Electroweak baryogenesis, dark matter, and dark $CP$ symmetry

With the motivation of explaining the dark matter and achieving the electroweak baryogenesis via the spontaneous $CP$ violation at high temperature, we propose a complex singlet scalar ($S=\frac{\chi +i{\eta }_s}{\sqrt{2}}$) extension of the two-Higgs-doublet model respecting a discrete dark $CP$ symmetry: $S\to -S^{*}$. The dark $CP$ symmetry guarantees $\chi$ to be a dark matter candidate on one hand and on the other hand allows ${\eta }_s$ to have mixings with the pseudoscalars of the Higgs doublet fields, which play key roles in generating the $CP$ violation sources needed by the electroweak baryogenesis at high temperature. The Universe undergoes multistep phase transitions, including a strongly first-order electroweak phase transition during which the baryon number is produced. At the present temperature, the observed vacuum is produced and the $CP$ symmetry is restored so that the stringent electric dipole moment experimental bounds are satisfied. Considering relevant constraints, we study the simple scenario of $m_{\chi }$ around the Higgs resonance region, and find that the dark matter relic abundance and the baryon asymmetry can be simultaneously explained. Finally, we briefly discuss the gravitational wave signatures at future space-based detectors and the LHC signatures.

Figure 1

${\lambda }_h$ consistent with the relic data versus $m_{\chi }$. The dark thick line is allowed by the direct and indirect searches for DM, and the light thick line is excluded by the indirect searches.

Figure 2

The scattering plots achieving the three-step PTs with the characteristics mentioned in the text, where we take $m_H=m_{H^{\pm }}$ and $0.1<s_{\theta }<0.7$.

Figure 3

The phase histories of the BP1, where $⟨\chi ⟩$ is always 0.

Figure 4

The radial nucleation bubble wall VEV profiles for the first-order EWPT.

Figure 5

The ${\mu }_i$ and $u_i$ from the transport equations as functions of the position of the bubble wall.

Figure 6

$Y_B$ as a function of $v_w$ for the BP1.

Figure 7

$Y_B$ versus $\tan \beta$ and $Y_B$ versus $\mu$ for the left panel and right panel.