Spectral Lags of 90 Swift Gamma-Ray Bursts and the Constraint on the Lorentz Invariance Violation

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.