A method for testing the cosmic homogeneity with Shannon entropy

TL;DR

This paper introduces a Shannon entropy-based method to test cosmic homogeneity, demonstrating its potential through simulations and assessing its effectiveness in determining the scale of homogeneity in the universe.

Contribution

The paper presents a novel approach using Shannon entropy to evaluate cosmic homogeneity, tested on simulations to explore its capabilities and limitations.

Findings

The method can effectively distinguish between homogeneous and inhomogeneous distributions.

It shows promise in determining the scale of cosmic homogeneity.

The approach is computationally efficient for analyzing large datasets.

Abstract

We propose a method for testing cosmic homogeneity based on the Shannon entropy in Information theory and test the potentials and limitations of the method on Monte Carlo simulations of some homogeneous and inhomogeneous 3D point process in a finite region of space. We analyze a set of N-body simulations to investigate the prospect of determining the scale of homogeneity with the proposed method and show that the method could serve as an efficient tool for the study of homogeneity.