Minimum variance estimation of statistical anisotropy via galaxy survey

TL;DR

This paper introduces a novel method using tripolar spherical harmonics to detect cosmic statistical anisotropy from galaxy surveys, improving sensitivity over traditional plane-parallel approaches, especially in challenging noise conditions.

Contribution

It develops the first covariance and Fisher matrix formalism for TripoSH decomposition, enabling optimized anisotropy detection without plane-parallel approximation limitations.

Findings

Enhanced detectability of anisotropy compared to plane-parallel methods.

Better sensitivity in high shot noise and blue-tilted anisotropy scenarios.

Potential to constrain anisotropy tighter than current CMB measurements.

Abstract

We consider the benefits of measuring cosmic statistical anisotropy from redshift-space correlators of the galaxy number density fluctuation and the peculiar velocity field without adopting the plane-parallel (PP) approximation. Since the correlators are decomposed using the general tripolar spherical harmonic (TripoSH) basis, we can deal with wide-angle contributions untreatable by the PP approximation, and at the same time, target anisotropic signatures can be cleanly extracted. We, for the first time, compute the covariance of the TripoSH decomposition coefficient and the Fisher matrix to forecast the detectability of statistical anisotropy. The resultant expression of the covariance is free from nontrivial mixings between each multipole moment caused by the PP approximation and hence the detectability is fully optimized. Compared with the analysis under the PP approximation, the superiority in detectability is always confirmed, and it is highlighted, especially in the cases that the shot noise level is large and that target statistical anisotropy has a blue-tilted shape in Fourier space. The application of the TripoSH-based analysis to forthcoming all-sky survey data could result in constraints on anisotropy comparable to or tighter than the current cosmic microwave background ones.