Probing Lorentz invariance violation with the IceCube PeV neutrinos

It has been speculated that violations of Lorentz invariance might be generated by quantum-gravity effects. As a consequence, particles may not travel at the universal speed of light. In particular, superluminal extragalactic neutrinos would rapidly lose energy via the bremsstrahlung of electron-positron pairs, damping their initial energy into electromagnetic cascades, a figure constrained by Fermi Large Area Telescope data. This talk is aimed at showing how the two cascade PeV neutrino events recently detected by IceCube -if attributed to extragalactic diffuse events, as it appears likely- can place the strongest bound on Lorentz-invariance violation in the neutrino sector.