We study the domain wall solutions in the general two-Higgs-doublet model (2HDM) with a CP-violating phase. The 2HDM with the spontaneouse CP violation is found to have domain wall solutions whose tensions are $$ \mathcal{O} $$ O (106) GeV3, which are excluded by the Zel’dovich-Kobzarev-Okun bound. With the explicit CP-violating (CPV) terms as the so-called biased term in the scalar potential, domain walls can collapse in the early Universe. The sizes of the explicit CP violation can be constrained from the Big Bang nucleosynthesis. This constraint is converted to the CPV mixing of αc, and is mostly sensitive to the mass splittings between two heavy neutral Higgs bosons. We estimate the possible gravitational wave signals and the electric dipole moment (EDM) predictions due to the domain wall collapsing. It turns out that the peak spectrum of the GW from the domain wall collapsing cannot be probed in any future program. In contrast, the untenable regions with very tiny explicit CPV parameter in the Higgs potential has been partially excluded by the latest electron EDM measurements at the ACME-II and will be further confirmed or excluded by the future ACME-III projection.

We study a toy SU(6) model with the symmetry breaking pattern of the extended 331 symmetry of SU(3) c ⊗ SU(3) W ⊗ U(1) X . A "fermion-Higgs mismatching" symmetry breaking pattern is proposed for more realistic model building. Within such symmetry breaking pattern, only one Higgs doublet develops vacuum expectation value for the spontaneous electroweak symmetry breaking, and gives tree-level top quark mass. A natural VEV splittings in the 331 breaking Higgs fields gives treelevel masses to both bottom quark and tau lepton. The 125 GeV SM-like Higgs boson discovered at the LHC can have Yukawa couplings to bottom quark and tau lepton as in the SM prediction, and this sets the 331 symmetry breaking scale at ∼ O(10) TeV.

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