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Observational Constraints for Power-law spectra of Density Perturbations

We present an analysis of cosmological models with mixed dark matter (spectrum slope of density perturbations $n_S \in [0.6, 1.6]$, hot dark matter abundance $Ω_ν\in [0.0, 0.6]$) in spatially flat Universe, based on Press-Schechter formalism (P\&S). We found that the models with $n_S > 1$ and $Ω_ν< 0.5$ are preferable. Additionally, for all considered models we simulated $ΔT/T\vert_{10^0}$ and compared it with the COBE measured amplitude of CMB anisotropy. We found that the models favourable for galaxy cluster abundance need large amount of cosmological gravitational waves (T/S $> 1$).