Large scale structure formation in mixed dark matter models with a cosmological constant

We study linear power spectra and formation of large scale structures in flat cosmological models with $\Lambda \ge 0$ and cold plus hot dark matter components (MLM). The hot component consists of massive neutrinos with cosmological density $\Omega_H$. The linearized Einstein-Boltzmann equations for the evolution of the metric and density perturbations are integrated for a set of values of the cosmological parameters. For all the considered models we assume a scale-invariant primeval spectrum. The density weighted final linear power spectra are normalized to the four year COBE data and have been used to constrain the parameter space by a comparison of linear predictions with the current observational data on large scales. The consistency of MLM predictions with the observable data set is best obtained for models with one specie of massive neutrinos and $\Omega_H/\Omega_M \le0.2$. For this class of MLM models we obtain constraints from linear data on the present matter density. Consistency with the estimated cluster abundance can be achieved for COBE normalized MLM models with $\Omega_H/\Omega_M\le0.2$ and $ 0.45 \le \Omega_M \le 0.75$ for $h=0.5$. If $h=0.7$ then $ 0.3 \le \Omega_M \le 0.5$. These constraints are at $1\sigma$ level and standard MDM models are clearly ruled out. We note that the range of allowed values for $\Omega_M$, that we obtain for MLM models from linear analysis, is also approximately the same range that is needed in order to consistently satisfy a variety of independent observational constraints.