Pre-burst events of gamma-ray bursts with light speed variation

Previous researches on high-energy photon events from gamma-ray bursts~(GRBs) suggest a light speed variation $v(E)=c(1-E/E_{\mathrm{LV}})$ with $E_{\mathrm{LV}}=3.6\times10^{17}~\mathrm{ GeV}$, together with a pre-burst scenario that hight-energy photons come out about 10 seconds earlier than low-energy photons at the GRB source. However, in the Lorentz invariance violating scenario with an energy dependent light speed considered here, high-energy photons travel slower than low-energy photons due to the light speed variation, so that they are usually detected after low-energy photons in observed GRB data. Here we find four high-energy photon events which were observed earlier than low-energy photons from Fermi Gamma-ray Space Telescope~(FGST), and analysis on these photon events supports the pre-burst scenario of high energy photons from GRBs and the energy dependence of light speed listed above.