Correlation function as a measure of the structure

Abstract

Geometrical model of structure of the universe is examined to obtain analytical expression for the two points nonlinear correlation function. According to the model the objects (galaxies) are concentrated into two types of structure elements - filaments and sheets. We considered the filaments ( similar to galaxy filaments ) simply as straight lines and the sheets ( similar to superclusters of galaxies ) simply as planes. The homogeneously distributed objects are also taken into consideration. The spatial distribution of lines, planes and points is uncorrelated. The nonlinear correlation function depends on four parameters and is similar to the observed and simulated ones for different samples. It describes quite well the correlation of galaxies, clusters of galaxies and dark matter distribution. Possible interpretation of the parameters of nonlinear correlation function is discussed.