Beyond the standard $Λ$CDM cosmology: the observed structure of DM halos and the shape of the power spectrum

Abstract: Recent advances in observational astronomy allow to study various groups of Dark Matter (DM) dominated objects from the dwarf spheroidal (dSph) galaxies to clusters of galaxies that span the mass range from $10^{6} M_{\odot}$ to $10^{15} M_{\odot}$. To analyze data of this divers collection of objects we used a simple toy model of spherical DM halo formation that was initially proposed by Peebles. This model introduced the concept of the epoch or redshift of halo formation. Using this concept we analyzed selected sample of DM dominated objects and we have found empirical 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 result 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 differs from expectations of the standard $\Lambda$CDM cosmology and 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.