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 ${\cal O}(10^{-12})$ at a frequency of $10^{-2}$-$10^{-1}$ Hz,
which can be tested with future space-based instruments such as DECIGO and BBO.
