  We add a singlet right handed neutrino plus a charged and a neutral singlet
scalars to the standard model. This extension includes a discrete symmetry such
that we obtain a heavy sterile neutrino which couples only to the electron and
the new scalars. In this sense the singlet neutrino does not mix with ordinary
ones and thus has no effect on Big Bang Nucleosynthesis. However, such sterile
neutrino can be in equilibrium with electroweak particles in the early Universe
due to its couplings to electrons and also because the Higgs boson mixes with
the singlet scalars. We obtain that the sterile neutrino constitutes a dark
matter candidate and analyze its direct detection in the light of current
experiments. Our results show that if such a sterile neutrino is realized in
nature, and CDMS-II experiment confirms its positive signal, dark matter
demands a rather light Higgs boson with new Physics at some 500 GeV scale.
