  We examine CP-violating effects on electroweak phase transition (EWPT) in the
standard model with a complex singlet scalar focusing particularly on a
scenario where additional scalars have masses close to 125 GeV. Such a high
mass degeneracy makes collider signatures in the scenario standard model like,
and current experimental data cannot distinguish them from the standard model
predictions. We utilize a simplified scalar potential to understand impacts of
CP violation on EWPT qualitatively. Then, one-loop effective potential with a
thermal resummation is employed for full numerical evaluations. As a
phenomenological consequence, gravitational waves from the first-order EWPT are
also evaluated. We find that the strength of the first-order EWPT would get
weaker as the CP-violating effect becomes larger. As a result, gravitational
wave amplitudes are diminished by the size of the CP violation. Future
gravitational wave experiments may shed light on CP violation in the singlet
scalar sector as well as the experimental blind spot due to the high mass
degeneracy.
