CURRENT STATUS OF COSMOLOGICAL MDM MODELS
E.V. MIKHEEVA, V.N. LUKASH, N.A. ARKHIPOVA, A.M. MALINOVSKY
Astro Space Center of Lebedev Physical Institute,
84/32 Profsoyuznaya, Moscow 117810, Russia

Abstract:
An analysis of cosmological models in spatially flat Friedmann Universe with cosmic gravitational wave background and zero $\Lambda$-term is presented. The number of parameters is equal to 5, they are (1) $\sigma_8$, the dispersion of the mass fluctuations in the sphere with radius $8h^{-1}Mpc$, (2) $n$, the slope of the density perturbation spectrum, (3) $\Omega_\nu$, the density of hot dark matter, (4) $\Omega_b$, the density of baryons, and (5) $h$, the Hubble constant $H_0=100h\;km\,s^{-1}\,Mpc^{-1}$. The cold dark matter density parameter is equal to $\Omega_{cm}=1-\Omega_\nu-\Omega_b$. Our analysis is based on the confrontation with the number density and mass function of clusters of galaxies and CMBR anisotropy. The implication of Press-Schechter formalism allowed us to constrain $\sigma_8=0.52 \pm 0.04$. This normalization of the spectrum of density perturbations 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 $\Omega_\nu$ weaken 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${}^>_\sim 0.3$. In models with $\Omega_\nu\le 0.4$ 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 $h$ ($<0.6$). However, the parameter $\Omega_\nu$ is strongly constrained by $\Delta T/T$ data on the first acoustic peak of Sacharov oscilations ($\ell\simeq 200$). Assuming that T/S $\in[0,3]$ and taking into account observational data on the primordial nucleosynthesis and the amplitude of the acoustic peak we constrain the model parameters $\Omega_\nu$ and $n$: it is shown that the models considered 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 hight in the standard CDM normalized by COBE data.