Nature of Clustering of Large Scale Structures

TL;DR

This thesis applies multifractal analysis to large-scale cosmic structures, specifically calculating Minkowski-Bouligand dimensions to determine the universe's homogeneity scale, and verifies the homogeneous universe assumption using Sloan Digital Sky Survey data.

Contribution

It introduces a detailed multifractal analysis approach to characterize cosmic structure distribution and assesses the universe's homogeneity at large scales.

Findings

The universe exhibits a transition to homogeneity at large scales.

Finite sample size and clustering effects influence fractal dimension calculations.

Data from Sloan Digital Sky Survey supports the homogeneous universe hypothesis.

Abstract

This thesis focuses on characterizing the distribution of points and galaxies using multifractal analysis. In this attempt the main emphasis is on calculating the Minkowski-Bouligand fractal dimension (Dq) of the distribution of points over different scales and hence finding the scale of homogeneity of the distribution. Effects, of finite size of the sample and clustering in the distribution, on the Dq have been studied in detail. The assumption that the large scale distribution of matter in the Universe is homogeneous has been verified with multifractal analysis of the data from Sloan Digital Sky Survey.