Testing gaussianity, homogeneity and isotropy with the cosmic microwave background

TL;DR

This paper reviews statistical methods for analyzing the cosmic microwave background, focusing on testing assumptions of gaussianity, homogeneity, and isotropy, and discusses how to detect anomalies and asymmetries in the data.

Contribution

It provides a comprehensive overview of estimators for non-gaussianity and anisotropy, emphasizing their signatures and the impact of cosmic variance in CMB analysis.

Findings

Isotropic estimators of non-gaussianity can identify deviations from Gaussianity.

Statistically anisotropic estimators reveal potential anisotropies in the CMB.

Enhanced cosmic variance affects the detection of large-scale anomalies.

Abstract

We review the basic hypotheses which motivate the statistical framework used to analyze the cosmic microwave background, and how that framework can be enlarged as we relax those hypotheses. In particular, we try to separate as much as possible the questions of gaussianity, homogeneity and isotropy from each other. We focus both on isotropic estimators of non-gaussianity as well as statistically anisotropic estimators of gaussianity, giving particular emphasis on their signatures and the enhanced "cosmic variances" that become increasingly important as our putative Universe becomes less symmetric. After reviewing the formalism behind some simple model-independent tests, we discuss how these tests can be applied to CMB data when searching for large scale "anomalies"