🍩 Database of Original & NonTheoretical Uses of Topology
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The Persistence of Large Scale Structures I: Primordial NonGaussianity (2020)
Matteo Biagetti, Alex Cole, Gary ShiuAbstract
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 nonGaussianity on the latetime distribution of dark matter halos, using a set of Nbody 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\)\textasciicircum\3\\$, we detect \$f_\\rm NL\\textasciicircum\\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\\textasciicircum\\rm loc\\$ and variation of \$\sigma_8\$ and argue that correctly identifying nonzero \$f_\\rm NL\\textasciicircum\\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 scaledependent bias in the halo/galaxy power spectrum. Therefore, while still requiring a large volume, our method does not require sampling longwavelength modes to constrain primordial nonGaussianity. 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.