Production of dark-matter bound states in the early universe by three-body recombination

TL;DR

This paper investigates the formation of dark-matter bound states in the early universe through three-body recombination, focusing on a resonant interaction model that explains galaxy-scale observations.

Contribution

It provides the first calculation of two-body dark-matter bound state production via three-body recombination in the early universe for a specific resonant interaction model.

Findings

The fraction of dark matter in two-body bound states can increase significantly after formation.

Current bound state fractions are very small, less than 10^(-6).

Relaxing constraints can increase the bound state fraction to about 10^(-3).

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.