Hierarchical Formation of Dark Matter Halos and the Free Streaming Scale
  The smallest dark matter halos are formed first in the early universe.
According to recent studies, the central density cusp is much steeper in these
halos than in larger halos and scales as $\rho \propto r^{-(1.5-1.3)}$. We
present results of very large cosmological $N$-body simulations of the
hierarchical formation and evolution of halos over a wide mass range, beginning
from the formation of the smallest halos. We confirmed early studies that the
inner density cusps are steeper in halos at the free streaming scale. The cusp
slope gradually becomes shallower as the halo mass increases. The slope of
halos 50 times more massive than the smallest halo is approximately $-1.3$. No
strong correlation exists between inner slope and the collapse epoch. The cusp
slope of halos above the free streaming scale seems to be reduced primarily due
to major merger processes. The concentration, estimated at the present
universe, is predicted to be $60-70$, consistent with theoretical models and
earlier simulations, and ruling out simple power law mass-concentration
relations. Microhalos could still exist in the present universe with the same
steep density profiles.
