Lorentz invariance violation limits from GRB 221009A

It has been long conjectured that a signature of quantum gravity will be Lorentz invariance violation (LIV) that could be observed at energies much lower than the Planck scale. One possible signature of LIV is an energy-dependent speed of photons. This can be tested with a distant transient source of very high-energy photons. We explore time-of-flight limits on LIV derived from LHAASO's observations of tens of thousands of TeV photons from GRB 221009A, the brightest gamma-ray burst of all time. For a linear (n=1) dependence of the photon velocity on energy, we find a lower limit on the subluminal (superluminal) LIV scale of 5. 9 (6. 2) E₏₋. These are comparable to the stringent limits obtained so far and as an independent bound obtained from a different redshift confirm their robustness. For a quadratic model (n=2, corresponding to d=6 SME operators), the limits, which are currently the best available with the time-of-flight method, are 5. 8 (4. 6) 10^-8E₏₋. Our analysis uses the LHAASO data in the 0. 2--7 TeV range. Higher energy data would enable to improve our limits.