Signatures of Massive Neutrinos in the Cosmic Web via Persistent Homology

TL;DR

This paper demonstrates that persistent homology, a topological data analysis method, can detect signatures of massive neutrinos in the cosmic web with high sensitivity, offering a promising tool for cosmological parameter estimation.

Contribution

It provides the first clear evidence that persistent homology features are highly sensitive to neutrino mass, surpassing traditional two-point statistics in detecting these effects.

Findings

Apex points in persistent diagrams are sensitive to neutrino mass.

Betti curves broaden and flatten with increasing neutrino mass.

Signatures are detectable at the few-percent level for M_ν ~ 0.1 eV.

Abstract

We present the second paper in our program characterizing the impact of massive neutrinos on the multiscale cosmic web using global topology and persistent homology. Building on the methodology established in Paper I, based on discrete Morse theory, we analyze a subset of the Quijote simulations to compute persistent diagrams, Betti curves, and additional topological statistics for both dark matter and halo density fields, across redshifts z=0,1,2. A central result of our study is the first clear demonstration that apex points in persistent diagrams are especially sensitive to neutrino mass, with enhanced sensitivity for specific pairs of saddle points at high redshift. In addition, Betti curves from dark matter density fields broaden and flatten with increasing neutrino masses, exhibiting two characteristic density thresholds where Betti numbers remain invariant. These mass-dependent signatures are detectable at the few-percent level, even for $M_{\nu} \sim 0.1$ eV, providing a robust, physically grounded probe of massive neutrinos in the cosmic web. While traditional two-point statistics encode only pairwise correlations and cannot fully break parameter degeneracies, persistent homology captures higher-order, multiscale information that can lift these degeneracies. Moreover, its high sensitivity to the sum of neutrino masses makes it a promising complement to conventional analyses. Our results thus establish a solid foundation for forward-modeling or emulator-based approaches using persistent homology and environment-based statistics to constrain neutrino mass - potentially enabling direct detection - and additional cosmological parameters, with immediate relevance for ongoing and upcoming galaxy surveys, including DESI, Euclid, and Rubin-LSST.