Wasserstein distance as a new tool for discriminating cosmologies through the topology of large scale structure

Abstract

In this work we test Wasserstein distance in conjunction with persistent homology, as a tool for discriminating large scale structures of simulated universes with different values of ${\sigma }_8$ cosmological parameter (present root-mean-square matter fluctuation averaged over a sphere of radius 8 Mpc comoving). The Wasserstein distance (a.k.a. the pair-matching distance) was proposed to measure the difference between two networks in terms of persistent homology. The advantage of this approach consists in its non-parametric way of probing the topology of the Cosmic web, in contrast to graph-theoretical approach depending on linking length. By treating the halos of the Cosmic Web as points in a point cloud we calculate persistent homologies, build persistence (birth-death) diagrams and evaluate Wasserstein distance between them. The latter showed itself as a convenient tool to compare simulated Cosmic webs. We show that one can discern two Cosmic webs (simulated or real) with different ${\sigma }_8$ parameter. It turns out that Wasserstein distance's discrimination ability depends on redshift $z$, as well as on the dimensionality of considered homology features. We find that the highest discriminating power this tool obtains at $z=2$ snapshots, among the considered $z=2$, $1$, and $0.1$ ones.

12 pages, 11 figures

References in corpus (9)

• zCOSMOS: A Large VLT/VIMOS redshift survey covering 0 < z < 3 in the COSMOS field
• First detection of stacked X-ray emission from cosmic web filaments
• Magnetic field evolution in cosmic filaments with LOFAR data
• Power law correlations in galaxy distribution and finite volume effects from the Sloan Digital Sky Survey Data Release Four
• Persistent homology in cosmic shear II: A tomographic analysis of DES-Y1
• Fisher Forecasts for Primordial non-Gaussianity from Persistent Homology
• Topological signatures of interstellar magnetic fields - I. Betti numbers and persistence diagrams
• Persistent topology of the reionization bubble network. II: Evolution & Classification
• Differentiating small-scale subhalo distributions in CDM and WDM models using persistent homology

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