Current status of models with hot and cold dark matter

An analysis of a five-parameter family of cosmological models in a spatially flat Friedmann Universe with a zero Λ term is presented. The five parameters are (1) σ₈, the dispersion of the mass fluctuations in a sphere with radius 8h ^?1 Mpc, where h=H ₀/100 km s^?1 Mpc^?1 and H ₀ is the Hubble constant; (2) n, the slope of the density-perturbation spectrum; (3) Ω_v, the normalized energy density of hot dark matter; (4) Ω_b, the baryon density; and (5) h, the normalized Hubble constant. The density of cold dark matter is determined from the condition Ω _cdm >1?Ω_v?Ω _b . Analysis of the models is based on comparison of computational results with observational data for: (1) the number density and mass function of galaxy clusters (a so-called Press-Schechter formalism) and (2) the cosmic microwave background anisotropy. The first method enabled us to determine the value σ₈=0.52±0.01 with high accuracy. Using the resulting normalization of the density-perturbation spectrum, we calculated a model for the anisotropy of the cosmic microwave background radiation on large scales (l?10, where l is the harmonic number) and the required contribution of cosmological gravitational waves, characterized by the parameter T/S. The restrictions on T/S become weaker as Ω_v increases. Nevertheless, even when Ω_v≤0.4, models with h+n≥1.5 require a considerable contribution from gravitational waves: T/S?0.3. On the other hand, in models with Ω_v≤0.4 and a scale-invariant density-perturbation spectrum (n=1), we find T/S ?10(h?0.47). The minimization of T/S is possible only for the family of models with red spectra (n<1) and small h (<0.6). The value of Ω_v is determined most accurately by the data onΔT/T near the first acoustic peak (l?200). By imposing a general restriction on the amplitude of gravitational waves T/S∈0, 3] and taking into account the available observational data on the amplitude of the acoustic peak of Sakharov oscillations, ranges of possible values n and Ω_v are derived. If the baryon number is constrained by nucleosynthesis data, the models under consideration can have both moderately red and blue power spectra n∈0.9, 1.2] with a rather high concentration of hot particles Ω_v∈0.2,0.4]. The conditions that n<0.9 and/or Ω_v<0.2 decrease the relative amplitude of the acoustic peak by over 30% compared to its value in the standard cold-dark-matter (CDM) model normalized using COBE data.