  We analyse the process of reheating the Universe in the electroweak theory
where the Higgs field plays a role of the inflaton. We estimate the maximal
temperature of the Universe and fix the initial conditions for
radiation-dominated phase of the Universe expansion in the framework of the
Standard Model (SM) and of the nuMSM -- the minimal extension of the SM by
three right-handed singlet fermions. We show that the inflationary epoch is
followed by a matter dominated stage related to the Higgs field oscillations.
We investigate the energy transfer from Higgs-inflaton to the SM particles and
show that the radiation dominated phase of the Universe expansion starts at
temperature T_r~(3-15)*10^{13} GeV, where the upper bound depends on the Higgs
boson mass. We estimate the production rate of singlet fermions at preheating
and find that their concentrations at T_r are negligibly small. This suggests
that the sterile neutrino Dark Matter (DM) production and baryogenesis in the
nuMSM with Higgs-driven inflation are low energy phenomena, having nothing to
do with inflation. We study then a modification of the nuMSM, adding to its
Lagrangian higher dimensional operators suppressed by the Planck scale. The
role of these operators in Higgs-driven inflation is clarified. We find that
these operators do not contribute to the production of Warm Dark Matter (WDM)
and to baryogenesis. We also demonstrate that the sterile neutrino with mass
exceeding 100 keV (a Cold Dark Matter (CDM) candidate) can be created during
the reheating stage of the Universe in necessary amounts. We argue that the
mass of DM sterile neutrino should not exceed few MeV in order not to overclose
the Universe.
