and on the Compton scattering process. Both subluminal and superluminal modifications of the photon dispersion relation are considered. In the subluminal case, LIV effects may result in a significant reduction of the $\gamma -\gamma$ opacity for photons with energies $\gtrsim 10$ TeV. However, the effect is not expected to be sufficient to explain the apparent spectral hardening of several observed VHE $\gamma$-ray sources in the energy range from 100 GeV - a few TeV, even when including effects of plausible inhomogeneities in the cosmic structure. Superluminal modifications of the photon dispersion relation lead to a further enhancement of the EBL $\gamma \gamma$ opacity. We consider, for the first time, the influence of LIV on the Compton scattering process. We find that this effect becomes relevant only for photons at ultra-high energies, $E\gtrsim 1$ PeV. In the case of a superluminal modification of the photon dispersion relation, both the kinematic recoil effect and the Klein-Nishina suppression of the cross section are reduced. However, we argue that the effect is unlikely to be of astrophysical significance.