  It is shown that a positive non-minimal coupling of the Higgs field to
gravity can solve the two problems in inflation models in which
postinflationary universe is dominated by an energy with stiff equation of
state such as a kination, namely, overproduction of gravitons in gravitational
reheating scenario, and overproduction of curvature perturbation from Higgs
condensation. Furthermore, we argue that the non-minimal coupling parameter can
be constrained more stringently with the progress in observations of
large-scale structure and cosmic microwave background.
