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.
