Fisher Forecasts for Primordial non-Gaussianity from Persistent Homology

Abstract

We study the information content of summary statistics built from the multi-scale topology of large-scale structures on primordial non-Gaussianity of the local and equilateral type. We use halo catalogs generated from numerical N-body simulations of the Universe on large scales as a proxy for observed galaxies. Besides calculating the Fisher matrix for halos in real space, we also check more realistic scenarios in redshift space. Without needing to take a distant observer approximation, we place the observer on a corner of the box. We also add redshift errors mimicking spectroscopic and photometric samples. We perform several tests to assess the reliability of our Fisher matrix, including the Gaussianity of our summary statistics and convergence. We find that the marginalized 1-σ uncertainties in redshift space are ∆f loc NL ∼ 16 and ∆f equi NL ∼ 41 on a survey volume of 1 (Gpc/h) 3 . These constraints are weakly affected by redshift errors. We close by speculating as to how this approach can be made robust against small-scale uncertainties by exploiting (non)locality.

Persistent homology in cosmic shear II: A tomographic analysis of DES-Y1

“…This could either be a systematic effect that we have not properly taken into account, or a sign of deviations from the wCDM cosmological model that affects the topological structure of the data, but not its two-point statistics. For example, we know that persistent homology is very sensitive to primordial non-Gaussianities in the large-scale structure (Biagetti et al 2022), which can not be detected by two-point statistics. The fact that we achieve extraordinarily consistent results with HD+21 using a fully independent measurement and inference pipeline points to the conclusion that this tension is not caused by a bug in the pipeline.…”

Persistent homology in cosmic shear

“…This might be an unknown systematic or a sign of new physics. For example, 2PCF are not sensitive to primordial non-Gaussianities, whereas persistent homology is (Biagetti et al 2022).…”

“…More recently, Xu et al (2019) developed an effective cosmic void finder based on persistent homology, while Kono et al (2020) detected baryonic acoustic oscillations in the quasar sample from the extended Baryon Oscillation Spectroscopic Survey in SDSS. Moreover, Biagetti et al (2020Biagetti et al ( , 2022 showed with simulations that persistent homology is able to identify primordial non-Gaussian features. Heydenreich et al (2021, hereafter H+21) performed a mock analysis using persistent homology on cosmic shear simulations, highlighting its potential to break the degeneracy between S 8 and w 0 .…”

The Disordered Heterogeneous Universe: Galaxy Distribution and Clustering Across Length Scales

“…As discussed in §II, this may be computed from the dependence of the sample spanning cluster mass, M(η, L) (i.e. its number of constituent particles) on the simulation boxsize L at the percolation threshold η c (28). To explore this, we repeat the above analysis for the fiducial sample, computing the mass of the sample spanning cluster (when it exists) for five boxsizes in the range [700, 800]h −1 Mpc and five reduced densities in the range η c ± 0.1.…”

“…An open question is how best to analyze the data: most works focus on measuring the correlation functions of the galaxy distribution, and comparing them to physical models, though this is known to be suboptimal in terms of information content. Whilst a number of alternative statistics have been proposed (including void statistics [e.g., 9, 10], marked density fields [e.g., [11][12][13][14], Gaussianized fields [e.g., [15][16][17][18], reconstructed density fields [e.g, 19] field-level inference [e.g., [20][21][22], Minkowski functionals and other topological descriptors [e.g., [23][24][25][26][27][28][29][30], and beyond), there is little consensus on which have practical utility (with most having been applied only to the dark matter distribution), and few are natural from a theoretical standpoint. An important insight is that the galaxy distribution is simply a set of irregularly arranged point-like particles in three-dimensions; this is mathematically identical to the structure of many terrestrial materials, including atomic systems, colloids and sphere packing.…”