Relic density of asymmetric Dark Matter with Sommerfeld enhancement

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.Next,we discuss the effect of kinetic decoupling on the relic abundance of asymmetric Dark Matter when the interaction rate depends on velocity.Usually,the relic den sity of asymmetric Dark Matter is analyzed in the frame of chemical decoupling.In deed,after decoupling from chemical equilibrium,asymmetric Dark Matter particles and anti-particles are still in kinetic equilibrium for a while.This has no effect for the case of 5-wave annihilation since there is no temperature dependenee in this case.However,kinetic decoupling has impacts for the case of p-wave annihilation and Sommerfeld enhanced s-and p-wave annihilations.We investigate in detail the extent to which kinetic decoupling affects the relic abundanee of asymmetric Dark Matter particles and anti-particles.We find the constraints on the cross section and asymmetry factor using observational data of the relic density of Dark Matter.