Solar neutrino spectrum, sterile neutrinos and additional radiation in the Universe

Recent results from the SNO, Super-Kamiokande and Borexino experiments do not show the expected upturn of the energy spectrum of events (the ratio $R \equiv N_{obs}/N_{SSM}$) at low energies. At the same time, cosmological observations testify for possible existence of additional relativistic degrees of freedom in the early Universe: $\Delta N_{eff} = 1 - 2$. These facts strengthen the case of very light sterile neutrino, $\nu_s$, with $\Delta m^2_{01} \sim (0.7 - 2) \cdot 10^{-5}$ eV$^2$, which mixes weakly with the active neutrinos. The $\nu_s$ mixing in the mass eigenstate $\nu_1$ characterized by $\sin^2 2\alpha \sim 10^{-3}$ can explain an absence of the upturn. The mixing of $\nu_s$ in the eigenstate $\nu_3$ with $\sin^2 \beta \sim 0.1$ leads to production of $\nu_s$ via oscillations in the Universe and to additional contribution $\Delta N_{eff} \approx 0.7 - 1$ before the big bang nucleosynthesis and later. Such a mixing can be tested in forthcoming experiments with the atmospheric neutrinos as well as in future accelerator long baseline experiments. It has substantial impact on conversion of the supernova neutrinos.