SCALING IN THE UNIVERSE

The aim of this review article is to give a comprehensive description of the scaling properties detected for the distribution of cosmic stru ctures, like galaxies and galaxy clusters. I will also discuss the mor e popular theoretical models, which have been proposed to account for the huge body of observational data. Due to the great variety of stati stical methods, developed in the last twenty years to statistically de scribe the large-scale structure of the Universe, I will mainly concen trate on those methods which reveal remarkable regularities and scalin g in the structure of the Universe. Although in most cases I prefer no t to enter into the technical aspects of how implementing such methods , more details will be furnished about the description of galaxy clust ering in terms of fractal concepts. Statistical methods based on fract al analyses have been recently employed in cosmological context. Despi te recent claims for a Universe, which behaves like a fractal at arbit rarily large scales, I will show that the fractal language can be usef ully employed to disprove this picture. The emerging scenario is that of a Universe, which behaves like a self-similar structure at small sc ales, where fractality is dynamically generated by non-linear gravitat ional clustering, while preserving large-scale homogeneity. Neverthele ss, even at scales greater than or similar to 10h(-1) Mpc, where gravi ty still acts linearly, the distribution of galaxy clusters shows rema rkable scale-invariant features, which could give precise hints about the initial conditions for the evolution of the large-scale structure of the Universe.