  We study the electroweak symmetry breaking in the framework of a classically
conformal $U(1)_{B-L}$ theory, where three right-handed neutrinos (RHNs) and a
hidden scalar are introduced, with the latter playing the role of dark matter
(DM). It is found that the DM and RHN sectors are crucial for the spontaneous
symmetry breaking of the $U(1)_{B-L}$ symmetry, strong first order phase
transition in the conformal theory and the resultant gravitational wave (GW)
prospects at future space-based interferometer LISA and other GW experiments.
The baryon asymmetry of the Universe is addressed by the resonant leptogenesis
mechanism, which is potentially disturbed by the hidden scalar. To make the GW
spectra detectable by LISA and resonant leptogenesis work in the conformal
$U(1)_{B-L}$ theory, the hidden scalar can not fully saturate the observed DM
relic density.
