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Cosmological implications of Standard Model criticality and Higgs inflation

The observed Higgs mass indicates that the Standard Model can be valid up to near the Planck scale $M_\text{P}$. Within this framework, it is important to examine how little modification is necessary to fit the recent experimental results in particle physics and cosmology. As a minimal extension, we consider the possibility that the Higgs field plays the role of inflaton and that the dark matter is the Higgs-portal scalar field. We assume that the extended Standard Model is valid up to the string scale $10^{17}\,\text{GeV}$. (This translates to the assumption that all the non-minimal couplings are not particularly large, $ξ\lesssim 10^2$, as in the critical Higgs inflation, since $M_\text{P}/\sqrt{10^2}\sim 10^{17}\,\text{GeV}$.) We find a correlated theoretical bound on the tensor-to-scalar ratio $r$ and the dark matter mass $m_\text{DM}$. As a result, the Planck bound $r<0.09$ implies that the dark-matter mass must be smaller than 1.1\,TeV, while the PandaX-II bound on the dark-matter mass $m_\text{DM}>0.7\pm0.2\,\text{TeV}$ leads to $r\gtrsim 2\times10^{-3}$. Both are within the range of near-future detection. When we include the right-handed neutrinos of mass $M_\text{R}\sim 10^{14}$\,GeV, the allowed region becomes wider, but we still predict $r\gtrsim 10^{-3}$ in the most of the parameter space. The most conservative bound becomes $r>10^{-5}$ if we allow three-parameter tuning of $m_\text{DM}$, $M_\text{R}$, and the top-quark mass.