Higgs ξ-inflation for the 125-126 GeV Higgs: a two-loop analysis

A non-minimal coupling ξ of the Standard Model Higgs field to gravity can give rise to inflation, but large ξ is required and thus leads to a violation of perturbative unitarity at MPl/ξ, which is well below the inflationary scale \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$ {{{{M_{\mathrm{Pl}}}}} \left/ {{\sqrt{\xi }}} \right.} $\end{document}. We re-examine this claim for a Higgs mass in the range 125-126 GeV for which λeff(μ) runs to very small values near the Planck scale and can significantly reduce the value of ξ required for inflation. Using the two-loop renormalization group equations and effective potential for Higgs ξ-inflation, we find that familiar inflationary solutions can have a non-minimal coupling as small as ξ ~ 400 without the potential developing a second minimum. We also find a new observationally allowed region of Higgs ξ-inflation with ξ ~ 90 and distinct inflationary predictions, including an observable level of the tensor-to-scalar ratio r.