Sterile neutrinos, dark matter, and the pulsar velocities in models with a Higgs singlet

We identify the range of parameters for which the sterile neutrinos can simultaneously explain the cosmological dark matter and the observed velocities of pulsars. To satisfy all cosmological bounds, the relic sterile neutrinos must be produced sufficiently cold. This is possible in a class of models with a gauge-singlet Higgs boson coupled to the neutrinos. Sterile dark matter can be detected by the x-ray telescopes. The presence of the singlet in the Higgs sector can be tested at the Large Hadron Collider.