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 ${5.9} (6.2) mpl$. 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 $5.8 (4.6) \times 10^{-8} mpl$. Our analysis uses the publicly available LHAASO data, which is only in the $0.2-7$ TeV range. Higher energy data would enable us to improve these limits by a factor of 3 for $n=1$ and by an order of magnitude for $n=2$.