  In this work, we make the first study of electroweak baryogenesis (EWBG)
based on the LHC data in the CP-violating next-to-minimal supersymmetric model
(NMSSM) where a strongly first order electroweak phase transition (EWPT) is
obtained in the general complex Higgs potential. With representative benchmark
points which pass the current LEP and LHC constraints, we demonstrate the
structure of EWPT for those points and how a strongly first order EWPT is
obtained in the complex NMSSM where the resulting gravitational wave production
properties are found to be within the reaches of future space-based
interferometers like BBO and Ultimate-DECIGO. We further calculate the
generated baryon asymmetries where the CP violating sources are (1):
higgsino-singlino dominated, (2): higgsino-gaugino dominated or (3): from both
sources. It is shown that all three representing scenarios could evade the
strong constraints set by various electric dipole moments (EDM) searches where
cancellations among the EDM contributions occur at the tree level
(higgsino-singlino dominated) or loop level (higgsino-gaugino dominated). The
125 GeV SM like Higgs can be either the second lightest neutral Higgs $H_2$ or
the third lightest neutral Higgs $H_3$. Finally, we comment on the future
direct and indirect probe of CPV in the Higgs sector from the collider and EDM
experiments.
