Gravitational waves in models with multicritical-point principle

Abstract

Abstract 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 $$\phi $$ ϕ and S, and a dimensional transmutation occurs by the vacuum expectation value of $$\phi $$ ϕ . In this paper, we focus on the critical points that possess a $${\mathbb {Z}}_2$$ Z 2 symmetry $$S\rightarrow -S$$ S → - 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 $$\phi $$ ϕ does not possess further $${\mathbb {Z}}_2$$ 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 $${{\mathcal {O}}}(10^{-12})$$ O ( 10 - 12 ) at a frequency of $$10^{-2}{-}10^{-1}$$ 10 - 2 - 10 - 1 Hz, which can be tested with future space-based instruments such as DECIGO and BBO.