  We discuss the inflationary dynamics of a system with a non-minimal coupling
between the Higgs and the Ricci scalar as well as a Ricci scalar squared term.
There are two scalar modes in this system, i.e. the Higgs and the spin-zero
mode of the graviton, or the scalaron. We study the two-field dynamics of the
Higgs and the scalaron during inflation, and clarify the condition where
inflation is dominated by the Higgs/scalaron. We also find that the cut-off
scale at around the vacuum is as large as the Planck scale, and hence there is
no unitarity issue, although there is a constraint on the couplings from the
perturbativity of the theory at around the vacuum.
