Differentiating small-scale subhalo distributions in CDM and WDM models
  using persistent homology
  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 $\leq$ 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 $\sim100$~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.
