Probing topological relation between high density and low density region of 2MASS with hexagon cells

TL;DR

This paper introduces a novel hexagon-based method to analyze the topological structure of the universe by mapping galaxy density regions onto a 2D lattice, revealing significant differences between high and low density areas.

Contribution

The paper presents a new hexagon cell technique for topological analysis of galaxy distributions, applied to 2MASS data, highlighting differences in topological properties of density regions.

Findings

Significant topological differences between high and low density regions.

Both regions show >5 Sigma deviations from random distribution.

The method provides insights into the universe's evolution.

Abstract

We introduce a new 2-D hexagon technique to probe the topological structure of the universe, in which we map regions of the sky with high and low galaxy densities onto a 2-D lattice of hexagon unit cells, We define filled cells as corresponding to high density regions and empty cells as corresponding to low density region. The number of filled cells and empty cells are kept same by controlling the size of the cells. By analyzing the six neighbors of each hexagon we can get and compare statistical topological properties of the high density and low density regions in the universe, in order to have a better understanding of the evolution of the universe. We apply this hexagon method on 2MASS data and discover significant topological differences between the high density and low density regions. Both regions have significant (>5 Sigma) topological shifts from the binomial distribution or the random distribution.