Current status of models with hot and cold dark matter

An analysis of a five-parameter family of cosmological models in a spatiall y flat Friedmann Universe with a zero A term is presented. The five paramet ers are (1) sigma (3) the dispersion of the mass fluctuations in a sphere w ith radius 8h(-1) Mpc, where h H-0/100 km s(-1) Mpc and H-0 is the Hubble c onstant; (2) h, the slope of the density-perturbation spectrum; (3) Omega ( v), the normalized energy density of hot dark matter; (4) Omega (b), the ba ryon density; and (5) h, the normalized Hubble constant. The density of col d dark matter is determined from the condition Omega (cdm) = 1 - Omega (v) - Omega (b). Analysis of the models is based on comparison of computational results with observational data for: (1) the number density and mass funct ion of galaxy clusters (a so- called Press-Schechter formalism) and (2) the cosmic microwave background anisotropy. The first method enabled us to det ermine the value sigma (8) = 0.52 +/- 0.01 with high accuracy. Using the re sulting normalization of the density-perturbation spectrum, we calculated a model for the anisotropy of the cosmic microwave background radiation on l arge scales (l similar or equal to 10, where l is the harmonic number) and the required contribution of cosmological gravitational waves, characterize d by the parameter T/S. The restrictions on T/S become weaker as Omega, inc reases. Nevertheless, even when Omega (v) less than or equal to 0.4 models with h + n > 1.5 require a considerable contribution from gravitational wav es: T/S greater than or similar to 0.3. On the other hand, in models with O mega (v) less than or equal to 0.4 and a scale-invariant density-perturbati on spectrum (n = 0.4), we find T/S greater than or similar to 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 Omega (v), is determined most accurately by the data on DeltaT/T near the first acoustic peak (l sim ilar or equal to 200). By imposing a general restriction on the amplitude o f gravitational waves T/S is an element of [0, 3] and taking into account t he available observational data on the amplitude of the acoustic peak of Sa kharov oscillations, ranges of possible values n and Omega (v) are derived. If the baryon number is constrained by nucleosynthesis data, the models un der consideration can have both moderately red and blue power spectra n is an element of [0.9, 1.2] with a rather high concentration of hot particles Omega (v) is an element of [0.2, 0.4]. The conditions that n < 0.9 and/or < Omega>(v) < 0.2 decrease the relative amplitude of the acoustic peak by ove r 30% compared to its value in the standard cold-dark-matter (CDM) model no rmalized using COBE data. (C) 2001 MAIK "Nauka/Interperiodica".