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

In this work we test Wasserstein distance in conjunction with persistent homology, as a tool for discriminating large scale structures of simulated universes different values $\sigma_8$ cosmological parameter (present root-mean-square matter fluctuation averaged over sphere radius 8 Mpc comoving). The (a.k.a. the pair-matching distance) was proposed to measure difference between two networks terms homology. advantage approach consists its non-parametric way probing topology Cosmic web, contrast graph-theoretical depending on linking length. By treating halos Web points point cloud calculate homologies, build persistence (birth-death) diagrams and evaluate them. latter showed itself convenient compare webs. We show that one can discern webs (simulated or real) parameter. It turns out distance's discrimination ability depends redshift $z$, well dimensionality considered homology features. find highest power obtains at $z=2$ snapshots, among $z=2$, $1$, $0.1$ ones.