Cosmological constraints on Lorentz invariance violation in the neutrino sector

We derive the Boltzmann equation in the synchronous gauge for massive neutrinos with a deformed dispersion relation. Combining the 7-year WMAP data with lower-redshift measurements of the expansion rate, we give constraints on the deformation parameter and find that the deformation parameter is strong degenerate with the physical dark matter density instead of the neutrino mass. Our results show that there is no evidence for Lorentz invariant violation in the neutrino sector. The ongoing Planck experiment could provide improved constraints on the deformation parameter.