On the fractal structure of the universe: methods, results and theoretical implication

The fact that galaxy distribution exhibits fractal properties is well established since twenty years. Nowadays, the controversy concerns the range of the fractal regime, the value of the fractal dimension and the eventual presence of a cross-over to homogeneity. Fractal properties maybe studied with methods which do not assume homogeneity a priori as the standard statistical methods do. We show that complementary to the adoption of new methods of analysis there are important theoretical implications for the usual scenario of galaxy formation. For example, we focus on the concept of bias and we show that it needs a basic revision even if future redshift surveys will be able to identify an eventual tendency to homogenization.