Persistent homology in cosmic shear

Abstract

We demonstrate how to use persistent homology for cosmological parameter inference in a tomographic cosmic shear survey. We obtain the first cosmological parameter constraints from persistent homology by applying our method to the first-year data of the Dark Energy Survey. To obtain these constraints, we analyse the topological structure of the matter distribution by extracting persistence diagrams from signal-to-noise maps of aperture masses. This presents a natural extension to the widely used peak count statistics. Extracting the persistence diagrams from the cosmo-SLICS, a suite of N -body simulations with variable cosmological parameters, we interpolate the signal using Gaussian processes and marginalise over the most relevant systematic effects, including intrinsic alignments and baryonic effects.For the structure growth parameter, we find S8 = 0.747 +0.025 −0.031 , which is in full agreement with other late-time probes. We also constrain the intrinsic alignment parameter to A = 1.54 ± 0.52, which constitutes a detection of the intrinsic alignment effect at almost 3σ.

Dark Energy Survey Year 3 results: cosmology with moments of weak lensing mass maps – validation on simulations

“…However, a significant amount of the information contained in weak lensing mass maps lies in their non-Gaussian features, and these features are not fully captured by two-point statistics. Many recent studies, using a wide range of tools and statistics, have tried to extract the non-Gaussian information; examples include higherorder moments [19,39,41,83,84,86,[106][107][108], peak counts [4,27,49,60,62,68,77,83,97,111,112], onepoint probability distributions [12,16,100], Minkowski functionals [46,63,81,84,109], Betti numbers [32,82], persistent homology [52,53], scattering transform coefficients [21,102,103], wavelet phase harmonic moments * marcogatti29@gmail.com [5], kNN and CDFs [8,11], map-level inference [15,85], and machine-learning methods [34,35,56,70,89]. Many of these studies, however, are ...…”

“…Many of these studies, however, are limited to being proofs of concept, restricted to idealized simulated scenarios (due to the challenges associated with applying these techniques to real-world data). Nevertheless, the field is rapidly progressing, with a number of recent applications to observational data [33,34,41,52,56,60,68,70,77,111].…”

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

“…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. Most similar to our work is that of Bermejo et al (2022), where the authors explored the topology of DM haloes using persistent homology.…”

Cosmological Probes of Structure Growth and Tests of Gravity

“…The persistence diagram has been applied to a subsample of eBOSS DR14 quasars to detect BAO signals [295]. It has also been used to constrain the structure growth parameter S 8 and the intrinsic alignment parameter A on the cosmic shear data in DES-Y1 [296]. For further application of persistence diagrams and TDA on cosmic structures, see [297][298][299][300].…”