Self-similar gravitational clustering

Ignoring non-gravitational forces, clustering properties of galaxies can be described in terms of two-point correlation functions in a medium with small perturbations by gravitational instabilities. The assumption of a scaling relation for correlation functions permitting self-similar solutions, imposes simple initial conditions. In this paper, the author discusses the two-point correlation function, its properties, some consequences and some difficulties. Next, the mean square peculiar velocity between galaxy pairs calculated from three-point correlation functions is compared with its value derived from redshift data form the Kirshner and from the Anglo-Australian survey that contain 340 galaxies. Results are displayed in a figure. A value of the cosmological density parameter is derived. Further results suggest more complex initial conditions than those required for a similarity solution. (Auth.)