  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.
