Super-Kamiokande 0.07 eV Neutrinos in Cosmology: Hot Dark Matter and the Highest Energy Cosmic Rays

Relic neutrinos with mass in the range indicated by Super-Kamiokande results if neutrino masses are hierarchial (about 0.07 eV) are many times deemed too light to be cosmologically relevant. Here we remark that these neutrinos may significantly contribute to the dark matter of the Universe (with a large lepton asymmetry L) and that their existence might be revealed by the spectrum of ultra high energy cosmic rays (maybe even in the absence of a large L). Super-Kamiokande has provided a strong evidence for the oscillation in atmospheric showers of two neutrino species with masses m1, m2 and δm 2 = m21 −m2 = (1− 8)× 10 eV consisting mostly of about equal amounts of νμ and another flavor eigenstate neutrino, ντ or a sterile neutrino[1]. If neutrino masses are hierarchial, as those of the other leptons and quarks, then the heavier of the two oscillating neutrinos, call it νSK, has a mass mSK = √ δm ≃ 0.07 eV. The possibility of m1 and m2 being much larger than mSK has also been invoked, in part with the motivation to have m1 ∼ m2 of the order of eV, in the range previously considered necessary for relic neutrinos to constitute a cosmologically relevant component of the dark matter in the Universe. In fact, with no lepton asymmetry, i.e. with Lν ≡ [(nν−nν̄)/nγ] = 0, the number density of relic neutrinos and antineutrinos of each species is nν = nν̄ = 3nγ/22 = 56cm . With this number density, the contribution of relic neutrinos to the energy density of the Universe (in units of the critical density) is Ωνh 2 = ( ∑ i mνi/92 eV) (here h ≃ 0.7 is the Hubble constant in units of 100 km/Mpc sec). This amounts to only to Ωνh 2 = 0.8× 10, while a value about 10 times larger was considered necessary in the context of Cold-Hot Dark Matter (CHDM) models [2]. Talk given at the “4th International Symposium on Sources and Detection of Dark Matter in the Universe”, February 23-25, 2000, Marina del Rey, CA (to appear in its proceedings) and at the “Cosmic Genesis and Fundamental Physics” workshop, October 28-30, 1999, Sonoma State University, Santa Rosa, CA.