High‐Redshift Galaxy Clustering and \documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \usepackage[OT2,OT1]{fontenc} \newcommand\cyr{ \renewcommand\rmdefault{wncyr} \renewcommand\sfdefault{wncyss} \renewcommand\encodingdefault{OT2} \normalfont \selectfont} \DeclareTextFontCommand{\textcyr}{\cyr} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} \landscape $\Omega _{0}$ \end{document}

Abstract

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 ≈ 3. Analyses of the observed variance of counts-in-cells and of the probability for forming strongly overdense regions suggest Ω0 ≈ 0.3 ± 0.2 and 0.1 Ω0 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 Ω0 more precisely. For Ω0 0.3, these models predict that galaxies start clustering at redshifts z 10.