Abstract
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.
Highlights
When the center-of-mass collision energy E decreases below the energy scale 1/mr02 set by the range, the elastic cross section increases as 1/E, nearly saturating the Swave unitarity bound
We study 3-body recombination into dark deuterons during the Hubble expansion in the early universe under the assumption that the dark matter consists of dark nucleons that are identical bosons with a large positive scattering length, which is the most favorable case for the formation of universal bound clusters
The predictions of ΛCDM cosmology face a number of challenges at small scales
Summary
We summarize the universal two-body physics of particles with short-range self-interactions and a large scattering length. We determine the mass and the large scattering length of a dark nucleon that would be required to solve the small-scale structure problems of the universe
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