Omega from the skewness of the cosmic velocity divergence

We propose a method for measuring the cosmological density parameter from the statistics of the expansion scalar, H01r1v, { the divergence of peculiar velocity, expressed in units of the Hubble constant, H 100h km s 01 Mpc 01. The velocity eld is spatially smoothed over 10h01Mpc to remove strongly nonlinear e ects. Assuming weakly-nonlinear gravitational evolution from Gaussian initial uctuations, and using 3 00:6 2 second-order perturbative analysis, we show that / 0 2. The constant of proportionality depends on the smoothing window. For a top-hat of radius R and 2 volume-weighted smoothing, this constant is 26=7 0, where = 0d log =d log R. If the power spectrum is a power law, P (k) / kn, then = 3+n. A Gaussian window yields similar results. The resulting method for measuring is independent of any assumed biasing relation between galaxies and mass. The method has been successfully tested with numerical simulations. A preliminary application to real data, provided by the POTENT recovery procedure from observed velocities favors 1. However, because of an uncertain sampling error, this result should be treated as an assessment of the feasibility of our method rather than a de nitive measurement of.