  We investigate constraints on Lorentz invariance violation in the neutrino
sector from a joint analysis of big bang nucleosynthesis and the cosmic
microwave background. The effect of Lorentz invariance violation during the
epoch of big bang nucleosynthesis changes the predicted helium-4 abundance,
which influences the power spectrum of the cosmic microwave background at the
recombination epoch. In combination with the latest measurement of the
primordial helium-4 abundance, the Planck 2015 data of the cosmic microwave
background anisotropies give a strong constraint on the deformation parameter
since adding the primordial helium measurement breaks the degeneracy between
the deformation parameter and the physical dark matter density.
