The growth of correlations in an expanding universe and the clustering of galaxies

Abstract

From the BBGKY hierarchy of kinetic equations, an equation is derived for the growth of pair correlations in an expanding universe of self-gravitating point masses which is correlation-free at some initial time. This equation is solved explicitly and, from the full pair correlation function, the spatial correlation function is calculated. If t/sub 0/ is the time when clustering begins, the solutions are accurate until about 2t/sub 0/ when the mathematical approximations used for simplifying the kinetic equations no longer hold. During this period, the correlation function grows significantly. At time t, it has a characteristic length which is approximately (t-t/sub 0/) u, where u is the thermal speed of the galaxies. Although the correlation function derived from this analysis cannot be compared directly with the observed covariance function, its growth rate can be extrapolated. The results suggest that the present degree of galaxy clustering could have arisen from an initially unclustered state at the time of galaxy formation. (AIP)