Differentiating small-scale subhalo distributions in CDM and WDM models using persistent homology

Abstract

The spatial distribution of galaxies at sufficiently small scales will encode information about the identity of the dark matter. We develop a novel description of the halo distribution using persistent homology summaries, in which collections of points are decomposed into clusters, loops and voids. We apply these methods, together with a set of hypothesis tests, to dark matter haloes in MW-analog environment regions of the cold dark matter (CDM) and warm dark matter (WDM) Copernicus Complexio N -body cosmological simulations. The results of the hypothesis tests find statistically significant differences (p-values ≤ 0.001) between the CDM and WDM structures, and the functional summaries of persistence diagrams detect differences at scales that are distinct from the comparison spatial point process functional summaries considered (including the two-point correlation function). The differences between the models are driven most strongly at filtration scales ∼ 100 kpc, where CDM generates larger numbers of unconnected halo clusters while WDM instead generates loops. This study was conducted on dark matter haloes generally; future work will involve applying the same methods to realistic galaxy catalogues.

Is the observable Universe consistent with the cosmological principle?

“…These methods are supported by the power of an elaborate and solid mathematical framework, and complement the existing methods for gleaning meaningful information out of the ever-growing cosmological data sets. It is evident that these methodologies are valuable evaluation tools from a recent proliferation of their use in the astronomical and cosmological disciplines, in a variety of contexts including structure detection and identification [271][272][273][274], including detection of BAO signals [275], statistical characterization of ISM [276], statistical characterization of cosmological fields arising from various models, and a description of associated structures [254,266,[277][278][279][280], and detection and quantification of non-Gaussianities [281][282][283].…”

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

“…One of the most prominent applications of persistent homology in recent years is in our opinion the work by Cisewski-Kehe et al (2022), in which the authors directly develop the idea of discriminating power of persistence diagrams for cosmological models. They analyzed several metrics for computing the distance between persistence diagrams to check whether it is possible to tell apart the statistical difference between the persistence homologies of cold and warm dark matter Universes.…”

Topological data analysis reveals differences between simulated galaxies and dark matter haloes

“…Kono et al (2020) used persistent homology to identify the baryon acoustic oscillation features in the spatial distribution of galaxies. Cisewski-Kehe et al (2022) showed that TDA is able to discriminate between different DM models using only subhalo spatial distributions. Persistent homology has also been applied to study the period of re-ionization (Elbers & van de Weygaert 2019, 2023Thélie et al 2022), the analysis of weak lensing data (Heydenreich et al 2021(Heydenreich et al , 2022, and to detect signatures of non-Gaussianity in the primordial density fluctuations Cole et al (2020); Biagetti et al (2021Biagetti et al ( , 2022.…”