@article{biagetti_persistence_2020,
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{\textasciitilde}({\textbackslash}rm\{Gpc/h\}){\textasciicircum}\{3\}\$, we detect \$f\_\{{\textbackslash}rm {NL}\}{\textasciicircum}\{{\textbackslash}rm loc\}=10\$ at \$97.5{\textbackslash}\%\$ confidence on \${\textbackslash}sim 85{\textbackslash}\%\$ of the volumes. Additionally we test our ability to resolve degeneracies between the topological signature of \$f\_\{{\textbackslash}rm {NL}\}{\textasciicircum}\{{\textbackslash}rm loc\}\$ and variation of \${\textbackslash}sigma\_8\$ and argue that correctly identifying nonzero \$f\_\{{\textbackslash}rm {NL}\}{\textasciicircum}\{{\textbackslash}rm loc\}\$ in this case is possible via an optimal template method. Our method relies on information living at \${\textbackslash}mathcal\{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.},
author = {Biagetti, Matteo and Cole, Alex and Shiu, Gary},
date = {2020-09-10},
eprint = {2009.04819},
eprinttype = {arxiv},
journaltitle = {{arXiv}:2009.04819 [astro-ph, physics:hep-th]},
keywords = {1 - Cosmology, 1 - High Energy Physics, 2 - Persistent homology, 3 - Point cloud:3D},
shorttitle = {The Persistence of Large Scale Structures I},
title = {The Persistence of Large Scale Structures I: Primordial non-Gaussianity},
url = {http://arxiv.org/abs/2009.04819},
urldate = {2020-10-01}
}