Constraints on neutrino oscillations from big bang nucleosynthesis.

We discuss in detail the effect of neutrino oscillations in big bang nucleosynthesis between active and sterile neutrinos as well as between active and active neutrinos. We calculate the constraints on mixings between active and sterile neutrinos from the present observation of the primordial helium abundance and discuss the potential implications on various astrophysical and cosmological problems of such oscillations. In particular, we show that large-angle sterile neutrino mixing seems to be excluded as a MSW solution to the solar neutrino situation or a solution to the atmospheric neutrino mixing hinted at in some underground experiments. We show how, with this constraint, the next generation of solar neutrino experiments should be able to determine the resolution of the solar neutrino problem. It is also shown how sterile neutrinos remain a viable dark matter candidate.