Some Quantum Gravity (QG) theories allow for a violation of Lorentz invariance (LIV), manifesting as a dependence of the velocity of light in vacuum on its energy. If such a dependence exists, then photons of different energies emitted together by a distant source will arrive at the Earth at different times. High-energy (GeV) transient emissions from distant astrophysical sources such as Gamma-ray Bursts (GRBs) and Active Galaxy Nuclei can be used to search for and constrain LIV. The Fermi collaboration has previously analyzed two GRBs in order to put constraints on the dispersion parameter in vacuum, and on the energy scale at which QG effects causing LIV may arise. We used three different methods on four bright GRBs observed by the Fermi-LAT to get more stringent and robust constraints. No delays have been detected and strong limits on the QG energy scale are derived: for linear dispersion we set tight constraints placing the QG energy scale above the Planck mass; a quadratic leading LIV effect is also constrained.
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