Dark Matter and Electroweak Phase Transition in the $Z_2$ Symmetric Georgi-Machacek Model

We present a comprehensive investigation of the $Z_2$ symmetric Georgi-Machacek (GM) model, focusing on the dark matter (DM) in the model and the electroweak phase transition (EWPT). Our analysis encompasses multiple detections for the DM candidates, including collider searches at the LHC and LEP, the direct detection and indirect detection. Furthermore, we also explore the possibility of a first-order EWPT in this framework. The gravitational wave (GW) generated from the first-order EWPT also provides a detection method for the parameter space in the $Z_2$ symmetric GM model providing viable DM candidate. It is found that the current DM searches, especially the direct detection, provide strong constraints on the parameter space, while the GW signal can be complementary around the Higgs resonant region.