Testing the statistical isotropy of large scale structure with multipole vectors

TL;DR

This paper adapts multipole vector techniques from CMB analysis to galaxy surveys to test the universe's statistical isotropy, evaluating the method's accuracy with synthetic data under various survey conditions.

Contribution

It introduces a formalism for reconstructing multipole vectors from galaxy data and assesses the method's sensitivity to survey parameters.

Findings

Reconstruction accuracy depends on survey density and coverage.

The method is effective on synthetic galaxy maps with varying parameters.

Potential for applying to real galaxy survey data to test isotropy.

Abstract

A fundamental assumption in cosmology is that of statistical isotropy - that the universe, on average, looks the same in every direction in the sky. Statistical isotropy has recently been tested stringently using Cosmic Microwave Background (CMB) data, leading to intriguing results on large angular scales. Here we apply some of the same techniques used in the CMB to the distribution of galaxies on the sky. Using the multipole vector approach, where each multipole in the harmonic decomposition of galaxy density field is described by unit vectors and an amplitude, we lay out the basic formalism of how to reconstruct the multipole vectors and their statistics out of galaxy survey catalogs. We apply the algorithm to synthetic galaxy maps, and study the sensitivity of the multipole vector reconstruction accuracy to the density, depth, sky coverage, and pixelization of galaxy catalog maps.