Scaleinvariant matter distribution in the universe.
Abstract
We calculate the galaxy counts or the matter content within a randomly placed cell, under the sole hypothesis of scaleinvariance of the manybody correlation functions. At whatever scale this assumption holds, our calculations replace, in the nonlinear regime, the estimates of counts usually done in the linear theory. The various forms taken by the probability for finding N objects in a given volume are obtained as a function of its size. At small scales (< 0.5 h^1^ Mpc), this probability decreases exponentially with N. At larger scales (0.5 h^1^ Mpc to 10 h^1^ Mpc) it behaves as a powerlaw with an upper and possibly a lower exponential cutoff, reminiscent of the current parametrizations of the galaxy and cluster luminosity functions. We show that the large scale void probability, whose logarithm is seen to be a powerlaw, is a scalefree extrapolation of its small scale bebaviour. As long as the correlation functions are powerlaws, this void distribution is not compatible with the linear theory, whatever large scale is considered. We relate this largescale behaviour of the void probability to the powerlaw observed at the faint end of the luminosity functions. A scaling law is round, the galaxy and cluster distributions being expressed by the same universal function. We show that the counts in cells are approximately gaussian, as in the linear theory, only at very large scales, above 50 h^1^ Mpc, provided the density fluctuations are less than 10 % of the mean. In the intermediate range of 10 h^1^ to 50 h^1^ Mpc, considerable deviations from gaussian statistics are predicted. Counts in cells ar, seen to provide a cleaner statistical tool than the mass or luminosity functions and are as easy to obtain either from theoretical information on correlation functions or from observations.
 Publication:

Astronomy and Astrophysics
 Pub Date:
 August 1989
 Bibcode:
 1989A&A...220....1B
 Keywords:

 Cosmology;
 Galactic Clusters;
 Mass Distribution;
 Statistical Distributions;
 Universe;
 Luminosity;
 Probability Distribution Functions;
 Scaling Laws;
 Statistical Correlation;
 Voids;
 Astrophysics