The optical depth including Lorentz invariance violation energy threshold shifts

Lorentz invariance violation (LIV) introduced as a generic modification to particle dispersion relations can change the photon energy threshold of pair-production, which modifies the expected gamma-ray flux from astrophysical sources. In this work, we review this phenomenon and explore its consequences through the derived effects in the optical depth. Then, by looking for subluminal LIV signatures in TeV gamma-ray spectra, we present stringent limits to the LIV energy scale at leading order n=1 and 2. And finally, we present the predicted flux of GZK-photons including LIV, in the astrophysical scenario which best describes UHECR data.