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

arXiv2009.04819MaRDI QIDQ6348825

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Publication date: 10 September 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 $40(mGpc/h{)}^3$, we detect $f_{mNL}^{mloc}=10$ at $97.5\mathrm{\%}$ confidence on $sim85\mathrm{\%}$ of the volumes. Additionally we test our ability to resolve degeneracies between the topological signature of $f_{mNL}^{mloc}$ and variation of $sigm{a}_8$ and argue that correctly identifying nonzero $f_{mNL}^{mloc}$ in this case is possible via an optimal template method. Our method relies on information living at $mathcalO(10)$ 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.

Has companion code repository: https://gitlab.com/mbiagetti/persistent_homology_lss

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