{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/cmb-statistical-isotropy-confirmation-at-all","title":"CMB statistical isotropy confirmation at all scales using multipole vectors","arxiv_id":"1812.02654","date":"2018-12-06","proceeding":null,"authors":["Renan A. Oliveira","Thiago S. Pereira","Miguel Quartin"],"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.","url_abs":"https://arxiv.org/abs/1812.02654v5","url_pdf":"https://arxiv.org/pdf/1812.02654v5.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"links_only","authors_date_abstract":"arXiv metadata, CC0 1.0 (https://info.arxiv.org/help/license), from the Kaggle arXiv metadata snapshot of 2026-09-12"},"code_links":[{"paper_slug":"cmb-statistical-isotropy-confirmation-at-all","repo_url":"https://github.com/oliveirara/polyMV","is_official":1,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":null,"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}