Structure Formation Constraints on Sommerfeld-Enhanced Dark Matter Annihilation

We study the growth of cosmic structure under the assumption that dark matter self-annihilates with an averaged cross section times relative velocity that grows with the scale factor, an increase known as Sommerfeld-enhancement. Such an evolution is expected in models in which a light force carrier in the dark sector enhances the annihilation cross section of dark matter particles, and has been invoked, for instance, to explain anomalies in cosmic ray spectra reported in the past. In order to make our results as general as possible, we assume that dark matter annihilates into a relativistic species that only interacts gravitationally with the standard model. This assumption also allows us to test whether the additional relativistic species mildly favored by cosmic-microwave background data could originate from dark matter annihilation. We do not find evidence for Sommerfeld-enhanced dark matter annihilation and derive the corresponding upper limits on the annihilation cross-section.