Dark matter and electroweak phase transition in the mixed scalar dark matter model

We study the electroweak phase transition in the framework of scalar singlet-doublet mixed dark matter model, where the particle dark matter candidate is the lightest neutral Higgs that comprised of the CP-even component of inert doublet and a singlet scalar. The dark matter can be dominated by the inert doublet or singlet scalar depending on the mixing. We present several benchmark models to investigate the two situations after imposing several theoretical and experimental constraints. An additional singlet scalar and the inert doublet drive the electroweak phase transition to be strongly first order. A strong first order electroweak phase transition and a viable dark matter candidate can be accomplished in two benchmark models simultaneously, where a proper mass splitting among the neutral and charged Higgs masses is needed.