Threshold anomalies of ultra-high energy cosmic photons due to Lorentz invariance violation

From special relativity, photon annihilation process HepProcess{{Pgg}{Pgg}{to}{Pep}{Pem}} prevents cosmic photons with energies above a threshold to propagate a long distance in cosmic space due to their annihilation with low energy cosmic background photons. However, modifications of the photon dispersion relation from Lorentz invariance violation~(LIV) can cause novel phenomena beyond special relativity to happen. In this paper, we point out that these phenomena include optical transparency, threshold reduction and reappearance of ultra-high energy photons in cosmic space. The recent observation of near and above PeV photon events by the LHAASO Collaboration reveals the necessity to consider the threshold anomalies. Future observations of above threshold photons from extragalactic sources can testify LIV properties of photons.