Multiscaling and Nonextensivity of Large-scale Structures in the Universe

There has been a trend in the past decade to describe the large-scale structures in the Universe as a (multi)fractal set. However, one of the main objections raised by the opponents of this approach deals with the transition to homogeneity. Moreover, they claim there is not enough sampling space to determine a scaling index which characterizes a (multi)fractal set. In this work we propose an alternative solution to this problem, using the generalized thermostatistics formalism. We show that applying the idea of nonextensivity, intrinsic to this approach, it is possible to derive an expression for the correlation function, describing the scaling properties of large-scale structures in the Universe and the transition to homogeneity, which is in good agreement with observational data.