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: $\mathrm{\Delta }{N}_{eff}=1-2$. 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$^2$,whichmixesweaklywiththeactiveneutrinos\mathrm{.}The$\nu_s$mixinginthemasseigenstate$\nu_1$characterizedby$\sin^2 2\alpha \sim 10^{-3}$canexplainanabsenceoftheupturn\mathrm{.}Themixingof$\nu_s$ 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.