  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.
