Dark matter from CP symmetry of order 4: evolution in the asymmetric regime

Multi-Higgs models equipped with global symmetries produce scalar dark matter (DM) candidates stabilized by the unbroken symmetry. It is remarkable that a conserved CP symmetry can also stabilize DM candidates, provided it is a CP symmetry of order higher than two. CP4 3HDM, the three-Higgs-doublet model with CP symmetry of order 4, is the simplest example of this kind. It contains two mass-degenerate scalar DM candidates $\varphi$ and $\bar\varphi$, each of them being a CP4 eigenstate and, therefore, its own antiparticle. A novel phenomenological feature of this model is the presence of $\varphi\varphi \leftrightarrow \bar\varphi\bar\varphi$ conversion process, which conserves CP. It offers a rare example of DM models in which self-interaction in the dark sector can significantly affect cosmological and astrophysical observables. Here, we explore the thermal evolution of these DM species in the asymmetric regime. We assume that a mechanism external to CP4 3HDM produces an initial imbalance of the densities of $\varphi$ and $\bar\varphi$. As the Universe cools down, we track the evolution of the asymmetry through different stages, and determine how the final asymmetry depends on the interplay between the conversion and annihilation $\varphi\bar\varphi \to $ SM and on the initial conditions. We begin with the analytic treatment of Boltzmann equations, present a detailed qualitative description of the process, and then corroborate it with numerical results obtained using a dedicated computer code. Finally, we check if the model can produce an observable indirect detection signal.