{"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/the-persistence-of-large-scale-structures-i","title":"The Persistence of Large Scale Structures I: Primordial non-Gaussianity","arxiv_id":"2009.04819","date":"2020-09-10","proceeding":null,"authors":["Matteo Biagetti","Alex Cole","Gary Shiu"],"abstract":"We develop an analysis pipeline for characterizing the topology of large scale structure and extracting cosmological constraints based on persistent homology. Persistent homology is a technique from topological data analysis that quantifies the multiscale topology of a data set, in our context unifying the contributions of clusters, filament loops, and cosmic voids to cosmological constraints. We describe how this method captures the imprint of primordial local non-Gaussianity on the late-time distribution of dark matter halos, using a set of N-body simulations as a proxy for real data analysis. For our best single statistic, running the pipeline on several cubic volumes of size $40~(\\rm{Gpc/h})^{3}$, we detect $f_{\\rm NL}^{\\rm loc}=10$ at $97.5\\%$ confidence on $\\sim 85\\%$ of the volumes. Additionally we test our ability to resolve degeneracies between the topological signature of $f_{\\rm NL}^{\\rm loc}$ and variation of $\\sigma_8$ and argue that correctly identifying nonzero $f_{\\rm NL}^{\\rm loc}$ in this case is possible via an optimal template method. Our method relies on information living at $\\mathcal{O}(10)$ Mpc/h, a complementary scale with respect to commonly used methods such as the scale-dependent bias in the halo/galaxy power spectrum. Therefore, while still requiring a large volume, our method does not require sampling long-wavelength modes to constrain primordial non-Gaussianity. Moreover, our statistics are interpretable: we are able to reproduce previous results in certain limits and we make new predictions for unexplored observables, such as filament loops formed by dark matter halos in a simulation box.","url_abs":"https://arxiv.org/abs/2009.04819v3","url_pdf":"https://arxiv.org/pdf/2009.04819v3.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":"the-persistence-of-large-scale-structures-i","repo_url":"https://gitlab.com/mbiagetti/persistent_homology_lss","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=2009.04819","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}