H E ] 2 3 D ec 2 02 0 Can dispersion of light in interstellar medium cause the delays of gamma-ray bursts without invoking the drastic assumption of Lorentz invariance violation ?

Experimental observations indicate that gamma-ray bursts (GRB) and high-energy neutrino bursts may travel at different speeds with a typical delay measured at the order of hours or days. We consider a potential interpretation where GRB is slowed down due to dispersion of light in interstellar medium. In addition to standard media such as electrons and photons, we consider the case of an axion plasma. We find that none of the considered media are able to account for the long GRB delays. The GRB delays have occasionally been interpreted as a sign of Lorentz invariance violation. That interpretation has its own problems: since the modification of the dispersion relation should not be dependent on particle type, delays between photons and neutrinos are hard to explain. We conclude that the two aforementioned interpretations of the GRB delay can be distinguished observationally due to the different frequency dependencies of the propagation speed of radiation.