  Observations of clusters and super clusters of galaxies have indicated that
the Universe is more dominated by baryons than ever estimated in the
homogeneous cosmological model for primordial nucleosynthesis. Recent
detections of possibly low deuterium abundance in Lyman-$\alpha$ clouds along
the line of sight to high red-shift quasars have raised another potential
difficulty that \he4 is overproduced in any cosmological models which satisfy
the low deuterium abundance constraint. We show that the inhomogeneous
cosmological model with degenerate electron-neutrino can resolve these two
difficulties.
