# CMB statistical isotropy confirmation at all scales using multipole vectors

## TL;DR

This study introduces a new, efficient, model-independent method using Multipole Vectors to test the statistical isotropy of the CMB across all scales, confirming isotropy at large scales and identifying noise-related anisotropies at smaller scales.

## Contribution

The paper presents the first null, model-independent CMB statistical isotropy test using Multipole Vectors at all scales, avoiding a posteriori biases and analyzing multiple data releases.

## Key findings

- Large-scale (up to rac{1}{30}) isotropy confirmed across all maps.
- Anisotropies detected at small scales (rac{1}{1300}) due to noise.
- Variation in anisotropy levels among different mapmaking procedures.

## Abstract

We present an efficient numerical code and conduct, for the first time, a null and model-independent CMB test of statistical isotropy using Multipole Vectors (MVs) at all scales. Because MVs are insensitive to the angular power spectrum $C_\ell$, our results are independent from the assumed cosmological model. We avoid a posteriori choices and use pre-defined ranges of scales $\ell\in[2,30]$, $\ell\in[2,600]$ and $\ell\in[2,1500]$ in our analyses. We find that all four masked Planck maps, from both 2015 and 2018 releases, are in agreement with statistical isotropy for $\ell\in[2,30]$, $\ell\in[2,600]$. For $\ell\in[2,1500]$ we detect anisotropies but this is indicative of simply the anisotropy in the noise: there is no anisotropy for $\ell < 1300$ and an increasing level of anisotropy at higher multipoles. Our findings of no large-scale anisotropies seem to be a consequence of avoiding \emph{a posteriori} statistics. We also find that the degree of anisotropy in the full sky (i.e. unmasked) maps vary enormously (between less than 5 and over 1000 standard deviations) among the different mapmaking procedures and data releases.