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 $M_\text{ P}/\sqrt{ 10^2}\sim 10^{ 17}\,\text{ GeV}$.) 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.
Categories: hep-ph astro-ph.CO hep-th