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We consider a standard model extension equipped with a dark sector where the$U(1)_X^{}$ Abelian gauge symmetry is spontaneously broken by the dark Higgsmechanism. In this framework, we investigate patterns of the electroweak phasetransition as well as those of the dark phase transition, and examinedetectability of gravitational waves (GWs) generated by such strongly firstorder phase transition. It is pointed out that the collider bounds on theproperties of the discovered Higgs boson exclude a part of parameter space thatcould otherwise generate detectable GWs. After imposing various constraints onthis model, it is shown that GWs produced by multi-step phase transitions aredetectable at future space-based interferometers, such as LISA and DECIGO, ifthe dark photon is heavier than 25 GeV. Furthermore, we discuss thecomplementarity of dark photon searches or dark matter searches with the GWobservations in these models with the dark gauge symmetry.

Gravitational waves from first order electroweak phase transition in models with the $U(1)_X^{}$ gauge symmetry