  We examine renormalization of Higgs inflation 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 simplified 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 field regime, and indicate that Higgs
inflation is not a predictive theory.
