Gravitational waves in models with multicritical-point principle

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 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 Srightarrow -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.