Description
The self coupling $\lambda$ of the Higgs boson in the
Standard Model may show critical behavior, i.e. the Higgs potential
may have a point at an energy scale $\sim 10^{17-18}$ GeV where both
the first and second derivatives (almost) vanish. Since $\lambda$ is
very small in this region, the Higgs boson can serve as inflaton
even if its nonminimal coupling to the curvature scalar is only
${\cal O}(10)$, thereby alleviating concerns about the perturbative
unitarity of the theory. We find that just before the Higgs as
inflaton enters the flat region of the potential the usual
slow--roll conditions are violated. This leads to ``overshooting''
behavior, which in turn strongly enhances scalar curvature
perturbations because of the excitation of entropic (non--adiabatic)
perturbations. For appropriate choice of the free parameters these
large density perturbations occur at length scales relevant for the
formation of primordial black holes. Even if these perturbations are
not quite large enough to trigger copious black hole formation, they
source second order tensor perturbations, i.e. primordial
gravitational waves; the corresponding energy density can be
detected by the proposed space-based gravitational wave detectors
DECIGO and BBO.