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Minimal scenario of Criticality for Electroweak scale, Neutrino Masses, Dark Matter, and Inflation

We propose a minimal model that can explain the electroweak scale, neutrino masses, Dark Matter (DM), and successful inflation all at once based on the multicritical-point principle (MPP). The model has two singlet scalar fields that realize an analogue of the Coleman-Weinberg mechanism, in addition to the Standard Model with heavy Majorana right-handed neutrinos. By assuming a $Z_2 $ symmetry, one of the scalars becomes a DM candidate whose property is almost the same as the minimal Higgs-portal scalar DM. In this model, the MPP can naturally realize a saddle point in the Higgs potential at high energy scales. By the renormalization-group analysis, we study the critical Higgs inflation with non-minimal coupling $ξ|H|^2 R$ that utilizes the saddle point of the Higgs potential. We find that it is possible to realize successful inflation even for $ξ=25$ and that the heaviest right-handed neutrino is predicted to have a mass around $10^{14}$ GeV to meet the current cosmological observations. Such a small value of $ξ$ can be realized by the Higgs-portal coupling $λ_{SH}\simeq 0.32$ and the vacuum expectation value of the additional neutral scalar $\langleϕ\rangle\simeq 2.7$ TeV, which correspond to the dark matter mass 2.0 TeV, its spin-independent cross section $1.8\times10^{-9}$ pb, and the mass of additional neutral scalar 190 GeV.