Best-fit parameters of MDM model from Abell-ACO power spectra and mass function

Abstract

The possibility of determining MDM model parameters on the basis of observable data on the Abell-ACO power spectrum and mass function is analysed. It is shown that spectrum area corresponding to these data is sensitive enough to such MDM model parameters as neutrino mass $m_ν$, number species of massive neutrino $N_ν$, baryon content $Ω_b$ and Hubble constant $h\equiv H_0/100km/s/Mpc$. The $χ^2$ minimization method was used for their determination. If all these parameters are under searching then observable data on the Abell-ACO power spectrum and mass function prefer models which have parameters in the range $Ω_ν$ ($\sim 0.4-0.5$), low $Ω_b$ ($\le 0.01$) and $h$ ($\sim 0.4-0.6$). The best-fit parameters are as follows: $N_ν=3$, $m_ν=4.4eV$, $h=0.56$, $Ω_b\le 0.01$. The high-$Ω_b\sim 0.4-0.5$ solutions are obtained when mass of neutrino is fixed and $\le 3eV$. To explain the observable excessive power at $k\approx 0.05h/Mpc$ the peak of Gaussian form was introduced in primordial power spectrum. Its parameters (amplitude, position and width) were determined along with the MDM model parameters. It decreases $χ^2$, increases the bulk motions, but does not change essentially the best-fit MDM parameters. It is shown also that models with the median $Ω_ν\sim 0.2-0.3$ ($m_ν\sim 2.5$, $N_ν\sim 2-3$) and $Ω_b=0.024/h^2$, which match constraints arising from cosmological nucleosynthesis and high redshift objects, are not ruled out by these data ($Δχ^2<1$).