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Wasserstein distance as a new tool for discriminating cosmologies through the topology of large scale structure
Maksym Tsizh, Vitalii Tymchyshyn, Franco Vazza
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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 σ₈ 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 σ₈ 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.
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