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arxiv: 2604.16853 · v1 · submitted 2026-04-18 · 🌌 astro-ph.CO

Signatures of Massive Neutrinos in the Cosmic Web via Persistent Homology

Hogyun Yu , Micha\"el Michaux , Donghyun Kim , Changhee Song , Ingyu Yun , Donghyeon Lee , Yoonyoung Lee , Graziano Rossi This is my paper

Pith reviewed 2026-05-10 06:56 UTC · model grok-4.3

classification 🌌 astro-ph.CO
keywords persistent homologymassive neutrinoscosmic webBetti curvespersistent diagramsdark matter densityhalo fieldstopological statistics
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The pith

Persistent homology detects neutrino mass effects in the cosmic web through apex points in diagrams and changes to Betti curves.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper shows that massive neutrinos produce measurable changes in the topology of the cosmic web as captured by persistent homology on simulated density fields. Apex points in persistent diagrams respond strongly to the sum of neutrino masses, with particular sensitivity at high redshift for certain saddle-point pairs. Betti curves from dark matter fields broaden and flatten with rising neutrino mass while remaining invariant at two specific density thresholds. These shifts reach a few percent even for masses near 0.1 eV. Because the method encodes multiscale, higher-order structure beyond pairwise correlations, it offers a route to tighter neutrino constraints that two-point statistics alone cannot achieve.

Core claim

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_ν ∼ 0.1 eV, providing a robust, physically grounded probe of massive neutrinos in the cosmic web.

What carries the argument

Persistent diagrams and Betti curves obtained via discrete Morse theory on dark matter and halo density fields.

If this is right

  • Mass-dependent signatures reach few-percent detectability for neutrino masses around 0.1 eV.
  • Persistent homology supplies multiscale information that can help break degeneracies left by two-point statistics.
  • The approach supplies a basis for forward-modeling or emulator pipelines that combine topological statistics with conventional analyses.
  • Results apply directly to parameter constraints from surveys such as DESI, Euclid, and Rubin-LSST.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • If baryonic feedback and observational systematics can be forward-modeled to sufficient accuracy, the same topological statistics could be applied to real catalogs without major loss of signal.
  • Pairing persistent homology with other higher-order probes might further isolate the neutrino mass sum from other cosmological parameters.
  • Repeating the analysis on hydrodynamical simulations with varied feedback prescriptions would test how robust the apex-point and Betti-curve shifts remain under realistic galaxy formation.

Load-bearing premise

Topological signatures measured in simulated dark matter and halo fields will survive in real galaxy surveys without being erased by baryonic physics, redshift-space distortions, or selection effects.

What would settle it

If galaxy survey data yield Betti curves and persistent diagrams that match massless-neutrino predictions to better than a few percent across the relevant density thresholds, the claimed detectability would not hold.

Figures

Figures reproduced from arXiv: 2604.16853 by Changhee Song, Donghyeon Lee, Donghyun Kim, Graziano Rossi, Hogyun Yu, Ingyu Yun, Micha\"el Michaux, Yoonyoung Lee.

Figure 1
Figure 1. Figure 1: Projection of the DM density field at z = 0 from Quijote simulations with different neutrino masses. Panels, from left to right, correspond to Mν = 0.0 eV, 0.1 eV and 0.4 eV, respectively. Top panels show a 100 h −1 Mpc × 100 h −1 Mpc area, averaged over a 50 h −1 Mpc thick slice. Bottom panels show corresponding zoom-ins of the 20 h −1 Mpc × 20 h −1 Mpc region indicated by squares on the top panels. Morph… view at source ↗
Figure 2
Figure 2. Figure 2: Illustration of the construction of Betti curves (top panel) from the persistence diagram (bottom panel) for a given pair of type k. The vertical dashed line indicates an example filtration value. The colors and shapes of points in the diagram show which pairs are counted or not at this filtration value for different persistence (σ) levels. See the main text in Section 3.3 for details. ber P1 counts one-di… view at source ↗
Figure 3
Figure 3. Figure 3: Projection of 200 h −1 Mpc × 200 h −1 Mpc, 30 h −1 Mpc thick slices of Quijote DM density fields, shar￾ing the same initial random noise, with overlaid critical point positions at z = 0. The top row shows a fiducial, massless neutrinos simulation, while the middle and bottom rows cor￾respond to 0.1 eV and 0.4 eV massive neutrino simulations, respectively—similarly to [PITH_FULL_IMAGE:figures/full_fig_p008… view at source ↗
Figure 4
Figure 4. Figure 4: Mean persistence diagrams for Quijote DM den￾sity fields at z = 2 (top block), 1 (middle block), and 0 (bot￾tom block), averaged over 100 simulations per model. Colors indicate the number density of persistence pairs. No simpli￾fication is applied (σ=0). Each row shows a different pair type, and each column corresponds to a different cosmology, as specified in the panels. See the main text for additional d… view at source ↗
Figure 5
Figure 5. Figure 5: Difference in the number density of per￾sistence pairs between each massive neutrino model (Mν = 0.1 eV and 0.4 eV) and the fiducial, massless neutrino scenario in the birth-death plane at z = 2 (top block), 1 (mid￾dle block), and 0 (bottom block), for Quijote DM density fields. Colors indicate the pair number density difference, computed using a Gaussian kernel density estimator (KDE). and the ellipses ar… view at source ↗
Figure 6
Figure 6. Figure 6: Mean positions (points) of the persistence diagram apexes and their 1σ variations (ellipses) over 100 simulations per cosmology for the Quijote DM density fields. Panels are arranged from top to bottom by redshift (z = 2, 1 and 0) and from left to right by pair type (P0, P1, P2). The fiducial, massless neutrino model is shown in solid blue, the 0.1 eV neutrino model in dashed green, and the 0.4 eV model in… view at source ↗
Figure 8
Figure 8. Figure 8: Positions of the Betti curve relative-difference crossing points derived from the Quijote DM fields, as shown in [PITH_FULL_IMAGE:figures/full_fig_p012_8.png] view at source ↗
Figure 7
Figure 7. Figure 7: Mean Betti curves computed from Quijote DM density fields for each simulation set at z = 2, 1 and 0 (top to bottom) and for P0, P1 and P2 (left to right). Black lines show the fiducial massless neutrino case, blue lines the 0.1 eV scenario, and red lines the 0.4 eV model. In each block, the middle-row inset shows the ratio relative to the fiducial case, and the bottom-most panel provides a zoom-in on the B… view at source ↗
Figure 9
Figure 9. Figure 9 [PITH_FULL_IMAGE:figures/full_fig_p013_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: Persistence diagram differences for the Qui￾jote halo density fields at z = 2 (top block), z = 1 (middle block), and z = 0 (bottom block), showing the change in pair number density between the massive neutrino simula￾tions and the fiducial massless neutrino case. Within each block, columns correspond to pair types: P0 (left), P1 (mid￾dle), and P2 (right). The layout follows [PITH_FULL_IMAGE:figures/full_… view at source ↗
Figure 11
Figure 11. Figure 11: Mean positions (points) of the persistence diagram apexes for the Quijote halo mass density fields, with ellipses indicating the 1σ variation over 100 simulations per cosmology. The layout mirrors [PITH_FULL_IMAGE:figures/full_fig_p015_11.png] view at source ↗
Figure 12
Figure 12. Figure 12: Mean Betti curves for the Quijote halo mass density fields. The figure is organized in three blocks, from top to bottom corresponding to z = 2, 1 and 0, respectively. Within each block, the top row shows the mean Betti curves for the three different cosmologies considered, the middle row presents their ratios relative to the fiducial, massless neutrino case, and the bottom row zooms in on the Betti curve … view at source ↗
Figure 13
Figure 13. Figure 13: Crossing points of the mean Betti curves for the Quijote halo mass density fields. The figure layout mirrors that of [PITH_FULL_IMAGE:figures/full_fig_p017_13.png] view at source ↗
read the original 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.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

1 major / 0 minor

Summary. The paper analyzes persistent homology on dark matter and halo density fields from the Quijote simulations at z=0,1,2 for varying neutrino masses. It reports that apex points in persistent diagrams are especially sensitive to neutrino mass (with enhanced sensitivity for specific saddle-point pairs at high redshift), that Betti curves broaden and flatten with increasing M_ν, and that two characteristic density thresholds show invariant Betti numbers. These signatures are stated to be detectable at the few-percent level even for M_ν ~ 0.1 eV, establishing persistent homology as a higher-order, multiscale complement to two-point statistics for neutrino-mass constraints with immediate relevance to DESI, Euclid, and LSST.

Significance. If the reported sensitivities are robust, the work introduces a topological probe that captures multiscale information beyond pairwise correlations, potentially helping to break degeneracies in neutrino-mass constraints. Credit is due for the direct use of the public Quijote suite with no parameter fitting and for the parameter-free computation of persistent diagrams and Betti curves, which provides a clean, reproducible baseline for future emulator development.

major comments (1)
  1. Abstract: the claim that the signatures constitute a probe 'with immediate relevance for ongoing and upcoming galaxy surveys' is not supported by the presented evidence. The analysis is restricted to ideal dark-matter and halo fields; no forward modeling or even qualitative assessment of redshift-space distortions, galaxy bias, baryonic feedback, or survey masks is provided. Because the neutrino-induced shifts are only a few percent, any of these effects could dominate or erase the reported sensitivity, rendering the relevance claim load-bearing and unsubstantiated.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the constructive and detailed review. We agree that the abstract's phrasing regarding immediate relevance to galaxy surveys overstates the current scope of the work, which is limited to ideal dark-matter and halo fields. We have revised the manuscript to address this concern.

read point-by-point responses

  1. Referee: Abstract: the claim that the signatures constitute a probe 'with immediate relevance for ongoing and upcoming galaxy surveys' is not supported by the presented evidence. The analysis is restricted to ideal dark-matter and halo fields; no forward modeling or even qualitative assessment of redshift-space distortions, galaxy bias, baryonic feedback, or survey masks is provided. Because the neutrino-induced shifts are only a few percent, any of these effects could dominate or erase the reported sensitivity, rendering the relevance claim load-bearing and unsubstantiated.

    Authors: We agree with the referee that the analysis is performed exclusively on dark-matter and halo density fields from the Quijote simulations in real space, without any forward modeling or assessment of redshift-space distortions, galaxy bias, baryonic feedback, or survey masks. The reported neutrino-mass sensitivities are at the few-percent level, so these effects could indeed dominate or mask the signals. In the revised manuscript, we have updated the abstract to replace 'with immediate relevance for ongoing and upcoming galaxy surveys' with 'establishing a solid foundation for forward-modeling or emulator-based approaches using persistent homology to constrain neutrino mass and additional cosmological parameters, with potential relevance for ongoing and upcoming galaxy surveys.' We have also added a dedicated paragraph in the conclusions section that explicitly acknowledges these limitations and outlines the need for future work to incorporate observational effects. This revision ensures the claims are fully supported by the presented evidence while preserving the motivation for the topological approach. revision: yes

Circularity Check

0 steps flagged

Minor self-citation to Paper I for methodology; central results are direct measurements from external Quijote simulations with no fitted predictions or self-definitional reductions.

full rationale

The paper computes persistent diagrams, Betti curves, and related statistics directly on density fields from the Quijote simulation suite (external to this work) at multiple neutrino mass values and redshifts. The reported sensitivities (apex-point shifts, Betti curve broadening/flattening at few-percent level for M_nu ~ 0.1 eV) are measured outcomes, not derived by fitting parameters to reproduce them or by any self-referential definition. The sole self-reference is the phrase 'Building on the methodology established in Paper I' (abstract), which supplies the discrete Morse theory framework but does not bear the load of the neutrino-mass claims or force any result by construction. No uniqueness theorems, ansatzes, or renamings of known results are invoked in a circular manner. The derivation chain consists of standard empirical analysis on independent simulations and is therefore self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The work relies on standard cosmological simulations and topological data analysis; no new entities postulated.

axioms (1)
  • domain assumption The Quijote simulations accurately model the effects of massive neutrinos on structure formation.
    Central to interpreting the topological differences as due to neutrino mass.

pith-pipeline@v0.9.0 · 5609 in / 1350 out tokens · 68757 ms · 2026-05-10T06:56:06.975526+00:00 · methodology

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Works this paper leans on

3 extracted references · 3 canonical work pages

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