Nonequilibrium effect of the neutrino distribution on primordial helium synthesis

We study the effect of the deviation of the electron-neutrino spectrum from the thermal equilibirum distribution, originating from residual interactions between neutrinos and electrons which have different temperatures after decoupling. It is found that this effect causes an appreciable spectral distortion of the order of 1% or more in the higher-energy side of the distribution, when the temperature drops below 1 MeV. The resulting modification in the helium abundance, however, is small, and only of the order of $\Delta Y\approx 1.3\times {10}^{-4\mathrm{}}$.