On the Naturalness of Higgs Inflation

Abstract

We critically examine the recent claim that the Standard Model Higgs boson $\mathcal{H}$ could drive inflation in agreement with observations if $|\mathcal{H}{|}^2$ has a strong coupling $\xi \sim 10^4$ 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 $\Lambda =m_p/\xi$, where $m_p$ is the reduced Planck mass. We then argue that knowing the Higgs potential profile for the field values relevant for inflation ($|\mathcal{H}|>m_p/\sqrt{\xi }\gg \Lambda$) requires knowledge of the ultraviolet completion of the SM beyond $\Lambda$. In absence of such microscopic theory, the extrapolation of the pure SM potential beyond $\Lambda$ 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.

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