Hybrid Higgs inflation: The use of disformal transformation

We propose a hybrid type of the conventional Higgs inflation and new Higgs inflation models. We perform a disformal transformation into the Einstein frame and analyze the background dynamics and the cosmological perturbations in the truncated model, in which we ignore the higher-derivative terms of the Higgs field. From the observed power spectrum of the density perturbations, we obtain the constraint on the nonminimal coupling constant ξ and the mass parameter M in the derivative coupling. Although the primordial tilt ns in the hybrid model barely changes, the tensor-to-scalar ratio r moves from the value in the new Higgs inflationary model to that in the conventional Higgs inflationary model as |ξ| increases. We confirm our results by numerical analysis by ADM formalism of the full theory in the Jordan frame.