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 $5.9(6.2)E_{\mathrm{pl}}$. 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 $5.8(4.6)\times {10}^{-8}{E}_{\mathrm{pl}}$. Our analysis uses the LHAASO data in the 0.2–7 TeV range. Higher energy data would enable to improve our limits.

Figure 1

LHAASO data for GRB 221909A [1] and its fitting with $n=1$ LIV. Top: The light curve, $\mathrm{\Phi }(t)$, fitted by Eq. (9). Bottom: The Spectra $\psi (E)\times E^2$ for three time bins fited by Eq. (10). The error bars reflect $1\sigma$. The solid, dashed, and dotted lines correspond to ${\mathcal{E}}_{\mathrm{QG},1}^{(\pm )}\to \infty$, ${\mathcal{E}}_{\mathrm{QG},1}^{(-)}=6$, and ${\mathcal{E}}_{\mathrm{QG},1}^{(+)}=6$. The latter demonstrate that $|{\mathcal{E}}_{\mathrm{QG},1}^{(\pm )}|\gtrsim 6$.

Figure 2

The same as in Fig. 1 but for the quadratic LIV model, $n=2$. The solid, dashed, and dotted lines correspond to ${\mathcal{E}}_{\mathrm{QG},1}^{(\pm )}\to \infty$, ${\mathcal{E}}_{\mathrm{QG},2}^{(-)}=5\times {10}^{-8}$, and ${\mathcal{E}}_{\mathrm{QG},2}^{(+)}=5\times {10}^{-8}$.