The cosmology of a standard model (SM) gauge singlet complex scalar dark matter (DM), stabilized by a reflection symmetry, is studied including all renormalizable interactions that preserve the reflection symmetry but can break the larger global U(1) symmetry of DM number. We find an interesting interplay of the ensuing DM self-scatterings and annihilations in generating the present DM density, and possible particle-antiparticle asymmetry in the DM sector. The role of DM self-scatterings in determining its present density and composition is a novel phenomenon. The simultaneous presence of the self-scatterings and annihilations is required to obtain a non-zero asymmetry, which otherwise vanishes due to unitarity sum rules.
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