Gravitational Clustering of Gaussian Density Fluctuations and the Origin of Hierarchy Correlations

We present here a theory of gravitational clustering based only on (a) the assumption that the primordial density fluctuations (PDF) were Gaussian and (b) identifying galaxies and groups and clusters of galaxies with regions of PDF whose turnaround time was less than the age of the universe. It is shown that (1) properties of the hierarchy thus produced depend uniquely on the power spectrum P(k) of PDF; (2) the resultant distribution of galaxies and groups and clusters is non-Gaussian; (3) two-point and higher order correlations depend in a complicated, but unique for a given P(k), way on the mass scales of groups and clusters and, hence, can be used to constrain P(k) on scales from 1 to (50-100)h^-1^ Mpc on the basis of the available data; (4) presented theory successfully reproduces both the observed two- and three-point correlation functions for clusters of galaxies for n = - 1 spectrum; the data are, however, inconsistent with n > 0 on large scales as required in the conventional cold dark matter model; (5) the hierarchy constructed here specifies unique higher order correlations for various hierarchy members.