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 $m_{\nu}$, number species of massive neutrino $N_{\nu}$, baryon content $\Omega_b$ and Hubble constant $h\equiv H_0/100km/s/Mpc$. The $\chi^2$ 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 $\Omega_{\nu}$ ($\sim 0.4-0.5$), low $\Omega_b$ ($\le 0.01$) and $h$ ($\sim 0.4-0.6$). The best-fit parameters are as follows: $N_{\nu}=3$, $m_{\nu}=4.4eV$, $h=0.56$, $\Omega_b\le 0.01$. The high-$\Omega_b\sim 0.4-0.5$ 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 $\chi^2$, increases the bulk motions, but does not change essentially the best-fit MDM parameters. It is shown also that models with the median $\Omega_{\nu}\sim 0.2-0.3$ ($m_{\nu}\sim 2.5$, $N_{\nu}\sim 2-3$) and $\Omega_b=0.024/h^2$, which match constraints arising from cosmological nucleosynthesis and high redshift objects, are not ruled out by these data ($\Delta \chi^2<1$).