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Electroweak Baryogenesis, CDM and Anomaly-free Supersymmetric U(1)-prime Models

We construct two anomaly-free supersymmetric $U(1)'$ models with a secluded $U(1)'$-breaking sector. For the one with $E_6$ embedding we show that there exists a strong enough first order electroweak phase transition for electroweak baryogenesis (EWBG) because of the large soft trilinear terms in the Higgs potential. Unlike the Minimal Supersymmetric Standard Model (MSSM), the stop masses can be very heavy. We then discuss possible CP violation in the Higgs sector, which can be both spontaneous and explicit, even at tree level. The spontaneous violation provides a direct source for baryogenesis, while its magnitude is mediated by an explicit phase from the secluded sector. These new CP sources do not introduce significant new contributions to electric dipole moments. EWBG in the thin wall ($τ$ leptons) and thick wall regimes (top squarks, charginos and top quarks) are systematically discussed. We find that the CP-violating stop and chargino currents are very different from those obtained in the MSSM. Due to the space-dependence of the relevant CP phases, they do not require a variation of $\tan β$ in the bubble wall to have a non-trivial structure at the lowest order of Higgs insertion. In addition to $τ$ leptons, top squarks and charginos, we find that top quarks can also play a significant role. Numerical results show that the baryon asymmetry is large enough to explain the cosmological observation today. We illustrate that EWBG and neutralino cold dark matter can be accommodated in the same framework, i.e., there exists parameter space where a strong enough first order EWPT, large CP phase variations across the bubble wall, a reasonable baryon asymmetry as well as an acceptable neutralino dark matter relic density can be achieved simultaneously.