Current status of cosmological MDM model

Abstract

An analysis of cosmological models in spatially flat Friedmann Universe with cosmic gravitational wave background and zero $Λ$-term is presented. The number of free parameters is equal to 5, they are $σ_8$, $n$, $Ω_ν$, $Ω_b$, and $h$. The normalization of the spectrum of density perturbations on galaxy cluster abundance ($σ_8 = 0.52\pm 0.04$) has been used to calculate numerically the value of the large scale CMB anisotropy ($\ell\simeq 10$) and the relative contribution of cosmological gravitational waves T/S. Increasing $Ω_ν$ weaken the requirements to the value of T/S, however even for $Ω_ν\le 0.4$ the models with $h+n\ge 1.5$ suggest considerable abundance of gravitational waves: T/S${}^>_\sim 0.3$. In models with $Ω_ν\le 0.4$ and scale-invariant spectrum of density perturbations ($n=1$): T/S${}^>_\sim 10(h-0.47)$. Minimization of the value T/S is possible only in the range of the red spectra ($n<1$) and small $h$ ($<0.6$). It is shown that the models with T/S$\in [0, 3]$ admit both moderate red and blue spectra of density perturbations, $n\in[0.9,1.2]$, with rather high abundance hot dark matter, $Ω_ν\in [0.2,0.4]$. Any condition, $n<0.9$ or $Ω_ν<0.2$, decreases the relative amplitude of the first acoustic peak for more than 30% in comparison with its hight in the standard CDM normalized by COBE data.