Cosmology with Persistent Homology: a Fisher Forecast

TL;DR

This paper demonstrates that persistent homology effectively captures multi-scale topological features of large-scale structures, providing tighter constraints on cosmological parameters and primordial non-Gaussianity than traditional methods.

Contribution

It introduces the use of persistent homology as a novel summary statistic for cosmological data analysis, showing its advantages over power spectrum and bispectrum in parameter constraints.

Findings

Persistent homology yields 13-50% tighter parameter constraints.

Combining persistent homology with traditional statistics breaks degeneracies.

Results support incorporating persistent homology into cosmological inference pipelines.

Abstract

Persistent homology naturally addresses the multi-scale topological characteristics of the large-scale structure as a distribution of clusters, loops, and voids. We apply this tool to the dark matter halo catalogs from the Quijote simulations, and build a summary statistic for comparison with the joint power spectrum and bispectrum statistic regarding their information content on cosmological parameters and primordial non-Gaussianity. Through a Fisher analysis, we find that constraints from persistent homology are tighter for 8 out of the 10 parameters by margins of 13-50%. The complementarity of the two statistics breaks parameter degeneracies, allowing for a further gain in constraining power when combined. We run a series of consistency checks to consolidate our results, and conclude that our findings motivate incorporating persistent homology into inference pipelines for cosmological survey data.