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arxiv: 2604.09148 · v1 · submitted 2026-04-10 · 🌌 astro-ph.CO

The Cosmic Web and Its Filaments: Neutrino Mass from Topology and Persistent Homology

Graziano Rossi , Hogyun Yu , Micha\"el Michaux This is my paper

Pith reviewed 2026-05-10 17:07 UTC · model grok-4.3

classification 🌌 astro-ph.CO
keywords cosmic webfilamentsneutrino masspersistent homologytopologylarge-scale structureN-body simulations
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The pith

Massive neutrinos produce mass-dependent signatures in cosmic filament topology detectable at the few-percent level.

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

The authors use discrete Morse theory and persistent homology to analyze how massive neutrinos shape the multiscale structure of the cosmic web, with particular focus on filaments. They compare N-body simulations with varying neutrino masses and find that these particles create distinct, mass-dependent changes in filament connectivity and in the persistence of topological features. The signatures are clearest at redshift around 2 and remain measurable even for neutrino masses near 0.1 eV. This topological approach captures more information than standard statistics and suggests a new route for measuring neutrino mass with data from galaxy surveys.

Core claim

Applying persistent homology to the cosmic density field reveals that neutrinos of different masses produce distinct patterns in the longevity of topological features within the filamentary skeleton. Filament statistics and persistence diagrams differ systematically between cosmologies with massive neutrinos and those with massless neutrinos. These differences grow with neutrino mass, appear most strongly at high redshift, and reach a few percent in amplitude for masses as small as 0.1 eV. The framework works with particle-based neutrino simulations despite their shot noise because it focuses on the salient features of the underlying field.

What carries the argument

Persistent homology on the cosmic web, which tracks the birth and death of connected components, loops, and voids across varying density thresholds to measure the persistence of filamentary structures.

If this is right

  • Filaments offer an environment where neutrino effects can be isolated from other cosmic structures.
  • The method provides a parameter-free way to extract multiscale neutrino signals from large-scale structure data.
  • It can be applied to tracers in galaxy redshift surveys to constrain neutrino mass.
  • Comparison of different neutrino implementations helps assess systematic uncertainties in the measurements.

Where Pith is reading between the lines

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

  • Topological measures might distinguish between normal and inverted neutrino mass hierarchies when combined with other cosmological probes.
  • Extending the analysis to lower redshifts could test whether the high-redshift signals persist in observable galaxy distributions.
  • The same tools could quantify the impact of warm dark matter or other exotic particles on web topology.

Load-bearing premise

The differences seen in persistence diagrams and filament statistics are caused by neutrino mass rather than by differences in how the simulations are run or analyzed.

What would settle it

If persistence diagrams computed from a new set of simulations with varied resolution or neutrino modeling techniques show no clear mass-dependent trend, the claim that neutrinos leave distinct topological imprints would be falsified.

Figures

Figures reproduced from arXiv: 2604.09148 by Graziano Rossi, Hogyun Yu, Micha\"el Michaux.

Figure 1
Figure 1. Figure 1: Visualizations of 100 × 100 × 50h −1Mpc slices at z = 0 with identical spatial locations, from the fiducial MassiveNuS simulations. From left to right, the neutrino mass values are Mν = 0.0 eV (left), Mν = 0.1 eV (center), and Mν = 0.6 eV (right). The top panels display voids (depicted in blue-to-white colors, varying with the corresponding density as indicated by the side color bar), overlaid with wall st… view at source ↗
Figure 2
Figure 2. Figure 2: Three cubic slices at z = 0 with identical spatial locations and 100h −1Mpc side, obtained from the QUIJOTE simulations with Mν = 0.0 eV (left, fiducial model), Mν = 0.1 eV (center), and Mν = 0.4 eV (right), respectively. In all of the panels, wall structures are shown using a blue-to-red palette, with the corresponding density indicated by the right-side color bar. Superimposed, the filamentary skeleton s… view at source ↗
Figure 3
Figure 3. Figure 3: Schematic view of our pipeline for computing the filtered discrete Morse-Smale complex, starting from a subset of N-body particles. See the main text and Appendix A for more details. extract and classify critical points—faithful tracers of cosmological structures. 4.2. Pipeline: Details Our pipeline is schematically shown in [PITH_FULL_IMAGE:figures/full_fig_p012_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Examples of upskeletons at z = 0 from DisPerSE applied to selected MassiveNuS simulations. Top panels show a massless neutrino cosmology, while bottom panels depict a scenario with Mν = 0.1 eV. Left panels display 2D density fields (in 100 × 100h −1Mpc projections) with the density scale indicated in the bottom color bar, and the upskeletons traced in grey. Insets show progressive zoom-ins, with upskeleton… view at source ↗
Figure 5
Figure 5. Figure 5: A 25 × 25h −1Mpc 2D slice at z = 0 from a Mν = 0.6 eV cosmology in the MassiveNuS suite, illustrating the definition of DisPerSE filaments. Filaments are derived from the upskeleton, where arcs connect saddle-2 points and maxima. Each filament consists of two arcs sharing a com￾mon saddle-2 point. Individual filaments are shown in dis￾tinct colors for clarity. a series of tests. Notably, Sousbie et al. (20… view at source ↗
Figure 6
Figure 6. Figure 6: Summary of tests assessing the impact of subsampling, smoothing, and persistence thresholds on arc statistics in the MassiveNuS simulations at z = 0. Each panel shows the ratio of arc lengths in Mν = 0.1 eV (dashed blue lines) and Mν = 0.6 eV (dotted red lines) cosmologies relative to the massless neutrino scenario, with the shaded light brown regions representing a ±2% variation. These tests reveal the in… view at source ↗
Figure 7
Figure 7. Figure 7: [Top Left] Filament length distribution P(L) at z = 0 for massless (Mν = 0 eV, black solid line) and massive neutrino cosmologies (Mν = 0.1 eV, dashed light blue; Mν = 0.6 eV, dotted orange). [Bottom Left] Ratios relative to the massless scenario, with the shaded light brown region indicating a ±2% variation. A transition scale around 10h −1Mpc, nearly independent of Mν, is observed, alongside a neutrino-m… view at source ↗
Figure 8
Figure 8. Figure 8: Persistence diagrams of the MassiveNuS simulations at z = 0 for massless and massive neutrino cosmologies (Mν = 0.1, 0.6 eV). Rows show P0, P1, and P2 persistence pairs, while columns correspond to increasing neutrino mass. White dotted lines indicate persistence thresholds at σ = 3, 4.5, and 6. High-persistence apexes trace key connectivity transitions of the cosmic web and exhibit systematic shifts with … view at source ↗
Figure 9
Figure 9. Figure 9: Comparison of P0 (minima to saddle-1) persistence diagrams for the fiducial, massless-neutrino cosmology (blue) and massive-neutrino models with Mν = 0.1 eV (left panel, red) and Mν = 0.6 eV (right panel, red). Filled contours indicate the number density of persistence pairs, with higher opacity corresponding to more pairs. Massive neutrinos shift the baseline toward higher density thresholds, reflecting a… view at source ↗
Figure 10
Figure 10. Figure 10: Number of persistence pairs as a function of significance threshold (σ) for P2 (left), P1 (center), and P0 (right) pairs from the MassiveNuS simulations at z = 0. The massless-neutrino model is shown as a solid line (“BG”), Mν = 0.1 eV as a dotted line (“NU01”), and Mν = 0.6 eV as a dashed line (“NU06”). The σ ∼ 6 bump in P2 indicates high-persistence halos and filaments, which decrease with increasing ne… view at source ↗
Figure 11
Figure 11. Figure 11: Redshift evolution of filament lengths from the MassiveNuS (top) and QUIJOTE (bottom) simulations at z = 2, 1, 0 (left to right). Top subpanels show the probability distributions of filament lengths, while bottom subpanels display ratios relative to the fiducial massless-neutrino model (black line). The Mν = 0.1 eV model is shown as a dashed blue line, and the Mν = 0.4 eV model (for QUIJOTE only) as an or… view at source ↗
Figure 12
Figure 12. Figure 12: Saddle-2 autocorrelation functions for the MassiveNuS (top row, 2% subsampling) and QUIJOTE (bottom row, 16% subsampling) simulations at z = 2, 1, 0 (left to right). A simplification threshold of σ = 4 is applied to all simulations. Line styles and error bars follow the conventions of the previous figure. The BAO peak around 100 h −1 Mpc is clearly visible and remains consistent across redshifts, cosmolog… view at source ↗
Figure 13
Figure 13. Figure 13: P0 persistence diagrams for the MassiveNuS simulations at z = 2, 1, 0 (left to right), using a simplification threshold of σ = 4 and a 2% subsampling. Blue shading represents the massless-neutrino model, and red shading the Mν = 0.1 eV massive-neutrino model. The diagrams shift toward lower densities with decreasing redshift, reflecting the evacuation of cosmic voids. The relative shift between the two co… view at source ↗
Figure 14
Figure 14. Figure 14: Number of P2 persistence pairs–tracing primarily filaments–as a function of significance threshold for the MassiveNuS simulations at z = 2, 1, 0 (left to right), using a 2% subsampling and a simplification threshold σ = 4. Solid brown lines represent the massless-neutrino model, and dotted red lines the Mν = 0.1 eV massive-neutrino framework. Bottom panels show the relative differences between the two cos… view at source ↗
read the original abstract

We apply discrete Morse theory, global topology, and persistent homology to characterize the impact of massive neutrinos on the multiscale cosmic web, focusing on filaments. The topology of the cosmic web is sensitive to neutrino imprints, and persistence diagrams provide more information than commonly used summary statistics by quantifying the longevity of topological features across densities. This scale-adaptive, parameter-free formalism is powerful, as massive neutrinos affect halos, walls, filaments, and voids in distinct ways. Within this framework, we simultaneously assess their impact on tracers and skeleton structures and capture their multiscale signals across cosmic time. Discrete Morse theory is also well suited for particle-based neutrino implementations, often affected by Poisson shot noise, as it preserves the salient features of the underlying smooth field. Using two independent sets of N-body simulations, we present filament statistics and persistence diagrams in massive-neutrino cosmologies. Our results show that neutrinos leave distinct imprints on filaments and skeleton connectivity, producing mass-dependent signatures most pronounced at high redshift (z~2) and detectable at the few-percent level for masses as small as $M_\nu \sim 0.1$ eV. Filaments thus provide an ideal environment for isolating neutrino effects. We also compare two implementations of massive neutrinos to assess systematics. Our study establishes a promising avenue for leveraging cosmic web topology, persistent homology, and environment-based statistics to constrain or directly detect neutrino mass and infer the mass hierarchy - a long-standing challenge in particle physics and a major objective of ongoing and upcoming galaxy redshift surveys (e.g., DES, DESI, Euclid, 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

3 major / 2 minor

Summary. The manuscript applies discrete Morse theory, global topology, and persistent homology to N-body simulations to study the effects of massive neutrinos on the cosmic web, with emphasis on filaments and skeleton connectivity. Using two independent simulation suites and comparing two neutrino implementations, it reports mass-dependent imprints in filament statistics and persistence diagrams that are strongest at z~2 and detectable at the few-percent level down to M_ν ~ 0.1 eV, positioning filaments as an environment for isolating neutrino effects and potentially constraining the mass hierarchy.

Significance. If the central results hold after addressing systematics, the work offers a promising topology-based probe complementary to power-spectrum or halo-mass-function methods, exploiting the distinct neutrino impacts across web elements and the parameter-free nature of persistent homology. The use of two independent simulation sets and explicit implementation comparisons is a positive step toward robustness, and the suitability of discrete Morse theory for mitigating Poisson noise in particle-based neutrinos is a clear strength.

major comments (3)
  1. [Abstract and §4] Abstract and §4 (Results): the claim of 'detectable at the few-percent level' for M_ν ~ 0.1 eV is presented without reported error bars, simulation variance estimates, bootstrap uncertainties, or explicit null tests (e.g., randomized realizations or controlled massless runs). This absence prevents verification that the reported mass-dependent differences in persistence diagrams and filament statistics exceed numerical or cosmic variance.
  2. [§4.2] §4.2 (neutrino implementation comparison): although two implementations are contrasted to assess systematics, the text does not quantify the inter-implementation scatter in persistence diagrams or filament/skeleton statistics relative to the 0.1 eV vs. massless contrast across density thresholds and redshifts. If this scatter is comparable to or larger than the claimed signal, the attribution of differences solely to neutrino mass cannot be established.
  3. [§3 and §4] §3 (Simulations) and §4: no resolution or volume convergence tests are shown for the topological measures at the scales and redshifts (particularly z~2) where the few-percent signals are reported. Given the sensitivity of persistent homology to small-scale noise, this leaves open whether the observed mass dependence could be contaminated by resolution or shot-noise residuals.
minor comments (2)
  1. [Abstract and §2] The abstract refers to a 'parameter-free formalism,' yet persistent homology involves choices in filtration and density estimation; a brief clarification in §2 would avoid potential confusion.
  2. [§4] Figure captions in §4 could explicitly state the number of realizations used and whether error bands (if any) represent standard deviation or standard error.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for their thorough review and valuable feedback on our manuscript. We appreciate the recognition of the potential of our topological approach and the positive comments on the use of two simulation suites and implementation comparisons. Below, we address each major comment point by point, providing clarifications and outlining the revisions we will make to strengthen the manuscript.

read point-by-point responses

  1. Referee: [Abstract and §4] Abstract and §4 (Results): the claim of 'detectable at the few-percent level' for M_ν ~ 0.1 eV is presented without reported error bars, simulation variance estimates, bootstrap uncertainties, or explicit null tests (e.g., randomized realizations or controlled massless runs). This absence prevents verification that the reported mass-dependent differences in persistence diagrams and filament statistics exceed numerical or cosmic variance.

    Authors: We agree that providing quantitative error estimates is essential for substantiating the significance of our results. In the original manuscript, the 'few-percent level' refers to the relative differences observed consistently across the two independent simulation suites and between massive and massless neutrino cases. However, to address this concern, we will add bootstrap resampling uncertainties on the persistence diagrams and filament statistics, include comparisons with randomized realizations, and explicitly show the differences relative to the massless case with error bars in the revised §4. This will allow readers to verify that the mass-dependent signals exceed the estimated variances. revision: yes

  2. Referee: [§4.2] §4.2 (neutrino implementation comparison): although two implementations are contrasted to assess systematics, the text does not quantify the inter-implementation scatter in persistence diagrams or filament/skeleton statistics relative to the 0.1 eV vs. massless contrast across density thresholds and redshifts. If this scatter is comparable to or larger than the claimed signal, the attribution of differences solely to neutrino mass cannot be established.

    Authors: We thank the referee for highlighting this important point on systematics. In the revised manuscript, we will include a quantitative comparison of the inter-implementation scatter (between the two neutrino implementations) versus the neutrino mass signal (0.1 eV vs. massless) for the key statistics at various redshifts and density thresholds. We will add panels or tables showing the ratio of scatter to signal, demonstrating that the implementation differences are smaller than the mass-dependent effects, thereby supporting the attribution to neutrino mass. revision: yes

  3. Referee: [§3 and §4] §3 (Simulations) and §4: no resolution or volume convergence tests are shown for the topological measures at the scales and redshifts (particularly z~2) where the few-percent signals are reported. Given the sensitivity of persistent homology to small-scale noise, this leaves open whether the observed mass dependence could be contaminated by resolution or shot-noise residuals.

    Authors: We acknowledge that convergence tests are crucial given the sensitivity of persistent homology to small-scale features. Although our use of two independent simulation sets with different resolutions and volumes provides some indication of robustness, we did not explicitly present dedicated convergence tests in the original submission. In the revision, we will add resolution and volume convergence tests for the persistence diagrams and filament statistics at z~2, including comparisons at different particle numbers and box sizes to confirm that the reported mass-dependent signals are not affected by numerical artifacts or shot noise. revision: yes

Circularity Check

0 steps flagged

No circularity: direct simulation comparison with cross-checks

full rationale

The paper performs a comparative analysis of N-body simulation outputs (two independent sets, two neutrino implementations) using persistent homology and discrete Morse theory on the cosmic web. No parameter is fitted to a subset of data and then relabeled as a prediction; no derivation chain reduces by construction to its inputs; no self-citation is invoked as a uniqueness theorem or load-bearing premise for the central claim. The mass-dependent signals are extracted directly from the topology of the simulated fields, with explicit systematics checks noted in the abstract. This is a standard, self-contained empirical study whose conclusions rest on the simulation data rather than on any tautological re-expression of its own assumptions.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim rests on the assumption that the chosen N-body implementations faithfully capture neutrino effects and that the topological measures are insensitive to simulation artifacts.

axioms (1)
  • domain assumption N-body simulations with the chosen neutrino implementations accurately reproduce the true impact of massive neutrinos on structure formation
    All reported differences are attributed to neutrino mass; any mismatch between simulation and reality would invalidate the claimed signatures.

pith-pipeline@v0.9.0 · 5596 in / 1319 out tokens · 56078 ms · 2026-05-10T17:07:18.995424+00:00 · methodology

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Works this paper leans on

5 extracted references · 5 canonical work pages

  1. [1]

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  5. [5]

    N., Arnold , K., Austermann , J., et al

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    work page doi:10.1016/j.astropartphys.2014.05.014 2017