Perturbative unitarity of Higgs inflation in the Riemannian and generalized geometry

In a simple Higgs inflation model in metric-affine gravity, it is known that its UV cutoff is much smaller than the Planck scale. While it calls for UV completion, a concrete example has not yet been found, even with the large-N limit known as a successful technique to complete an original Higgs inflation defined on the Riemannian geometry. In this talk, after a review of the unitarity issue and previous attempts to complete Higgs inflation models, we investigate how small deformation of the simple Higgs inflation affects the emergence and properties of dynamical fields particularly in the large-N limit.