The Persistence of Large Scale Structures I: Primordial non-Gaussianity

Abstract

We develop an analysis pipeline for characterizing the topology of large scale structure and extracting cosmological constraints based on persistent homology. Persistent homology is a technique from topological data analysis that quantifies the multiscale topology of a data set, in our context unifying the contributions of clusters, filament loops, and cosmic voids to cosmological constraints. We describe how this method captures the imprint of primordial local non-Gaussianity on the late-time distribution of dark matter halos, using a set of N-body simulations as a proxy for real data analysis. For our best single statistic, running the pipeline on several cubic volumes of size 40 (Gpc/h) 3 , we detect f loc NL = 10 at 97.5% confidence on ∼ 85% of the volumes. Additionally we test our ability to resolve degeneracies between the topological signature of f loc NL and variation of σ 8 and argue that correctly identifying nonzero f loc NL in this case is possible via an optimal template method. Our method relies on information living at O(10) Mpc/h, a complementary scale with respect to commonly used methods such as the scale-dependent bias in the halo/galaxy power spectrum. Therefore, while still requiring a large volume, our method does not require sampling long-wavelength modes to constrain primordial non-Gaussianity. Moreover, our statistics are interpretable: we are able to reproduce previous results in certain limits and we make new predictions for unexplored observables, such as filament loops formed by dark matter halos in a simulation box.

Topology and geometry of Gaussian random fields II: on critical points, excursion sets, and persistent homology

“…We choose this representation specifically in the case of Gaussian fields to appreciate the symmetry in the structure of the maps, which is otherwise not discernible in the birth-death maps. Note that this symmetry is not a general feature of diagrams, and vanishes in general for non-Gaussian cases, as pointed out in Feldbrugge et al (2019) and Biagetti et al (2020).…”

Topological Echoes of Primordial Physics in the Universe at Large Scales

“…To remove this systematic, we subsample each simulation to have the same number of halos. Without subsampling, two cosmologies that increase the total number of halos are much more difficult to distinguish via persistent homology, while subsampled simulations can be distinguished [16].…”

“…In a cosmology context, the statistics derived from persistent homology have the advantage over other ML techniques of interpretability: we are able to reproduce previous results in certain limits and we make new predictions for unexplored observables, such as filament loops formed by dark matter halos. This is a condensed version of the paper [16].…”

Persistent homology of the cosmic web. I: Hierarchical topology in $Λ$CDM cosmologies

“…Recently, Kimura & Imai (2017) determined persistence diagrams for (small) volume-limited samples of the DR12 release of the SDSS galaxy redshift survey in an attempt to characterize the topology of the spatial galaxy distribution, while Xu et al (2019) used persistence to identify individual voids and filaments in heuristic models of the cosmic matter distribution (also see Shivashankar et al 2016). Kono et al (2020) applied topological data analysis towards studying baryonic acoustic oscillations in the galaxy distribution, while Biagetti et al (2020) studied persistence properties of the large scale matter distribution in cosmologies with non-Gaussian primordial conditions (also see Feldbrugge et al 2019). The explicit application of homology measures in the study of the primordial temperature perturbations in the cosmic microwave background are reported in Pranav et al (2019b) and Adler et al (2017).…”