We critically examine the recent claim that the Standard Model Higgs boson ${\cal H}$ could drive inflation in agreement with observations if $|{\cal H}|^2$ has a strong coupling $ξ\sim 10^4$ to the Ricci curvature scalar. We first show that the effective theory approach upon which that claim is based ceases to be valid beyond a cutoff scale $Λ=m_p/ξ$, where $m_p$ is the reduced Planck mass. We then argue that knowing the Higgs potential profile for the field values relevant for inflation ($|{\cal H}|>m_p/\sqrtξ\gg Λ$) requires knowledge of the ultraviolet completion of the SM beyond $Λ$. In absence of such microscopic theory, the extrapolation of the pure SM potential beyond $Λ$ is unwarranted and the scenario is akin to other ad-hoc inflaton potentials afflicted with significant fine-tuning. The appealing naturalness of this minimal proposal is therefore lost.

9 pages. Replaced with published version, plus a footnote clarifying the use of power counting estimates