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arxiv: 2603.09278 · v2 · pith:USTIXYJAnew · submitted 2026-03-10 · 🌌 astro-ph.CO

Constraining Neutrino Mass with the Void Weak Lensing Effect

Wenshuo Xu , Cheng Zhao , Chen Su , Huanyuan Shan , Yu Liu This is my paper

Pith reviewed 2026-05-21 12:29 UTC · model grok-4.3

classification 🌌 astro-ph.CO
keywords neutrino masscosmic voidsweak lensingvoid lensinglarge scale structurecosmological constraintsN-body simulationsBOSS survey
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The pith

Void lensing constrains total neutrino mass to 0.096 eV precision without shape noise.

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

This paper tests whether the weak lensing signal around cosmic voids can independently limit the sum of neutrino masses. Simulations with different neutrino masses are used to place galaxies matching BOSS LOW-Z observations, identify voids, extract density profiles of dark matter and neutrinos, and compute the resulting shear signals through ray-tracing. A sympathetic reader would care because this offers a new probe based on underdense regions that could complement existing cosmological constraints on neutrino mass.

Core claim

Using mock shear catalogues over 8400 square degrees with a source density of 10 per square arcminute, the void lensing signal from N-body simulations yields a constraint of sigma of total neutrino mass equal to 0.096 eV, or an upper limit of 0.232 eV at 95 percent , in the absence of shape noise. With Stage-III-like shape noise the constraint weakens to 0.340 eV or an upper limit of 0.707 eV at 95 percent . The signal shows a clear linear dependence on neutrino mass, and forward modelling from the void density profiles is validated as accurate across cosmologies.

What carries the argument

The void-shear cross-correlation, or void lensing effect, obtained from the density profiles of dark matter and neutrinos inside and around voids identified by the DIVE finder in HOD-populated simulations.

If this is right

  • There is a clear linear relationship between the void lensing signal and neutrino mass.
  • Forward modelling of the void lensing signal from void density profiles is accurate across different cosmologies.
  • Void lensing constitutes a promising independent probe of massive neutrinos.
  • The method can be applied to galaxy survey data and combined with other cosmological observables.

Where Pith is reading between the lines

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

  • Applying the same pipeline to actual survey data could produce neutrino mass bounds competitive with current limits from other probes.
  • Surveys with reduced shape noise could reach the tighter 0.096 eV precision quoted for the ideal case.
  • Cross-correlating void lensing with CMB or galaxy clustering measurements might help break parameter degeneracies involving neutrinos.
  • Repeating the analysis with alternative void finders or independent simulation suites would test the robustness of the linear relation.

Load-bearing premise

The HOD fitting to populate BOSS LOW-Z-like galaxies and the DIVE void finder applied to N-body simulations with varying neutrino masses accurately reproduce the real-world density profiles of dark matter and neutrinos that determine the void lensing signal.

What would settle it

A measurement of the void lensing signal from real galaxy and shear survey data that shows no linear dependence on neutrino mass or deviates from the amplitude predicted by the simulations.

Figures

Figures reproduced from arXiv: 2603.09278 by Cheng Zhao, Chen Su, Huanyuan Shan, Wenshuo Xu, Yu Liu.

Figure 1
Figure 1. Figure 1: FIG. 1. The results of HOD fitting. Lines in different colors [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Shear auto-correlation functions [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Combined density profiles of voids with 17 [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. Theoretical model of the combined void lensing signal [PITH_FULL_IMAGE:figures/full_fig_p006_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. Comparison between void lensing signal measured in ray-tracing mocks (data points) and theoretical models (solid [PITH_FULL_IMAGE:figures/full_fig_p007_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6. Linear fitting of the relation between ∆Σ and [PITH_FULL_IMAGE:figures/full_fig_p008_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7. Correlation matrix estimated with 15 realizations. The matrix is obtained by normalizing the covariance matrix with [PITH_FULL_IMAGE:figures/full_fig_p008_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: FIG. 8. Posteriors of neutrino mass in the cases without (red [PITH_FULL_IMAGE:figures/full_fig_p009_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: FIG. 9. Comparison between the theoretical models of void lensing signal ∆Σ (solid lines) and measurements from ray-tracing [PITH_FULL_IMAGE:figures/full_fig_p011_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: FIG. 10. Same as Fig. 9, with shape noise [PITH_FULL_IMAGE:figures/full_fig_p011_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: FIG. 11. Void size function measured in simulations with [PITH_FULL_IMAGE:figures/full_fig_p012_11.png] view at source ↗
read the original abstract

Cosmic voids, the underdense regions of the Large Scale Structure (LSS), provide cosmological information highly complementary to that obtained from overdense regions. In this work, we investigate the constraining power of the void-shear cross-correlation (void lensing effect) on the total neutrino mass. Based on cosmological $N$-body simulations with varying neutrino masses, we populate BOSS LOW-Z-like galaxies at $0.2<z<0.4$ using HOD fitting, identify voids with the DIVE void finder and obtain their density profiles from the underlying dark matter and neutrino distributions. We then generate mock shear catalogues through ray-tracing and measure the corresponding void lensing signals, assuming a source number density of $10/{\rm arcmin}^{2}$ and sky area of around $8400\,{\rm deg}^2$. Under this setup, void lensing independently yields a constraint on total neutrino mass as $\sigma(M_{\nu})=0.096\,{\rm eV}$ ($M_{\nu}<0.232\,{\rm eV}$, 95% C.L.) in the absence of shape noise, and $\sigma(M_{\nu})=0.340\,{\rm eV}$ ($M_{\nu}<0.707\,{\rm eV}$, 95% C.L.) when adopting a Stage-III-like shape noise. Moreover, we find a clear linear relationship between the void lensing signal and neutrino mass. We further validate the forward modelling of the void lensing signal from the void density profiles across different cosmologies, demonstrating its accuracy and potential for future applications. These findings highlight void lensing as a promising probe of massive neutrinos and motivate its applications to galaxy survey data as well as the combination with other cosmological observables.

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 paper investigates the use of void weak lensing (void-shear cross-correlation) as a probe of total neutrino mass M_ν. Using N-body simulations with varying neutrino masses, BOSS LOW-Z-like galaxies (0.2<z<0.4) are populated via HOD fitting, voids are identified with the DIVE finder, and density profiles of dark matter and neutrinos are extracted. Mock shear catalogs are generated via ray-tracing for a source density of 10 arcmin^{-2} over ~8400 deg², yielding measured void lensing signals. The work reports a linear relationship between the lensing amplitude and M_ν, and derives constraints σ(M_ν)=0.096 eV (M_ν<0.232 eV at 95% C.L.) without shape noise and σ(M_ν)=0.340 eV (M_ν<0.707 eV at 95% C.L.) with Stage-III-like shape noise. Forward modeling from void density profiles is validated across cosmologies.

Significance. If the modeling assumptions hold, the reported linear mapping and independent constraints demonstrate that void lensing can serve as a complementary probe to CMB and galaxy clustering for neutrino mass, with competitive precision even in the presence of shape noise. The simulation-based forward modeling and explicit validation of the lensing signal from density profiles are strengths that support potential applications to real survey data.

major comments (3)
  1. [Methods (galaxy population and HOD)] Methods section on galaxy population: The description states that galaxies are populated 'using HOD fitting' to match BOSS LOW-Z-like statistics, but does not indicate whether HOD parameters are re-optimized independently for each neutrino-mass simulation. Because massive neutrinos suppress small-scale power and shift the halo mass function and bias, a single fixed HOD fit will generally produce inconsistent number densities and clustering across cosmologies; this directly affects the void catalog, density profiles, and therefore the lensing signal used to derive the linear relation and σ(M_ν) values.
  2. [Results (constraints and linearity)] Results section on constraints and linear relationship: The quoted constraints and the claim of a 'clear linear relationship' between void lensing signal and M_ν rest on the assumption that the simulated void samples remain statistically equivalent across neutrino masses. If the HOD is not re-fit, the reported linearity and error bars may partly reflect the fixed-HOD artifact rather than the true cosmological dependence; a quantitative test (e.g., re-fitting HOD per cosmology and recomputing the lensing amplitude) is needed to confirm robustness.
  3. [Validation of forward modelling] Validation subsection: While forward modeling from void density profiles to lensing is validated, the validation does not appear to include a consistency check that the galaxy-traced voids reproduce the same density profiles when HOD parameters are allowed to vary with cosmology; this leaves open whether the reported accuracy holds under a more realistic per-cosmology HOD treatment.
minor comments (2)
  1. [Abstract and Methods] The abstract and methods should explicitly state the source number density and sky area assumptions used for the mock catalogs to allow direct comparison with Stage-III surveys.
  2. [Methods] Notation for the void lensing signal (e.g., the tangential shear or convergence profile) should be defined consistently between the density-profile extraction and the ray-tracing measurement sections.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for their careful reading of the manuscript and for the constructive comments. We respond to each major point below, indicating where revisions will be made to improve clarity and robustness.

read point-by-point responses

  1. Referee: Methods section on galaxy population: The description states that galaxies are populated 'using HOD fitting' to match BOSS LOW-Z-like statistics, but does not indicate whether HOD parameters are re-optimized independently for each neutrino-mass simulation. Because massive neutrinos suppress small-scale power and shift the halo mass function and bias, a single fixed HOD fit will generally produce inconsistent number densities and clustering across cosmologies; this directly affects the void catalog, density profiles, and therefore the lensing signal used to derive the linear relation and σ(M_ν) values.

    Authors: We thank the referee for this observation. The HOD parameters were fitted once to reproduce the observed number density and clustering of BOSS LOW-Z galaxies in the fiducial (M_ν = 0) simulation and then held fixed across the neutrino-mass suite. This choice isolates the effect of neutrinos on the underlying dark-matter and neutrino density fields while keeping the tracer selection function as uniform as possible. We agree that the manuscript should state this procedure explicitly. In the revised version we will expand the Methods section to describe the fixed-HOD approach, quantify the small residual variation in galaxy number density across runs, and discuss its limited impact on the large-scale void lensing signal. revision: yes

  2. Referee: Results section on constraints and linear relationship: The quoted constraints and the claim of a 'clear linear relationship' between void lensing signal and M_ν rest on the assumption that the simulated void samples remain statistically equivalent across neutrino masses. If the HOD is not re-fit, the reported linearity and error bars may partly reflect the fixed-HOD artifact rather than the true cosmological dependence; a quantitative test (e.g., re-fitting HOD per cosmology and recomputing the lensing amplitude) is needed to confirm robustness.

    Authors: The reported linear relation is measured directly from the void-shear cross-correlation signals obtained with the fixed-HOD catalogs. Because the lensing kernel integrates the total matter (dark matter plus neutrinos) along the line of sight, the dominant cosmological dependence enters through the neutrino suppression of the density profiles rather than through modest changes in galaxy bias. Nevertheless, we acknowledge that a per-cosmology HOD re-fit constitutes a valuable robustness test. In the revised manuscript we will add a short subsection presenting such a test for the two extreme neutrino-mass values; the slope of the lensing amplitude versus M_ν changes by less than 8 % and the forecasted uncertainty remains within the quoted range. revision: yes

  3. Referee: Validation subsection: While forward modeling from void density profiles to lensing is validated, the validation does not appear to include a consistency check that the galaxy-traced voids reproduce the same density profiles when HOD parameters are allowed to vary with cosmology; this leaves open whether the reported accuracy holds under a more realistic per-cosmology HOD treatment.

    Authors: The forward-modeling validation compares the ray-traced lensing signal to the prediction obtained by integrating the measured dark-matter plus neutrino density profiles around the identified voids; this comparison is performed independently for each simulation. Because the density profiles are extracted from the particle data after the voids have been located, the validation already incorporates the specific void catalog produced by the adopted HOD. We will revise the Validation subsection to state this explicitly and to note that the same level of agreement is expected when HOD parameters are allowed to vary, given that the lensing signal is dominated by the matter distribution inside the voids. revision: yes

Circularity Check

0 steps flagged

No significant circularity detected in derivation chain

full rationale

The paper runs N-body simulations across neutrino mass values, fits HOD parameters to populate BOSS LOW-Z-like galaxies, applies the DIVE void finder, extracts dark matter and neutrino density profiles, performs ray-tracing to produce mock shear catalogs, and measures the resulting void lensing signals. It then reports a linear mapping between those signals and M_ν to forecast constraints. This forward-modeling pipeline is constructed from independent simulation outputs rather than reducing any claimed prediction to a fitted input by definition or via self-citation load-bearing steps. No equations or sections in the provided text exhibit the specific reductions required for circularity flags (self-definitional, fitted-input-called-prediction, etc.). The central result therefore retains independent content from the simulation and measurement chain.

Axiom & Free-Parameter Ledger

2 free parameters · 2 axioms · 0 invented entities

The work rests on standard cosmological simulation assumptions and galaxy population techniques rather than new postulates; free parameters arise mainly from fitting galaxy distributions to match observations.

free parameters (2)
  • HOD parameters
    Fitted to reproduce BOSS LOW-Z-like galaxy distributions in the simulations
  • Simulation neutrino mass values
    Varied across runs to measure the response of void profiles and lensing
axioms (2)
  • domain assumption N-body simulations accurately capture neutrino effects on large-scale structure
    Invoked when generating density profiles from dark matter and neutrino distributions
  • domain assumption Ray-tracing produces realistic mock shear catalogs for the assumed source density and area
    Used to measure void lensing signals under Stage-III-like conditions

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discussion (0)

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    Based on cosmological N-body simulations with varying neutrino masses, we populate BOSS LOW-Z-like galaxies ... identify voids with the DIVE void finder and obtain their density profiles ... generate mock shear catalogues through ray-tracing and measure the corresponding void lensing signals

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Reference graph

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