Statistical evaluation of the observational information on $\Omega_m$ and $\Omega_\Lambda$

Abstract

We undertake a critical evaluation of recent observational information on $\Omega_m$ and $\Omega_\Lambda$ in order to identify possible sources of systematic errors and effects of simplified statistical analyses. We combine observations for which the results have been published in the form of likelihood contours in the $\Omega_m ,\Omega_\Lambda$ plane. We approximate the contours by fifth order polynomials, and we then use the maximum likelihood method to obtain joint likelihood contours for the combined data. In the choice of statistical merits we aim at minimum loss of information rather than at minimum variance. We find that $\Omega_0 = \Omega_m + \Omega_\Lambda = 0.99\pm 0.04 \pm 0.03$, where the first error is mainly statistical and the second error is systematical. In a flat Universe we find $\Omega_m^{flat} = 0.31 \pm 0.04 \pm 0.04$.