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We discuss various aspects of the inner structure formation in virializeddark matter (DM) halos that form as primordial density inhomogeneities evolvein the cosmological standard model. The main focus is on the study of centralcusps/cores and of the profiles of DM halo rotation curves, problems thatreveal disagreements among the theory, numerical simulations, and observations.A method that was developed by the authors to describe equilibrium DM systemsis presented, which allows investigating these complex nonlinear structuresanalytically and relating density distribution profiles within a halo both tothe parameters of the initial small-scale inhomogeneity field and to thenonlinear relaxation characteristics of gravitationally compressed matter. Itis shown that cosmological random motions of matter `heat up' the DM particlesin collapsing halos, suppressing cusp-like density profiles within developinghalos, facilitating the formation of DM cores in galaxies, and providing anexplanation for the difference between observed and simulated galactic rotationcurves. The analytic conclusions obtained within this approach can be confirmedby the N-body model simulation once improved spatial resolution is achieved forcentral halo regions.

A solution to the problems of cusps and rotation curves in dark matter halos in the cosmological standard model