Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the fractal structure of galaxy distribution and its implications for
  cosmology   Two fundamental empirical laws have been established in the analysis of
galaxy space distribution. First, recent analyses have revealed that the three
dimensional distribution of galaxies and clusters is characterized by large
scale structures and huge voids: such a distribution shows fractal correlations
up to the limits of the available samples. This has confirmed the earlier de
Vaucouleurs power-law density - distance relation, now corresponding to a
fractal structure with dimension $D \approx 2$, at least, in the range of
scales $ \sim 1 \div 200 Mpc$ ($H_0 = 55 km/sec/Mpc$). An eventual cut-off
towards homogenization has not been yet identified. Second, since Hubble's
discovery, the linear redshift-distance law has been well established within
$200 Mpc$ and also much deeper. The co-existence of these laws within the same
scales is a challenge for the standard cosmology where the linear Hubble law is
a strict consequence of homogeneity of the expanding universe. This puzzle is
now sufficiently strong to raise doubts for the standard cosmology.

31
The categories of this paper are: ao-sci
2
The categories of this paper are: math
15
The categories of this paper are: nucl-ex
25
The categories of this paper are: patt-sol
33
The categories of this paper are: plasm-ph
14
The categories of this paper are: math-ph
24
The categories of this paper are: dg-ga
20
The categories of this paper are: acc-phys
36
The categories of this paper are: cmp-lg
9
The categories of this paper are: nlin
0
The categories of this paper are: hep-ph
3
The categories of this paper are: physics
34
The categories of this paper are: chem-ph
13
The categories of this paper are: quant-ph
30
The categories of this paper are: q-alg
29
The categories of this paper are: funct-an