  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.
