Roman Juszkiewicz (1,2), Pedro Ferreira (3), Ruth Durrer (2)
(1) Copernicus Astronomical Center, Warsaw, Poland,
(2) D{\'e}partement de Physique Th{\'e}orique, Universit{\'e} de Gen{\`e}ve, Switzerland,
(3) Astronomy Department, University of California, Berkeley, USA

We have recently proposed a new dynamical estimator of $\Omega_m$ - the mean density of the pressureless, nonrelativistic matter in the Universe. The statistic we use is the mean relative peculiar velocity of pairs of galaxies at fixed separation $r$, called the galaxy streaming velocity, $v_{12}(r)$. The streaming velocity is measured directly from a peculiar velocity-distance indicator survey. Our method is nonlinear and non-perturbative, and it can be used to estimate $\Omega_m$ separately from $\sigma_8$ - the standard normalization parameter. Our approach is simpler and more direct than reconstruction schemes used in this context; it is free from procedures which amplify observational errors (e.g, taking spatial derivatives of noisy data). We also report the results obtained by applying our technique to the Mark III survey. We find $\sigma_8 \geq 0.75$ and $\Omega_m = 0.35 \pm 0.25$. Fixing $\sigma_8 = 1$ (an ``unbiased'' model) gives $\Omega_m = 0.35 \pm 0.1$. The unbiased Einstein-de Sitter cosmological model $(\Omega_m = \sigma_8 = 1)$ is inconsistent with our data at the 99\% confidence level. Our results are consistent with estimates of $\Omega_m$ based on distances to the type Ia supernovae, taken together with the MAXIMA and Boomerang measurements of the angular power spectrum of the cosmic microwave background fluctuations.