Using a combination of N-body simulations with different resolutions , we study in detail how the concentrations of cold dark matter ( CDM ) halos depend on halo mass at different redshifts .
We confirm that halo concentrations at the present time depend strongly on halo mass , but our results also show marked differences from the predictions of some early empirical models .
Our main result is that the mass dependence of the concentrations becomes weaker at higher redshifts , and at z \gtrsim 3 halos of mass greater than 10 ^ { 11 } { h ^ { -1 } M _ { \odot } } all have a similar median concentration , c \sim 3.5 .
While the median concentrations of low-mass halos grow significantly with time , those of massive halos change only little with redshifts .
These results are quantitatively in good agreement with the empirical model proposed by Zhao et al .
which shows that halos in the early fast accretion phase all have similar concentrations .