Reconstructing the cosmological puzzle

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In the debate about galaxy correlation there are different questions which can be addressed separately: Which are the statistical methods able to properly detect scale invariance and describe, in general, the properties of irregular and regular distributions? Which are the implications for cosmology of the fractal behavior of galactic structures, up to a certain scale lambda₀? Which is the homogeneity scale lambda₀, i.e. the scale beyond which galaxy distribution has an eventual crossover to homogeneity? These are three different, but related, problems, which must be considered in different steps, from the point of view of data analysis as well as from the theoretical perspective.