  We study the stability of the electroweak vacuum during and after the
Starobinsky inflation, assuming the existence of the non-minimal Higgs coupling
to the Ricci scalar. In the Starobinsky inflation, there exists $R^2$ term
(with $R$ being the Ricci scalar), which modifies the evolution equation of the
Higgs field. We consider the case that the non-minimal coupling is sizable so
that the quantum fluctuation of the Higgs field is suppressed and that the
Higgs amplitude is settled near the origin during the inflation. In such a
case, the Higgs amplitude may be amplified in the preheating epoch after
inflation because of the parametric resonance due to the non-minimal coupling.
We perform a detailed analysis of the evolution of the Higgs field in the
preheating epoch by a numerical lattice simulation and derive an upper bound on
the non-minimal coupling constant $\xi$ in order to realize the electroweak
vacuum in the present universe. We find that the upper bound on $\xi$ in the
Starobinsky inflation model is more stringent than that in conventional
inflation models without the $R^2$ term.
