Gravitational wave and collider signals in complex two-Higgs doublet model with dynamical CP-violation at finite temperature

Extra CP-violating source for electroweak baryogenesis can dynamically appear at finite temperature in the complex two-Higgs doublet model, which might help to alleviate the strong constraints from the electric dipole moment experiments. In this scenario, we study the detailed phase transition dynamics and the corresponding gravitational wave signals in synergy with the collider signals at future lepton colliders. For some parameter spaces, various phase transition patterns can occur, such as the multi-step phase transition and supercooling. Gravitational waves complementary to collider signals can help to pin down the underlying phase transition dynamics or different phase transition patterns.