Correlation functions and multifractal analysis for galaxy distribution

Abstract

Advanced mathematics is not a best seller to ordinary people. Among the few exceptions I know there are fractals. That fractals has something to do with the large scale structure in the Universe had been noticed since long. The fact that the 2-point correlation function has the shape

$$ \xi \left( r \right) = \left( {\frac{{r_o }} {r}} \right)^\gamma $$

(1)

can be interpreted by saying that, up to a scale ~r_o, galaxy distribution looks like a fractal of dimension 3 - γ. In the classical Peebles works (see, e.g., (Peebles 1980), and references therein), starting from 2-dimensional projected samples, it was found that

$$ {r_0} \simeq 5{h^{ - 1}}MpcH = 100{\text{ }}h{\text{ }}km{s^{ - 1}}Mp{c^{ - 1}}{\text{ is the Hubble parameter}}$$

(2)