---
res:
bibo_abstract:
- We study the topology of the Megaparsec Cosmic Web in terms of the scale-dependent
Betti numbers, which formalize the topological information content of the cosmic
mass distribution. While the Betti numbers do not fully quantify topology, they
extend the information beyond conventional cosmological studies of topology in
terms of genus and Euler characteristic. The richer information content of Betti
numbers goes along the availability of fast algorithms to compute them. For continuous
density fields, we determine the scale-dependence of Betti numbers by invoking
the cosmologically familiar filtration of sublevel or superlevel sets defined
by density thresholds. For the discrete galaxy distribution, however, the analysis
is based on the alpha shapes of the particles. These simplicial complexes constitute
an ordered sequence of nested subsets of the Delaunay tessellation, a filtration
defined by the scale parameter, α. As they are homotopy equivalent to the sublevel
sets of the distance field, they are an excellent tool for assessing the topological
structure of a discrete point distribution. In order to develop an intuitive understanding
for the behavior of Betti numbers as a function of α, and their relation to the
morphological patterns in the Cosmic Web, we first study them within the context
of simple heuristic Voronoi clustering models. These can be tuned to consist of
specific morphological elements of the Cosmic Web, i.e. clusters, filaments, or
sheets. To elucidate the relative prominence of the various Betti numbers in different
stages of morphological evolution, we introduce the concept of alpha tracks. Subsequently,
we address the topology of structures emerging in the standard LCDM scenario and
in cosmological scenarios with alternative dark energy content. The evolution
of the Betti numbers is shown to reflect the hierarchical evolution of the Cosmic
Web. We also demonstrate that the scale-dependence of the Betti numbers yields
a promising measure of cosmological parameters, with a potential to help in determining
the nature of dark energy and to probe primordial non-Gaussianities. We also discuss
the expected Betti numbers as a function of the density threshold for superlevel
sets of a Gaussian random field. Finally, we introduce the concept of persistent
homology. It measures scale levels of the mass distribution and allows us to separate
small from large scale features. Within the context of the hierarchical cosmic
structure formation, persistence provides a natural formalism for a multiscale
topology study of the Cosmic Web.@eng
bibo_authorlist:
- foaf_Person:
foaf_givenName: Rien
foaf_name: Van De Weygaert, Rien
foaf_surname: Van De Weygaert
- foaf_Person:
foaf_givenName: Gert
foaf_name: Vegter, Gert
foaf_surname: Vegter
- foaf_Person:
foaf_givenName: Herbert
foaf_name: Edelsbrunner, Herbert
foaf_surname: Edelsbrunner
foaf_workInfoHomepage: http://www.librecat.org/personId=3FB178DA-F248-11E8-B48F-1D18A9856A87
orcid: 0000-0002-9823-6833
- foaf_Person:
foaf_givenName: Bernard
foaf_name: Jones, Bernard
foaf_surname: Jones
- foaf_Person:
foaf_givenName: Pratyush
foaf_name: Pranav, Pratyush
foaf_surname: Pranav
- foaf_Person:
foaf_givenName: Changbom
foaf_name: Park, Changbom
foaf_surname: Park
- foaf_Person:
foaf_givenName: Wojciech
foaf_name: Hellwing, Wojciech
foaf_surname: Hellwing
- foaf_Person:
foaf_givenName: Bob
foaf_name: Eldering, Bob
foaf_surname: Eldering
- foaf_Person:
foaf_givenName: Nico
foaf_name: Kruithof, Nico
foaf_surname: Kruithof
- foaf_Person:
foaf_givenName: Patrick
foaf_name: Bos, Patrick
foaf_surname: Bos
- foaf_Person:
foaf_givenName: Johan
foaf_name: Hidding, Johan
foaf_surname: Hidding
- foaf_Person:
foaf_givenName: Job
foaf_name: Feldbrugge, Job
foaf_surname: Feldbrugge
- foaf_Person:
foaf_givenName: Eline
foaf_name: Ten Have, Eline
foaf_surname: Ten Have
- foaf_Person:
foaf_givenName: Matti
foaf_name: Van Engelen, Matti
foaf_surname: Van Engelen
- foaf_Person:
foaf_givenName: Manuel
foaf_name: Caroli, Manuel
foaf_surname: Caroli
- foaf_Person:
foaf_givenName: Monique
foaf_name: Teillaud, Monique
foaf_surname: Teillaud
bibo_doi: 10.1007/978-3-642-25249-5_3
bibo_volume: 6970
dct_date: 2011^xs_gYear
dct_language: eng
dct_publisher: Springer@
dct_title: 'Alpha, Betti and the Megaparsec Universe: On the topology of the Cosmic
Web@'
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