An analysis of cosmological mixed dark matter models in spatially flat Friedmann Universe with zero \Lambda -term 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 ) \sigma _ { 8 } , the dispersion of the mass fluctuations in the sphere with radius 8 h ^ { -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 } = 100 h km s ^ { -1 } Mpc ^ { -1 } .
The cold dark matter density parameter is equal to \Omega _ { cdm } = 1 - \Omega _ { \nu } - \Omega _ { b } .
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 \sigma _ { 8 } = 0.52 \pm 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 \Omega _ { \nu } weakens the requirements to the value of T/S , however even for \Omega _ { \nu } \leq 0.4 the models with h + n \geq 1.5 suggest considerable abundance of gravitational waves , T/S ^ { > } _ { \sim } 0.3 .
In models with \Omega _ { \nu } \leq 0.4 and scale-invariant spectrum of density perturbations ( n = 1 ) , T/S ^ { > } _ { \sim } 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 \Omega _ { \nu } is strongly constrained by \Delta T / T data on the first acoustic peak of Sakharov oscillations .
Assuming that T/S \in [ 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 \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 height measured by BOOMERanG and MAXIMA-1 .