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.
