  A large amount of observations have constrained cosmological parameters and
the initial density fluctuation spectrum to a very high accuracy. However,
cosmological parameters change with time and the power index of the power
spectrum varies with mass scale dramatically in the so-called concordance
Lambda CDM cosmology. Thus, any successful model for its structural evolution
should work well simultaneously for various cosmological models and different
power spectra. We use a large set of high-resolution N-body simulations of a
variety of structure formation models (scale-free, standard CDM, open CDM, and
Lambda CDM) to study the mass accretion histories (MAHs), the mass and redshift
dependence of concentrations and the concentration evolution histories of dark
matter halos. We find that there is significant disagreement between the
much-used empirical models in the literature and our simulations. According to
two simple but tight correlations we find from the simulation results, we
develop new empirical models for both the MAHs and the concentration evolution
histories of dark matter halos, and the latter can also be used to predict the
mass and redshift dependence of halo concentrations. These models are accurate
and universal: the same set of model parameters works well for different
cosmological models and for halos of different masses at different redshifts
and the model predictions are highly accurate even when the histories are
traced to very high redshift. These models are also simple and easy to
implement. A web calculator and a user-friendly code to make the relevant
calculations are available from http://www.shao.ac.cn/dhzhao/mandc.html . We
explain why Lambda CDM halos on nearly all mass scales show two distinct phases
in their evolution histories.
