Revealing the neutrino mass through persistent homology of the cosmic web

Abstract Cosmological constraints on neutrino mass offer a promising avenue for advancing our understanding of both fundamental particle physics and the evolution of cosmic large-scale structure. To overcome challenges associated with traditional probes of neutrino mass, particularly degeneracies with other parameters, we consider topological summaries of the cosmic web based on the formalism of persistent homology. We introduce persistence strips, a novel representation that segments Betti curves by topological persistence, effectively condensing two-dimensional persistence diagrams into a set of one-dimensional curves. Applied to the FLAMINGO suite of cosmological simulations, these topological descriptors demonstrate pronounced sensitivity to neutrino mass. By constructing an emulator spanning a 10-dimensional w0waCDM + ν cosmological parameter space that includes parameters degenerate with neutrino masses in conventional approaches, assuming a volume of only (350 Mpc)3, we obtain neutrino mass constraints with an uncertainty of 0.05 eV for the total matter field and 0.13 eV for the dark matter-only field, with the strongest constraints coming from void topology. Persistence strips exhibit roughly twice the constraining power of unbinned Betti curves and, through their multi-scale, environment-dependent sensitivity, systematically break degeneracies between neutrino mass and other cosmological parameters. We pinpoint the precise physical origin of the signal, identifying two equally important contributions: sensitivity to the neutrino mass fraction, which is highest in underdense regions, and the impact of neutrinos on the distribution of dark matter. Our findings highlight the particular promise of applying topological statistics to weak lensing measurements, which directly probe the total matter distribution.