Perturbative Analysis of the Electron EDM and CP Violation in Two Higgs Doublet Models

I consider a general two Higgs doublet model with CP violation. I give a perturbative expansion for the mass eigenstates in terms of the small CP violating phase. I use these analytical expressions to show that $\mathcal{O}(10^{-2})$ CP violation is allowed by the experimental bounds on the electron electric dipole momnent in some regions of the parameter space. These regions also include parameters that are expected to give a strongly first order electroweak phase transition required for electroweak baryogenesis. I also comment on how to incorporate the CP violation into the searches for a strongly first order electroweak phase transition which could explain the matter/anti-matter asymmetry in the universe.