Top-Goldstone coupling spoils renormalization of Higgs inflation

We examine renormalization of Higgs ination in the context of the full Standard Model. In the fermionic sector of the theory there is a parametrically large top-Goldstone coupling which prevents renormalization of the theory. Using a simplied model with a global U(1) symmetry, a Higgs and a fermion, we show that the one-loop contribution to 4-Goldstone scattering cannot be absorbed in any tree level terms, and hence forbids a consistent renormalization of the theory. Our results apply for large non-minimal Higgs-gravity coupling in the large eld regime, and indicate that Higgs ination is not a predictive theory.