On the classical description of the recombination of dark matter particles with a Coulomb-like interaction

Cold dark matter (DM) scenario may be cured of several problems by involving self-interaction of dark matter. Viability of the models of long-range interacting DM crucially depends on the effectiveness of recombination of the DM particles, making thereby their interaction short-range. Usually in numeric calculations, recombination is described by cross section obtained on a feasible quantum level. However in a wide range of parameter values, a classical treatment, where the particles are bound due to dipole radiation, is applicable. The cross sections, obtained in both approaches, are very different and lead to diverse consequences. Classical cross section has a steeper dependence on relative velocity, what leads to the fact that, after decoupling of DM particles from thermal background of dark photons (carriers of DM long-range interaction), recombination process does not freeze out, diminishing gradually density of unbound DM particles. Our simplified estimates show, that at the taken parameter values (the mass of DM particle is 100 GeV, interaction constant is 100(-1), and quite natural assumptions on initial conditions, from which the result is very weakly dependent) the difference in residual density reaches about 5 orders of magnitude on pre-galactic stage. This estimate takes into account thermal effects induced by dipole radiation and recombination, which resulted in the increase of both temperature and density of DM particles by a half order of magnitude. (C) 2016 The Author(s). Published by Elsevier B.V.