Production of dark-matter bound states in the early universe by
  three-body recombination
  The small-scale structure problems of the universe can be solved by
self-interacting dark matter that becomes strongly interacting at low energy. A
particularly predictive model for the self-interactions is resonant short-range
interactions with an S-wave scattering length that is much larger than the
range. The velocity dependence of the cross section in such a model provides an
excellent fit to self-interaction cross sections inferred from dark-matter
halos of galaxies and clusters of galaxies if the dark-matter mass is about 19
GeV and the scattering length is about 17 fm. Such a model makes definite
predictions for the few-body physics of weakly bound clusters of the
dark-matter particles. The formation of the two-body bound cluster is a
bottleneck for the formation of larger bound clusters. We calculate the
production of two-body bound clusters by three-body recombination in the early
universe under the assumption that the dark matter particles are identical
bosons, which is the most favorable case. If the dark-matter mass is 19 GeV and
the scattering length is 17 fm, the fraction of dark matter in the form of
two-body bound clusters can increase by as much as 4 orders of magnitude when
the dark-matter temperature falls below the binding energy, but its present
value remains less than 10^(-6). The present fraction can be increased to as
large as 10^(-3) by relaxing the constraints from small-scale structure and
decreasing the mass of the dark matter particle.
