Overshooting, Critical Higgs Inflation and Second Order Gravitational
  Wave Signatures
  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. In this case 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 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.
