The Cosmic Web and Its Filaments: Neutrino Mass from Topology and Persistent Homology

Abstract

We apply discrete Morse theory, global topology, and persistent homology to characterize the impact of massive neutrinos on the multiscale cosmic web, focusing on filaments. The topology of the cosmic web is sensitive to neutrino imprints, and persistence diagrams provide more information than commonly used summary statistics by quantifying the longevity of topological features across densities. This scale-adaptive, parameter-free formalism is powerful, as massive neutrinos affect halos, walls, filaments, and voids in distinct ways. Within this framework, we simultaneously assess their impact on tracers and skeleton structures and capture their multiscale signals across cosmic time. Discrete Morse theory is also well suited for particle-based neutrino implementations, often affected by Poisson shot noise, as it preserves the salient features of the underlying smooth field. Using two independent sets of N-body simulations, we present filament statistics and persistence diagrams in massive-neutrino cosmologies. Our results show that neutrinos leave distinct imprints on filaments and skeleton connectivity, producing mass-dependent signatures most pronounced at high redshift (z~2) and detectable at the few-percent level for masses as small as $M_\nu \sim 0.1$ eV. Filaments thus provide an ideal environment for isolating neutrino effects. We also compare two implementations of massive neutrinos to assess systematics. Our study establishes a promising avenue for leveraging cosmic web topology, persistent homology, and environment-based statistics to constrain or directly detect neutrino mass and infer the mass hierarchy - a long-standing challenge in particle physics and a major objective of ongoing and upcoming galaxy redshift surveys (e.g., DES, DESI, Euclid, Rubin-LSST).