Some Statistics for Measuring Large-Scale Structure

TL;DR

This paper evaluates statistical methods for distinguishing large-scale cosmic structures, demonstrating that counts in cell and genus statistics effectively differentiate between various theoretical models of structure formation.

Contribution

It introduces and applies a new discrete genus statistic alongside traditional counts in cell methods to compare different cosmological structure formation models.

Findings

Counts in cell and genus statistics effectively differentiate models

All three statistics show promise in distinguishing theories

The methods can be applied to toy models of structure formation

Abstract

Good statistics for measuring large-scale structure in the Universe must be able to distinguish between different models of structure formation. In this paper, two and three dimensional ``counts in cell" statistics and a new ``discrete genus statistic" are applied to toy versions of several popular theories of structure formation: random phase cold dark matter model, cosmic string models, and global texture scenario. All three statistics appear quite promising in terms of differentiating between the models.