On the Naturalness of Higgs inflation

Abstract

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