On de-Sitter Geometry in Cosmic Void Statistics

TL;DR

This paper applies de-Sitter geometry to model cosmic voids as spheres, deriving a power-law distribution for void sizes that aligns with observational data and offers new insights into large-scale structure self-similarity.

Contribution

It introduces a novel geometrical framework using de-Sitter configurations to analyze cosmic voids, connecting geometry with cosmological void statistics.

Findings

Power-law void size distribution consistent with data

Estimated scaling dimension of large-scale structure

Effect of survey geometry on void statistics

Abstract

Starting from the geometrical concept of a 4-dimensional de-Sitter configuration of spheres in Euclidean 3-space and modelling voids in the Universe as spheres, we show that a uniform distribution over this configuration space implies a power-law for the void number density which is consistent with results from the excursion set formalism and with data, for an intermediate range of void volumes. The scaling dimension of the large scale structure can be estimated as well. We also discuss the effect of restricting the survey geometry on the void statistics. This work is a new application of de-Sitter geometry to cosmology and also provides a new geometrical perspective on self-similarity in cosmology.