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We apply the well known semi analytical model of formation of DM halos todiscuss the process of formation and evolution of the relaxed objects dominatedby the DM component (such as the first and dSph galaxies and clusters ofgalaxies). On the one hand this approach allows us to obtain a simpledescription of evolution of the first galaxies. On the other hand it revealslinks between the observed characteristics of the relaxed DM halos and theinitial power spectrum of density perturbations. Results of our analysis of theobserved properties of 41 DM dominated dSph galaxies and data of $\sim 300$clusters of galaxies are consistent with the $\Lambda$CDM like power spectrumof initial perturbations down to the scale of $\sim 10kpc$.

Semi analytical description of formation of galaxies and clusters of galaxies