Constraining the Lorentz invariance violation from the continuous spectra of short gamma-ray bursts

In quantum gravity, a foamy structure of space-time leads to Lorentz invariance violation (LIV). As the most energetic astrophysical processes in the Universe, gamma-ray bursts (GRBs) provide an effective way to probe quantum gravity effects. We use continuous spectra of 20 short GRBs detected by the Swift satellite to give a conservative lower limit of quantum gravity energy scale $M_\textrm{QG} $. Due to the LIV effect, photons with different energy have different velocities. This will lead to the delayed arrival of high energy photons relative to the low energy ones. Based on the fact that the LIV-induced time delay can't be longer than the duration of a GRB, we present the most conservative estimation of the quantum gravity energy scales from 20 short GRBs. The most strict constraint, $M_\textrm{QG}>5.05\times10^{14}$ GeV, is from GRB 140622A.