  The Higgs not only induces the masses of all SM particles, the Higgs, given
its special mass value, is the natural candidate for the inflaton and in fact
is ruling the evolution of the early universe, by providing the necessary dark
energy which remains the dominant energy density. SM running couplings not only
allow us to extrapolate SM physics up to the Planck scale, but equally
important they are triggering the Higgs mechanism. This is possible by the fact
that the bare mass term in the Higgs potential changes sign at about mu_0 =
1.4x10^16 GeV and in the symmetric phase is enhanced by quadratic terms in the
Planck mass. Such a huge Higgs mass term is able to play a key role in
triggering inflation in the early universe. In this article we extend our
previous investigation by working out the details of a Higgs inflation
scenario. We show how different terms contributing to the Higgs Lagrangian are
affecting inflation. Given the SM and its extrapolation to scales mu>mu_0 we
find a calculable cosmological constant V(0) which is weakly scale dependent
and actually remains large during inflation. This is different to the Higgs
fluctuation field dependent Delta V(phi), which decays exponentially during
inflation, and actually would not provide a sufficient amount of inflation. The
fluctuation field has a different effective mass which shifts the bare Higgs
transition point to a lower value mu'_0 = 7.7x10^14 GeV. The vacuum energy V(0)
being proportional to M_Pl^4 has a coefficient which vanishes near the Higgs
transition point, such that the bare and the renormalized cosmological constant
match at this point. The role of the Higgs in reheating and baryogenesis is
emphasized.
