High-redshift galaxy clustering and Ω0

We develop the properties of cosmological many-body clustering at high redshift and compare the resulting theoretical distributions with recent observations of groups of galaxies around z approximate to 3. Analyses of the observed variance of counts-in-cells and of the probability for forming strongly overdense regions suggest Omega(0) approximate to 0.3 +/- 0.2 and 0.1 less than or similar to Omega(0) less than or similar to 0.3, respectively, for Einstein-Friedmann universes. Since these models are essentially analytical, they allow us to examine statistical questions that have analogs in more complicated cold dark matter models based on small numbers of simulations. We show how future observations of the galaxy distribution function can test cosmological many-body clustering and determine Omega(0) more precisely. For Omega(0) less than or similar to 0.3, these models predict that galaxies start clustering at redshifts z greater than or similar to 10.