High-redshift galaxy clustering and Omega(0)

We develop the properties of cosmological many-body clustering at high reds hift and compare the resulting theoretical distributions with recent observ ations of groups of galaxies around z approximate to 3. Analyses of the obs erved variance of counts-in-cells and of the probability for forming strong ly overdense regions suggest Omega(0) approximate to 0.3 +/- 0.2 and 0.1 le ss than or similar to Omega(0) less than or similar to 0.3, respectively, f or Einstein-Friedmann universes. Since these models are essentially analyti cal, they allow us to examine statistical questions that have analogs in mo re complicated cold dark matter models based on small numbers of simulation s. We show how future observations of the galaxy distribution function can test cosmological many-body clustering and determine Omega(0) more precisel y. For Omega(0) less than or similar to 0.3, these models predict that gala xies start clustering at redshifts z greater than or similar to 10.