Possible cosmogenic neutrino constraints on Planck-scale Lorentz violation

We study, within an effective field theory framework, O (E-2/M-Pl(2)) Planck-scale suppressed Lorentz invariance violation (LV) effects in the neutrino sector, whose size we parameterize by a dimensionless parameter eta(nu). We find deviations from predictions of Lorentz invariant physics in the cosmogenic neutrino spectrum. For positive O (1) coefficients no neutrino will survive above 10(19) eV. The existence of this cutoff generates a bump in the neutrino spectrum at energies of 10(17) eV. Although at present no constraint can be cast, as current experiments do not have enough sensitivity to detect ultra-high-energy neutrinos, we show that experiments in construction or being planned have the potential to cast limits as strong as eta(nu) less than or similar to 10(-4) on the neutrino LV parameter, depending on how LV is distributed among neutrino mass states. Constraints on eta(nu) < 0 can in principle be obtained with this strategy, but they require a more detailed modeling of how LV affects the neutrino sector.