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, $\xi \lesssim {10}^2$, as in the critical Higgs inflation, since $M_{\text{P}}\mathrm{/}\sqrt{{10}^2}\sim {10}^{17}\text{GeV}$.) 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 $m_{\text{DM}}>0.7\pm 0.2\text{TeV}$ 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.