On Higgs inflation and naturalness

We reexamine recent claims that Einstein-frame scattering in the Higgs inflation model is unitary above the cut-off energy Λ ≃ Mp/ξ. We show explicitly how unitarity problems arise in both the Einstein and Jordan frames of the theory. In a covariant gauge they arise from non-minimal Higgs self-couplings, which cannot be removed by field redefinitions because the target space is not flat. In unitary gauge, where there is only a single scalar which can be redefined to achieve canonical kinetic terms, the unitarity problems arise through non-minimal Higgs-gauge couplings.