Relic density and CMB constraints on dark matter annihilation with Sommerfeld enhancement

Abstract

We calculate how the relic density of dark matter particles is altered when their annihilation is enhanced by the Sommerfeld mechanism due to a Yukawa interaction between the annihilating particles. Maintaining a dark matter abundance consistent with current observational bounds requires the normalization of the $s$-wave annihilation cross section to be decreased compared to a model without enhancement. The level of suppression depends on the specific parameters of the particle model, with the kinetic decoupling temperature having the most effect. We find that the cross section can be reduced by as much as an order of magnitude for extreme cases. We also compute the $\ensuremath{\mu}$-type distortion of the CMB energy spectrum caused by energy injection from such Sommerfeld-enhanced annihilation. Our results indicate that in the vicinity of resonances, associated with bound states, distortions can be large enough to be excluded by the upper limit $|\ensuremath{\mu}|\ensuremath{\le}9.0\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}5}$ found by the FIRAS (Far Infrared Absolute Spectrophotometer) instrument on the COBE (Cosmic Background Explorer) satellite.