Current Status of cosmological models with mixed dark matter

An analysis of cosmological mixed dark matter models in spatially flat Friedmann Universe with zero $\Lambda$-term is presented. We argue that the introduction of cosmic gravity waves helps to satisfy observational constraints. The analysis of models is based on the confrontation with the mass function of clusters of galaxies and the CMB anisotropy. The implication of Press-Schechter formalism allowed to constrain $\sigma_8=0.52 \pm 0.01$. This normalisation of the spectrum of density perturbations has been used to calculate numerically the value of the large scale CMB anisotropy and the relative contribution of cosmological gravitational waves, T/S. We found that increasing $\Omega_\nu$ weakens the requirements to the value of T/S, however even for $\Omega_\nu\le 0.4$ the models with $h+n\ge 1.5$ suggest considerable abundance of gravitational waves, T/S${}^>_\sim 0.3$. Minimisation of the value T/S is possible only in the range of the red spectra ($n<1$) and small $h$ ($<0.6$). However the parameter $\Omega_\nu$ is strongly constrained by $\Delta T/T$ data on the first acoustic peak of Sakharov oscillations. Assuming that T/S $\in[0,3]$ and taking into account observational data on the amplitude of the first acoustic peak we constrain the model parameters. We show that the considered models admit both moderate red and blue spectra of density perturbations $n\in [0.9,1.2]$ with rather high abundance hot dark matter, $\Omega_\nu \in [0.2,0.4]$. Any condition, $n<0.9$ or $\Omega_\nu<0.2$, decreases the relative amplitude of the first acoustic peak for more than 30% in comparison with its height measured by BOOMERanG.