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 $40~(\rm{Gpc/h})^{3}$, we detect $f_{\rm NL}^{\rm loc}=10$ at $97.5\%$ confidence on $\sim 85\%$ of the volumes. Additionally we test our ability to resolve degeneracies between the topological signature of $f_{\rm NL}^{\rm loc}$ and variation of $\sigma_8$ and argue that correctly identifying nonzero $f_{\rm NL}^{\rm loc}$ in this case is possible via an optimal template method. Our method relies on information living at $\mathcal{O}(10)$ 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.
- Publication:
-
Journal of Cosmology and Astroparticle Physics
- Pub Date:
- April 2021
- DOI:
- 10.1088/1475-7516/2021/04/061
- arXiv:
- arXiv:2009.04819
- Bibcode:
- 2021JCAP...04..061B
- Keywords:
-
- Astrophysics - Cosmology and Nongalactic Astrophysics;
- High Energy Physics - Theory;
- Mathematics - Algebraic Topology
- E-Print:
- 33+11 pages, 19 figures, code available at https://gitlab.com/mbiagetti/persistent_homology_lss