Self similarity of the dark matter dominated objects and the shape of small scale power spectrum

We analyzed available observational data of a sample of dark matter (DM) dominated galaxies and clusters of galaxies and we have found correlations between the virial mass, $M_{vir}$, of halos and basic parameters of their cores, namely, the mean DM density, pressure and entropy. These correlations are a natural consequence of similar evolution of all such objects. It is driven mainly by gravitational interactions what implies a high degree of self similarity of both the process of halos formation and their internal structure. We confirmed the CDM--like shape of both the small and large scale power spectrum. However, our reconstruction of the evolutionary history of observed objects requires either a multicomponent composition of DM or a more complex primordial power spectrum of density perturbations with significant excess of power at scales of clusters of galaxies and larger. We demonstrated that a model with suitable combination of the heavy DM particles (CDM) and DM particles with large damping scale (HDM) could provide a successful description of the observational data in a wide range of masses.