Omega and the initial fluctuations from velocity and density fields

We present a method for determining the cosmological density parameter OMEGA independently of biasing, while recovering the one-point probability distribution function of initial density fluctuations (IPDF) from quasi-linear velocity and density fields. The key idea is that IPDF recovered from a velocity field is sensitive to the assumed OMEGA, while the same IPDF could be determined from a density field independently of OMEGA. The density field of IRAS galaxies, assuming that galaxies trace mass, indicates a Gaussian IPDF. The velocity field by POTENT from observed velocities, free of density biasing, agrees with a Gaussian IPDF if and only if OMEGA is about unity or larger: an open universe is rejected at the 2 σ level, and OMEGA <= 0. 3 is ruled out at the 4-6 σ level using several different statistics. The fact that the simplest choices of OMEGA = 1, Gaussian initial fluctuations and IRAS galaxies tracing mass are all consistent with one another under gravitational instability is a remarkable result in favor of the standard model.