Constraints on Lorentz invariance violation from<i>Fermi</i>-Large Area Telescope observations of gamma-ray bursts

We analyze the MeV/GeV emission from four bright gamma-ray bursts (GRBs) observed by the Fermi Large Area Telescope to produce robust, stringent constraints on a dependence of the speed of light in vacuo on the photon energy (vacuum dispersion), a form of Lorentz invariance violation (LIV) allowed by some quantum gravity (QG) theories. First, we use three different and complementary techniques to constrain the total degree of dispersion observed in the data. Additionally, using a maximally conservative set of assumptions on possible source-intrinsic, spectral-evolution effects, we constrain any vacuum dispersion solely attributed to LIV. We then derive limits on the QG energy scale (the energy scale where LIV-inducing QG effects become strong, ${E}_{\mathrm{QG}}$) and the coefficients of the Standard Model Extension. For the subluminal case (where high-energy photons propagate more slowly than lower-energy photons) and without taking into account any source-intrinsic dispersion, our most stringent limits (at 95% C.L.) are obtained from GRB 090510 and are ${E}_{\mathrm{QG},1}&gt;7.6$ times the Planck energy (${E}_{\mathrm{Pl}}$) and ${E}_{\mathrm{QG},2}&gt;1.3\ifmmode\times\else\texttimes\fi{}{10}^{11}\text{ }\text{ }\mathrm{GeV}$ for linear and quadratic leading-order LIV-induced vacuum dispersion, respectively. These limits improve the latest constraints by Fermi and H.E.S.S. by a factor of $\ensuremath{\sim}2$. Our results disfavor any class of models requiring ${E}_{\mathrm{QG},1}\ensuremath{\lesssim}{E}_{\mathrm{Pl}}$.