  We show that the relic density of asymmetric dark matter with long-range
interactions is affected by the Sommerfeld enhancement. The annihilation cross
section of asymmetric dark matter is enhanced due to the Sommerfeld effect. It
results the relic density is decreased. Using the Planck date, the constraints
on the asymmetry factor and coupling required to attain the observed dark
matter density are obtained. We derive the upper bounds on the mass for
asymmetric dark matter in s-wave and p-wave annihilation cases.
