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 $w_0 w_a\text{CDM} +ν$ cosmological parameter space that includes parameters degenerate with neutrino masses in conventional approaches, assuming a volume of only $(350 \, \mathrm{Mpc})^3$, we obtain neutrino mass constraints with an uncertainty of $0.05 \, \mathrm{eV}$ for the total matter field and $0.13 \, \mathrm{eV}$ 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.

Figures (18)

• Figure 1: Topological structure of a 3D cosmic density field. (Left) Betti curves $\beta_k$ as a function of density threshold, showing the number of $k$-dimensional topological features. From left to right: cosmic voids ($\beta_2$, purple), filamentary tunnels ($\beta_1$, red), and halos ($\beta_0$, orange). Solid and dotted lines correspond to persistence thresholds of 0 and 0.2, respectively, applied to the underlying persistence diagrams. (Right) Visualizations of the identified structures at different density thresholds. Colour in the 3D renderings represents the local matter overdensity, as indicated by the colour bar.
• Figure 1: Similar to Fig. \ref{['fig:corner_bb_compare']}, but comparing the results for different training sets. The constraints are derived from ensembles of 50 and 100 simulations, all with CMB priors. The grey lines indicate the true value of each parameter.
• Figure 2: The relationship between Betti curves and persistence diagrams. Upper panel: Betti curves showing the count of topological features as a function of density threshold. The coloured dots on the curves mark the Betti numbers at three specific density thresholds: 0.2 (red), 0.5 (orange), and 0.7 (purple). Bottom panel: The corresponding persistence diagrams, where each point represents a topological feature's birth and death density. The coloured diamonds highlight the specific features that are active (i.e., born before and dying after) at each of the three density thresholds. Features active at multiple thresholds are shown with multiple colours. The three columns on the right demonstrate the effect of applying different persistence cuts (i.e., minimum feature lifetimes) when computing the Betti curves: [0, 0.2], [0.2, 0.5], and [0.5, 1.0], as indicated by the shaded regions in the persistence diagrams.
• Figure 2: Similar to Fig. \ref{['fig:corner_bb_compare']}, but with $A_s$ as prior. The grey lines indicate the true value of each parameter.
• Figure 3: Topological structure of different mass components in the FLAMINGO simulations. Top panel: Betti curves $\beta_k$ for the neutrino, cold dark matter, and total matter density fields. The curves show the count of connected components ($\beta_0$, dotted lines), loops ($\beta_1$, dashed lines), and voids ($\beta_2$, solid lines) as a function of density threshold. Colours indicate the total neutrino mass: 0.06 eV (yellow), 0.24 eV (red), and 0.48 eV (purple). Bottom panel: Persistence diagrams for the 0.06 eV neutrino mass case, corresponding to the density fields shown in the top row. Each point represents a topological feature, with its birth and death coordinates indicating the density thresholds at which it appears and disappears. Structures in dimension $k=0, 1,$ and $2$ are represented in purple, violet, and pink, respectively. This figure illustrates the imprint of neutrino mass on the multiscale topology of cosmic density fields, providing a qualitative basis for comparing the simulations.