Minimal scenario of criticality for electroweak scale, neutrino masses, dark matter, and inflation

Abstract

Abstract 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 $$Z_2 $$ 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 $$\xi |H|^2 R$$ 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 $$\xi =25$$ ξ = 25 and that the heaviest right-handed neutrino is predicted to have a mass around $$10^{14}$$ 10 14 $$\mathrm{GeV}$$ GeV to meet the current cosmological observations. Such a small value of $$\xi $$ ξ can be realized by the Higgs-portal coupling $$\lambda _{SH}\simeq 0.32$$ λ SH ≃ 0.32 and the vacuum expectation value of the additional neutral scalar $$\langle \phi \rangle \simeq 2.7$$ ⟨ ϕ ⟩ ≃ 2.7 TeV, which correspond to the dark matter mass 2.0 TeV, its spin-independent cross section $$1.8\times 10^{-9}$$ 1.8 × 10 - 9 pb, and the mass of additional neutral scalar 190 GeV.