"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"