The persistence of large scale structures. Part I Primordial non-gaussianity

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_NL^loc = 10 at 97.5% confidence on ~ 85% of the volumes. Additionally we test our ability to resolve degeneracies between the topological signature of f_NL^loc and variation of σ8 and argue that correctly identifying nonzero f_NL^loc 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.