SIMBAD references

The arrival times of photons with different energy could be different, even when they are emitted from the same source simultaneously. Such a spectral lag is a common property among high-energy astrophysics phenomena like gamma-ray bursts (GRBs). The potential violation of the Lorentz invariance caused by quantum fluctuations in background spacetime metrics could cause the spectral lag. In this paper, we try to make a constraint on Lorentz invariance violation (LIV) with multiple energy bands light curves of GRBs. With a sample of 90 Swift GRBs with redshifts, we calculate their spectral offsets from four fixed energy bands within their source frame. With help from the cross-correlation function and kernel smooth procedure, we extract improved spectral shifts. By using these more general spectral lags, we obtain an upper limit on LIV, equivalent to a lower limit on the quantum-gravitational energy scale of E_QG ≥ 2.2 × 10¹⁴GeV.