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 $\xi$|H|${}^2$R that utilizes the saddle point of the Higgs potential. We find that it is possible to realize successful inflation even for $\xi$ = 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 $\xi$ can be realized by the Higgs-portal coupling ${\lambda }_{SH}$$\simeq$ 0.32 and the vacuum expectation value of the additional neutral scalar $⟨\varphi ⟩$$\simeq$ 2.7 TeV, which correspond to the dark matter mass 2.0 TeV, its spin-independent cross section 1.8 $\times$ 10${}^{-9}$ pb, and the mass of additional neutral scalar 190 GeV.