Current Status of Cosmological Models with Mixed Dark Matter

An analysis of cosmological mixed dark matter models in spatially flat Friedmann Universe with zero Λterm is presented. We argue that the introduction of cosmic gravity waves helps to satisfy observational constraints. The number of parameters is equal to 5, they are (1) σ8, the dispersion of the mass fluctuations in the sphere with radius 8hMpc, (2) n, the slope of the density perturbation spectrum, (3) Ων, the density of hot dark matter, (4) Ωb, the density of baryons, and (5) h, the Hubble constant H0 = 100 h kms Mpc. The cold dark matter density parameter is equal to Ωcdm = 1−Ων −Ωb. 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 σ8 = 0.52 ± 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 Ων weakens the requirements to the value of T/S, however even for Ων ≤ 0.4 the models with h + n ≥ 1.5 suggest considerable abundance of gravitational waves, T/S> ∼ 0.3. In models with Ων ≤ 0.4 and scale-invariant spectrum of density perturbations (n = 1), T/S> ∼ 10(h − 0.47). 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 Ων is strongly constrained by ∆T/T data on the first acoustic peak of Sakharov oscillations. Assuming that T/S ∈ [0, 3] and taking into account observational data on the primordial nucleosynthesis and 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 ∈ [0.9, 1.2] with rather high abundance hot dark matter, Ων ∈ [0.2, 0.4]. Any condition, n < 0.9 or Ων < 0.2, decreases the relative amplitude of the first acoustic peak for more than 30% in comparison with its height measured by BOOMERanG and MAXIMA-