SCALE-INVARIANCE OF GALAXY CLUSTERING

Some years ago we proposed a new approach to the analysis of galaxy an d cluster correlations based on the concepts and methods of modern sta tistical Physics. This led to the surprising result that galaxy correl ations are fractal and not homogeneous up to the limits of the availab le catalogs. The usual statistical methods, which are based on the ass umption of homogeneity, are therefore inconsistent for all the length scales probed so far, and a new, more general, conceptual framework is necessary to identify the real physical properties of these structure s. In the last few years the 3-d catalogs have been significatively im proved and we have extended our methods to the analysis of number coun ts and angular catalogs. This has led to a complete analysis of all th e available data that we present in this review. In particular we disc uss the properties of the following catalogs: CfA, Perseus-Pisces, SSR S, IRAS, LEDA, APM-Stromlo, Las Campanas and ESP for galaxies and Abel l and ACO for galaxy clusters. The result is that galaxy structures ar e highly irregular and self-similar: all the available data are consis tent with each other and show fractal correlations (with dimension D s imilar or equal to 2) up to the deepest scales probed so far (1000 h(- 1) Mpc) and even more as indicated from the new interpretation of the number counts. The evidence for scale-invariance of galaxy clustering is very strong up to 150 h(-1) Mpc due to the statistical robustness o f the data but becomes progressively weaker (statistically) at larger distances due to the limited data. In addition, the luminosity distrib ution is correlated with the space distribution in a specific way. The se facts lead to fascinating conceptual implications about our knowled ge of the universe and to a new scenario for the theoretical challenge in this field. (C) 1998 Elsevier Science B.V.