Mixed Cold-Hot Dark Matter Model with Falling and Quasi-Flat Initial   Perturbation Spectra
  The mixed cold-hot dark matter cosmological model (CHDM) with $\Omega_{tot}=1$ and a falling power-law initial spectrum of Gaussian adiabatic perturbations ($n>1$) is tested using recent obserbational data. It is shown that its fit to the data becomes worse with the growth of $n-1$, and may be considered as unreasonable for $n>1.1$ for all possible values of the Hubble constant. Thus, the CHDM model with a falling initial spectrum is worse than the same model with the approximately flat $(|n-1|<0.1)$ spectrum. On the other hand, the CHDM model provides a rather good fit to the data if $n$ lies in the range $(0.9-1.0)$, the Hubble constant $H_0 < 60$ km/s/Mpc ($H_0 < 55$ for $n=1$) and the neutrino energy density $\Omega_{\nu}< 0.25$. So, the CHDM model provides the best possibility for the realization of the simplest variants of the inflationary scenario having the effective slope $n\approx (0.95-0.97)$ between galaxy and horizon scales, including a modest contribution of primordial gravitational wave background to large-angle $\Delta T/T$ fluctuations of the cosmic microwave background (resulting in the increase of their total {\it rms} amplitude by $(5-10)%$) expected in some variants. A classification of cosmological models according to the number of fundamental parameters used to fit observational data is presented, too. 
Dmitri Pogosyan and Alexei Starobinsky