Cosmic Topology, Persistent Homology, and Massive Neutrinos

We apply discrete Morse theory and the concept of persistent homology and global topology to characterize the impact of massive neutrinos on the multiscale cosmic web, with a particular focus on its filamentary structure. The topological properties of the cosmic web are sensitive to neutrino imprints, and persistence diagrams provide a higher level degree of information with respect to commonly used topological global summary statistics, along with a much richer landscape. This scale-adaptive, parameter-free formalism is particularly powerful, as massive neutrinos do affect the main constituents of the cosmic web differently: within such framework, one can simultaneously characterize their impact on individual tracers as well as on skeleton structures, and capture their unique local and global multiscale signals across cosmic time. Using two distinct sets of N-body simulations, we present here filament-based statistics and persistence diagrams in massive neutrino cosmologies. Noticeably, we consider two different implementations of massive neutrinos, thus assessing also systematic effects. In particular, we find that at high redshift the connectivity of the cosmic web is altered by massive neutrinos, leading to mass-dependent signatures in the filamentary network. Our study opens up a promising novel way and lays the ground to use persistent homology and the topology of the cosmic web to constrain or eventually directly detect the neutrino mass and type of hierarchy, a long-standing challenge in particle physics and one of the major goals of ongoing and future galaxy redshift surveys (i.e., DES, DESI, Euclid, Rubin-LSST).