Relic Density of Asymmetric Dark Matter with Sommerfeld enhancement

Abstract: We investigate the evolution of abundance of the asymmetric thermal Dark Matter when its annihilation rate at chemical decoupling is boosted by the Sommerfeld enhancement. Then we discuss the effect of kinetic decoupling on relic abundance of asymmetric Dark Matter when the interaction rate depends on the velocity. Usually the relic density of asymmetric Dark Matter is analyzed in the frame of chemical decoupling. Indeed after decoupling from the chemical equilibrium, asymmetric Dark Matter particles and anti--particles were still in kinetic equilibrium for a while. It has no effect on the case of $s-$wave annihilation since there is no temperature dependence in this case. However, the kinetic decoupling has impacts for the case of $p-$wave annihilation and Sommerfeld enhanced $s-$ and $p-$wave annihilations. We investigate in which extent the kinetic decoupling affects the relic abundances of asymmetric Dark Matter particle and anti--particle in detail. We found the constraints on the cross section and asymmetry factor by using the observational data of relic density of Dark Matter.