The topology of the cosmic web in terms of persistent Betti numbers Journal Article


Author(s): Pranav, Pratyush; Edelsbrunner, Herbert; van de Weygaert, Rien; Vegter, Gert; Kerber, Michael; Jones, Bernard J; Wintraecken, Mathijs H
Article Title: The topology of the cosmic web in terms of persistent Betti numbers
Affiliation IST Austria
Abstract: We introduce a multiscale topological description of the Megaparsec web-like cosmic matter distribution. Betti numbers and topological persistence offer a powerful means of describing the rich connectivity structure of the cosmic web and of its multiscale arrangement of matter and galaxies. Emanating from algebraic topology and Morse theory, Betti numbers and persistence diagrams represent an extension and deepening of the cosmologically familiar topological genus measure and the related geometric Minkowski functionals. In addition to a description of the mathematical background, this study presents the computational procedure for computing Betti numbers and persistence diagrams for density field filtrations. The field may be computed starting from a discrete spatial distribution of galaxies or simulation particles. The main emphasis of this study concerns an extensive and systematic exploration of the imprint of different web-like morphologies and different levels of multiscale clustering in the corresponding computed Betti numbers and persistence diagrams. To this end, we use Voronoi clustering models as templates for a rich variety of web-like configurations and the fractal-like Soneira-Peebles models exemplify a range of multiscale configurations. We have identified the clear imprint of cluster nodes, filaments, walls, and voids in persistence diagrams, along with that of the nested hierarchy of structures in multiscale point distributions. We conclude by outlining the potential of persistent topology for understanding the connectivity structure of the cosmic web, in large simulations of cosmic structure formation and in the challenging context of the observed galaxy distribution in large galaxy surveys.
Keywords: Cosmology: theory; Large-scale structure of Universe; Methods: data analysis; numerical; statistical
Journal Title: Monthly Notices of the Royal Astronomical Society
Volume: 465
Issue 4
ISSN: 00358711
Publisher: Oxford University Press  
Date Published: 2017-01-01
Start Page: 4281
End Page: 4310
URL:
DOI: 10.1093/mnras/stw2862
Notes: We are grateful toBob Eldering and NicoKruithof for important and contributions and discussions at the start of this project. Discussions with and insights obtained from Job Feldbrugge, Matti van Engelen, and Keimpe Nevelzeel have been of key significance in shaping this paper and are gratefully acknowledged. We are also very grateful to Robert Adler for insightful comments on this manuscript. Part of this work has been supported by the 7th Framework Programme for Research of the European Commission, under FETOpen grant number 255827 (CGL Computational Geometry Learning) and ERC advanced grant, URSAT (Understanding Random Systems via Algebraic Topology) number 320422.
Open access: yes (repository)
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