Exploring first order phase transition in $U(1)$ extended models by complementarity between collider measurements and cosmological observations

Abstract

We consider models with the $U(1)_X$ gauge symmetry, which is spontaneously broken by dark Higgs mechanism. We discuss patterns of the electroweak phase transition and detectability of gravitational waves (GWs) when strongly first order phase transition (1stOPT) occurs. It is pointed out that the collider bounds on the properties of the discovered Higgs boson exclude a part of parameter space that could otherwise generate detectable GWs. We find that GWs produced from multi-step PT can be detected at future observations such as LISA and DECIGO if the dark photon mass is $m_X^{} \gtrsim 25$ GeV with the $U(1)_X^{}$ gauge coupling being $g_X^{} \gtrsim 0.5$. In addition, we show that most of the parameter regions can be covered by precision measurements of various Higgs boson couplings and direct searches for the singlet scalar boson at future collider experiments. Furthermore, we expect the complementarity of the detection of GW observations from the strongly 1stOPT, collider bounds and dark photon searches in the models of the dark gauge symmetry.