Open AccessThe cluster distribution as a test of dark matter models — IV. Topology and geometry
Author(s) -
Peter Coles,
Pearson pearson,
S. Borgani,
M. Plionis,
Moscardini
Publication year - 1998
Publication title -
monthly notices of the royal astronomical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.058
H-Index - 383
eISSN - 1365-2966
pISSN - 0035-8711
DOI - 10.1046/j.1365-8711.1998.01147.x
Subject(s) - physics , cold dark matter , topology (electrical circuits) , euler characteristic , dark matter , cluster (spacecraft) , percolation (cognitive psychology) , dark energy , galaxy cluster , cosmological constant , geometry , statistical physics , astrophysics , theoretical physics , galaxy , cosmology , mathematical analysis , mathematics , combinatorics , neuroscience , computer science , biology , programming language
We study the geometry and topology of the large‐scale structure traced by galaxy clusters in numerical simulations of a box of side 320 h −1 Mpc, and compare them with available data on real clusters. The simulations we use are generated by the Zel’dovich approximation, using the same methods as we have used in the first three papers in this series. We consider the following models to see if there are measurable differences in the topology and geometry of the superclustering they produce: (i) the standard cold dark matter model (SCDM); (ii) a CDM model with Ω 0 = 0.2 (OCDM); (iii) a CDM model with a ‘tilted’ power spectrum having n = 0.7 (TCDM); (iv) a CDM model with a very low Hubble constant, h = 0.3 (LOWH); (v) a model with mixed CDM and HDM (CHDM); (vi) a flat low‐density CDM model with Ω 0 = 0.2 and a non‐zero cosmological Λ term (ΛCDM). We analyse these models using a variety of statistical tests based on the analysis of: (i) the Euler–Poincaré characteristic; (ii) percolation properties; (iii) the minimal spanning tree construction. Taking all these tests together we find that the best‐fitting model is ΛCDM and, indeed, the others do not appear to be consistent with the data. Our results demonstrate that despite their biased and extremely sparse sampling of the cosmological density field, it is possible to use clusters to probe subtle statistical diagnostics of models, which go far beyond the low‐order correlation functions usually applied to study superclustering.