Gravitational waves in models with multicritical-point principle

The multicritical-point principle (MPP) provides a natural explanation of the large hierarchy between the Planck and electroweak scales. We consider a scenario in which MPP is applied to the Standard Model extended by two real singlet scalar fields $$\phi $$ and S, and a dimensional transmutation occurs by the vacuum expectation value of $$\phi $$. In this paper, we focus on the critical points that possess a $${\mathbb {Z}}_2$$ symmetry $$S\rightarrow -S$$ and all the other fields are left invariant. Then S becomes a natural dark matter (DM) candidate. Further, we concentrate on the critical points where $$\phi $$ does not possess further $${\mathbb {Z}}_2$$ symmetry so that there is no cosmological domain-wall problem. Among such critical points, we focus on maximally critical one called CP-1234 that fix all the superrenormalizable parameters. We show that there remains a parameter region that satisfies the DM relic abundance, DM direct-detection bound and the current LHC constraints. In this region, we find a first-order phase transition in the early universe around the TeV-scale temperature. The resultant gravitational waves are predicted with a peak amplitude of $${{\mathcal {O}}}(10^{-12})$$ at a frequency of $$10^{-2}{-}10^{-1}$$ Hz, which can be tested with future space-based instruments such as DECIGO and BBO