Fractal Dimensions of a Weakly Clustered Distribution and the Scale of Homogeneity

Understand

Homogeneity and isotropy of the universe at sufficiently large scales is a fundamental premise on which modern cosmology is based.

• Fractal dimensions of matter distribution is a parameter that can be used to test the hypothesis of homogeneity.
• In this method, galaxies are used as tracers of the distribution of matter and samples derived from various galaxy redshift surveys have been used to determine the scale of homogeneity in the Universe.
• Ideally, for homogeneity, the distribution should be a mono-fractal with the fractal dimension equal to the ambient dimension.