Higgs scalaron mixed inflation

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.