The 3-Point Correlation Function of the Cosmic Matter Distribution

Abstract

The most widely used statistical measure of the clustering properties of galaxies is the two-point correlation function ξ. Observations give a simple power-law from ξ(r) ∝-1.8 for a wide range of separations r of the galaxy pair, 0.1 Mpc ≤ r < 10 Mpc. Theoretical models can reproduce the power law shape, but the amplitude ofξneeds some readjustment to agree with the observational results. This discrepancy is ascribed to a “bias”: the dark matter concentrations of the models are distributed differently from the real galaxies. Further investigation of such concepts must make use of higher-order correlation functions, since ξ (r) quantifies only some gross features of the clustering. Determination of the correlation functions of higher order requires much better observational data, than those needed for the 2-point correlation function. The large survyes of galaxies, such as the LCRS and Sloan survey which have become available, respectively, will be available in the near future, will produce data of sufficient precision. In this contribution we want to discuss some properties of the 3-point correlation functions, as they appear in numerical and analytic calculations, and in the data.