The $\nu$MSM, Dark Matter and Neutrino Masses

We investigate an extension of the Minimal Standard Model by right-handed neutrinos (the $\nu$MSM) to incorporate neutrino masses consistent with oscillation experiments. Within this theory, the only candidates for dark matter particles are sterile right-handed neutrinos with masses of a few keV. Requiring that these neutrinos explain entirely the (warm) dark matter, we find that their number is at least three. We show that, in the minimal choice of three sterile neutrinos, the mass of the lightest active neutrino is smaller than ${\cal O}(10^{-5})$ eV, which excludes the degenerate mass spectra of three active neutrinos and fixes the absolute mass scale of the other two active neutrinos.