Beyond the $\Lambda$CDM cosmology: complex composition of dark matter

The mass and composition of dark matter (DM) particles and the shape and damping scales of the power spectrum of density perturbations can be estimated from recent observations of the DM dominated relaxed objects -- dwarf galaxies and clusters of galaxies. We confirm that the observed velocity dispersion of dSph galaxies agrees with the possible existence of DM particles with mass $m_w\sim 15 - 20keV$. More complex analysis utilizes the well known semi analytical model of formation of DM halos in order to describe the basic properties of corresponding objects and to estimate their redshifts of formation. For the DM halos this redshift is determined by their masses and the initial power spectrum of density perturbations. This correlation allows us to partly reconstruct the small scale spectrum of perturbations. We consider the available sample of suitable observed objects that includes $\sim 40$ DM dominated galaxies and $\sim 40$ clusters of galaxies and we show that the observed characteristics of these objects are inconsistent with expectations of the standard $\Lambda$CDM cosmological model. However, they are consistent with a more complex DM model with a significant contribution of the hot DM--like power spectrum with relatively large damping scale ($\sim 10 - 30Mpc$). The HDM component of DM decelerates but does not prevent formation of low mass objects. These preliminary inferences require confirmation by a more representative observational data that should include -- if possible -- DM dominated objects with intermediate masses $M\sim 10^{10} - 10^{12} M_\odot$. Comparison of observed properties of such objects with numerical simulations will provide more detailed picture of the process of formation of DM halos.