A solution to the problems of cusps and rotation curves in dark matter
  halos in the cosmological standard model
  We discuss various aspects of the inner structure formation in virialized
dark matter (DM) halos that form as primordial density inhomogeneities evolve
in the cosmological standard model. The main focus is on the study of central
cusps/cores and of the profiles of DM halo rotation curves, problems that
reveal disagreements among the theory, numerical simulations, and observations.
A method that was developed by the authors to describe equilibrium DM systems
is presented, which allows investigating these complex nonlinear structures
analytically and relating density distribution profiles within a halo both to
the parameters of the initial small-scale inhomogeneity field and to the
nonlinear relaxation characteristics of gravitationally compressed matter. It
is shown that cosmological random motions of matter `heat up' the DM particles
in collapsing halos, suppressing cusp-like density profiles within developing
halos, facilitating the formation of DM cores in galaxies, and providing an
explanation for the difference between observed and simulated galactic rotation
curves. The analytic conclusions obtained within this approach can be confirmed
by the N-body model simulation once improved spatial resolution is achieved for
central halo regions.
