Reheating through the Higgs amplified by spinodal instabilities and gravitational creation of gravitons

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 a post-inflationary universe is dominated by energy with a stiff equation of state such as kination, namely, overproduction of gravitons in the 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.