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Nucleosynthesis constraint on Lorentz invariance violation in the neutrino sector

We investigate the nucleosynthesis constraint on Lorentz invariance violation in the neutrino sector which influences the formation of light elements by altering the energy density of the Universe and weak reaction rates prior to and during the big-bang nucleosynthesis epoch. We derive the weak reaction rates in the Lorentz-violating extension of the standard model. Using measurements of the primordial helium-4 and deuterium abundances, we give a tighter constraint on the deformed parameter than that derived from measurements of the cosmic microwave background anisotropies.