Constraining decaying dark matter models with gravitational lensing and cosmic voids

Earl Lester; Krzysztof Bolejko

REVIEW 4 major objections 6 minor 1 cited by

Constraining decaying dark matter models with gravitational lensing and cosmic voids

T0 review · 4 major / 6 minor · reviewed 2026-08-06 · deepseek-v4-flash

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Pith's one-line read Decaying dark matter should leave a measurable imprint in the weak-lensing signal of cosmic voids.

desk verdict A useful exploratory prediction for void lensing as a DDM probe, but the signature rests on an ad hoc interaction term that needs microphysical justification before the forecast means much. read the letter →

arxiv 2507.08275 v1 pith:CNK2KLU7 submitted 2025-07-11 astro-ph.CO gr-qchep-ph

Earl Lester , Krzysztof Bolejko This is my paper

classification astro-ph.COgr-qchep-ph PACS 95.35.+d98.62.Sb98.80.-k

keywords decayingdarkmattercosmicvoidsweakgravitationallensingvoidsizefunctionmasssplittingparameterinjectionvelocitytwo-fluidcosmologystructureformation

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

The paper tries to establish that cosmic voids, the largest underdense regions in the universe, can serve as probes of decaying dark matter (DDM). In its two-fluid model, a mother dark-matter particle decays into a lighter massive daughter that receives a kick velocity and flows into void interiors, 'flooding' the voids and making their density profiles shallower than standard cold dark matter predicts. The paper computes the weak-lensing convergence and shear that such voids would produce and finds that DDM shows up statistically as a deficit of high-convergence voids and an excess of low-convergence voids at a fixed shear. It concludes that detecting this signature requires lensing precision of a few percent, beyond current surveys but perhaps within reach of upcoming surveys such as LSST.

What carries the argument

The machinery is a covariant two-fluid description of dark matter in a locally rotationally symmetric spacetime. One dust fluid (density $\rho$, 4-velocity $u^a$) represents the mother particles; the other (density $\lambda$, 4-velocity $v^a$) represents the decay products. Decay is encoded in the interaction term $I^a_{(1)} = -\Gamma\rho\,(u^a + w^a)$ with $w^a = (4/\pi^2)\, v_i\, \delta\, z^a$, where $\Gamma$ is the decay rate, $v_i$ is the injection velocity, and $z^a$ is the preferred spatial direction; this term produces an effective acceleration $A = -(4/\pi^2)\Gamma\delta\sqrt{2\epsilon}$ that drives daughter particles into voids. The evolution equations (5)--(11) are integrated from Lemaître--Tolman initial conditions set at redshift 150, and the resulting density profiles are projected onto the lens plane to compute convergence $\kappa = \Sigma/\Sigma_c$ and shear $\gamma = (\bar{\Sigma}-\Sigma)/\Sigma_c$.

What would settle it

Stack the weak-lensing convergence and shear of several thousand voids at lens redshift $z\approx0.25$ with sources near $z\approx0.5$ and compare the $\kappa$--$\gamma$ distribution to the no-decay prediction at better than 2% precision. If the observed distribution matches the no-decay case and shows no deficit of high-convergence voids in the 10--40 Mpc radius range, the DDM scenario with $\Gamma\gtrsim0.5H_0$ and injection velocities of 25--75 km s$^{-1}$ is ruled out; a measured deficit that scales with void size and lifetime would confirm the model.

Watch

Extended reading notes

Core claim

The central claim is a new observational route to dark-matter microphysics: the decay rate $\Gamma$ and the mass-splitting parameter $\epsilon$ (equivalently the injection velocity $v_i$) leave a distinguishable imprint on the gravitational lensing produced by cosmic voids. In the model, decay transfers particles from the comoving mother dust into a daughter fluid moving with velocity $v_i$; because matter density is higher near void edges, more decay products flood inward, reducing the central density contrast and the edge gradient. The result is that the maximal weak-lensing convergence $\kappa$ and shear $\gamma$ are suppressed relative to the no-decay case. The suppression is not visible for individual voids but appears statistically, and it survives Gaussian noise only at roughly 2% measurement precision; at 5--10% the signal is washed out.

Load-bearing premise

The entire predicted signal rests on the ad hoc interaction term of Eq. (2), which assumes that dark-matter decay produces a coherent bulk velocity field directed along the density gradient; if actual decays do not generate such a velocity field, the flooding of voids and the associated lensing deficit do not occur.

Editorial extensions

If this is right

The void size function is not a useful probe: changes in injection velocity produce no statistically significant shift in the void number density as a function of radius.
Weak lensing is the sensitive observable: at fixed shear, decaying dark matter creates an excess of low-convergence voids and a deficit of high-convergence voids, with the effect stronger for smaller voids and shorter lifetimes.
Individual voids cannot be diagnosed one by one; the signature is statistical and requires stacking many voids, with a measurement precision of about 2% in convergence.
The nonlinear treatment reaches injection velocities as low as 75 km s$^{-1}$ and lifetimes of order the Hubble time, extending the parameter space accessible relative to earlier linear modelling that required 90 km s$^{-1}$ and 5 Gyr lifetimes.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

If the interaction term is replaced by a particle-physics-derived decay kernel, the effective velocity $w^a$ may not align with the void density gradient; the flooding signature would then weaken, so the paper's detectability forecast is an upper bound on what generic DDM models can do.
Because the signal enters through the combination $\Gamma\sqrt{\epsilon}$, void lensing alone cannot separate the decay rate from the mass splitting; combining it with Doppler magnification or void-galaxy correlations could break this degeneracy.
A direct testable prediction: in future deep surveys, the stacked void lensing signal should show a deficit of high-convergence voids that grows as void radius shrinks from 30--40 Mpc to 10--20 Mpc, and that strengthens as the assumed lifetime drops from $2H_0^{-1}$ to $0.5 H_0^{-1}$.

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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Desk Editor's Note

read the letter

The new thing here is concrete: the authors extend their earlier DDM void-evolution work to weak lensing, show the void size function is insensitive to decay while the lensing convergence and shear are not, and give a quantitative forecast that LSST-era stacking could detect the difference at roughly 2% precision. The internal logic is consistent, and they are candid that the interaction term is adopted and that the initial void parameters are tuned so the no-decay case matches the HSW profile. That disclosure is genuine credit.

The soft spot is exactly where the stress-test note points. Equation (2)-(3) gives the daughter fluid a coherent radial velocity proportional to the density contrast δ, not to its gradient. An isotropic two-body decay does not produce a net bulk flow; it produces velocity dispersion. So the "flooding" effect that does all the work in the lensing forecast is a property of the model, not of decaying dark matter generally. The authors say the form is "adopted," and they don't derive it from any particle process. If a future referee asks whether the prediction survives for a more realistic decay kinematics, the honest answer is: not shown. The 2% threshold is also inferred from one noise-injection exercise with no formal significance calculation, which is thin but not fatal for an exploratory paper.

The paper is a fair conditional-accept: the machinery is reasonable, the negative result on the void size function is worth having, and the lensing forecast is falsifiable in principle. But the central observable claim is only as good as Eq. (3). I would send it to a referee, and the referee should press hard on the microphysics, or the authors should reframe the conclusion as constraining this specific effective model rather than DDM broadly. It is not a paper I would cite as evidence against DDM; it is a paper I would cite as a worked example of how void lensing could in principle probe the dark sector.

Referee Report

4 major / 6 minor

Summary. The paper studies a phenomenological two-fluid model of decaying dark matter (DDM) in which a mother dust fluid decays into a massive daughter fluid with a nonzero injection velocity. The model is applied to spherically symmetric cosmic voids using covariant LRS evolution equations taken from the authors' earlier work. The authors first calibrate the initial void mass profile so that the no-decay LTB void reproduces the empirical HSW void profile, then evolve the same initial conditions with and without decay and compute the weak-lensing convergence and shear signals. They find that DDM 'floods' voids, making them shallower and reducing the lensing amplitude, and they conclude that a statistical detection via stacked void weak lensing would require percent-level precision, possibly achievable with LSST. The paper also shows that the void size function is not sensitive to the considered decay parameters.

Significance. If the predicted 'flooding' signature were robust, this would constitute a genuinely new astrophysical probe of dark matter decay, complementary to CMB and large-scale-structure constraints, and the paper is commendable for targeting cosmic voids, where baryonic contamination is minimized. The authors are explicit that the interaction term is phenomenological and they provide forward-modeled lensing distributions rather than a full survey simulator. The main value is therefore as a proof-of-concept: it identifies a possible observable signature and quantifies, in a preliminary way, the precision needed to see it. However, the significance is limited by the ad hoc nature of the decay interaction, the calibration of initial conditions to the HSW profile, and the absence of a formal statistical detection calculation. The manuscript is honest about many of these limitations, but the central claim as currently stated goes beyond what the analysis can support.

major comments (4)

[Sec. II B, Eqs. (2)-(3)] The spatial part of the interaction term, w^a = (4/pi^2) v_i delta z^a, is 'adopted' rather than derived from a particle decay model. For an isotropic two-body decay in a spherically symmetric environment, the mean daughter velocity at a given point should be controlled by the gradient of the parent density (a net flux from overdense to underdense regions), not by the local density contrast itself. A term proportional to delta is maximum at the void center and vanishes at the edge, whereas a diffusion-type flux would vanish at the center and peak at the boundary. Because this term is the sole agent producing the 'flooding' effect and hence the predicted lensing deficit, the central observable claim is conditional on an unvalidated phenomenological input. Please either derive the form from a concrete decay kinematics model, or explicitly treat the model as a toy and test the sensitivity of the lensing predictions to alternative spatial dependences (for example, a term proportional to the density gradient).
[Sec. II H and Fig. 4] The initial void parameters m0, r0, and Delta r are fine-tuned so that the no-decay LTB void reproduces the empirical HSW profile. This is a calibration step, not a derivation from cosmological initial conditions, and it means that the DDM prediction is a relative modification of an empirically matched profile rather than an absolute prediction from a power spectrum. The procedure is not circular in the sense that the DDM parameters are not fit to the target lensing observable, but the resulting lensing distributions inherit the HSW assumptions. The paper should state this explicitly and quantify how the DDM lensing signal changes when the calibration parameters are varied within the ranges quoted in Sec. II D.
[Sec. III, Fig. 8] The claim that detection 'requires measurements of weak lensing signal with a precision of 2%' is inferred from a single noise-injection exercise on one panel (the lower-left panel of Fig. 5) with Gaussian scatter at 2%, 5%, and 10%. No formal significance calculation is presented: there is no test statistic, no number of voids, no survey volume or area, and no detection threshold. The visual separation between the DDM and no-DDM distributions in Figs. 5-7 is also not quantified. Please provide a proper detectability estimate that specifies the survey parameters, the number of stacked voids, and a statistical test (e.g., a Kolmogorov-Smirnov or Anderson-Darling test on the convergence-shear distribution) with a stated significance level.
[Sec. II C] The evolution equations (5)-(10) are carried over from the authors' previous paper [26] without derivation or independent validation in this manuscript. Since the new physics enters precisely through the interaction term in Eq. (2) and the resulting acceleration A in Eq. (4), the reader cannot verify from this paper alone that the equations are consistent or that the numerical implementation conserves total energy-momentum. At minimum, please summarize the derivation of the system, state the assumptions under which it is valid, and provide a convergence test or a comparison with an independent method for at least one representative void.

minor comments (6)

[Abstract] There is a typo: 'phenomological' should be 'phenomenological'.
[Sec. II F] The section heading 'W eak gravitational lensing' contains an erroneous space; it should be 'Weak gravitational lensing'.
[Sec. II F, Eq. (17)] The quantity \bar{\Sigma} is called the differential surface mass density but is not defined before its first use; please define it explicitly and distinguish it from the shear scalar \Sigma used earlier in Sec. II C.
[Sec. II D and Sec. II H] The notation for the injection velocity is inconsistent: the text uses both v_in and v_i. Please use a single symbol throughout.
[Sec. II H] The void redshift and source redshift are drawn from normal distributions, but the number of realizations used to produce Figs. 5-7 is not stated. Please specify the sample size and whether the same realizations are used for the DDM and no-DDM cases.
[Fig. 3 caption] The caption says 'parameters increasing size and decay rate (from left to right)' but does not list the actual values; please state the void and source redshifts and the decay parameters for each panel.

Circularity Check

0 steps flagged · score 1.0 of 10

No significant circularity: the DDM parameters are scanned inputs, the lensing predictions are compared against a no-decay model with identical initial conditions, and the cited prior work is a derivation pointer rather than a load-bearing uniqueness claim.

full rationale

The paper's central claim is that decaying dark matter with massive daughters shallows cosmic voids and reduces weak-lensing convergence and shear. This is a derived consequence of the adopted interaction term in Eqs. (2)-(3), not a re-statement of the target observable. The decay parameters Gamma and v_i are scanned over a grid, and the resulting lensing distributions are compared with the no-decay LTB case evolved from the same randomized initial conditions. No parameter is fitted to the lensing signal it is then said to predict. The initial void parameters m0, Delta r, and r0 are calibrated to reproduce the empirical HSW void profile, which is an external N-body benchmark; this calibration affects the baseline no-decay model but does not force the DDM deficit, which is a model-dependent deviation from that baseline. The paper's self-citation of [26] is used to avoid re-deriving the propagation system (5)-(11), but the equations are displayed and the interaction term is introduced in this paper, so the central lensing claim does not reduce to the cited prior work. The main vulnerability is that the spatial interaction term w^a = (4/pi^2) v_i delta z^a is an ad hoc phenomenological choice, not derived from a particle model; if realistic DDM decay produces isotropic daughter velocities rather than a coherent radial bulk flow, the flooding effect and the predicted few-percent detectability would not follow. That is a correctness or robustness risk, not a circularity: the prediction is not equivalent to its input by construction. Overall the derivation chain is self-contained against an external benchmark, so no circular step is exhibited.

Assumptions & free parameters 4 free parameters · 7 assumptions · 1 invented entities

The DDM effect is built on a phenomenological two-fluid interaction rather than on a specific particle model. The evolution equations come from the authors' earlier paper, the initial void profile is fine-tuned to the HSW profile, and the lensing forecast assumes a particular noise model. These are the unstated costs that the central claim depends on.

free parameters (4)

Dark matter decay rate Γ = 0.5 H0, 1.0 H0, 2.0 H0
Scanned parameter setting the decay half-life to be of order the age of the universe. The strength of the lensing deficit scales with Γ; it is not fitted to data.
Injection velocity vi (mass splitting ϵ) = 25, 75, 100, 135 km/s (ϵ up to about 10^-7)
Controls how far daughter particles flood into voids. The central observable depends on it; it is scanned, not fitted.
Initial void mass profile parameters m0, r0, Δr = m0 in [-0.0225,-0.015], r0 in [45,200] kpc, Δr in (0.425-0.5) r0
Drawn randomly and fine-tuned in Sec. II H so that the no-decay LTB void reproduces the empirical HSW profile. The lensing baseline depends on these choices.
HSW profile parameters α, β, δc, rs = Empirically calibrated distributions from Hamaus et al. 2014, Fig. 2
Used to generate the mock void population. These are observational calibrations, not fitted to the DDM prediction.

assumptions (7)

domain assumption Two dark fluids are perfect dust in their own frames and permeate each other without interfaces (T^ab_(1)=ρu^a u^b, T^ab_(2)=λv^a v^b).
Sec. II A. No particle model for the decay products is given; the fluid description and the absence of interfacial instabilities are assumed.
domain assumption The daughter particle is non-relativistic (γ≈1) and the radiative decay component is negligible.
Secs. I and II A. The model is only valid for small injection velocities and ignores the energy density of radiation produced in the decay.
ad hoc to paper The interaction term has the form I^a_(1) = -Γρ(u^a + w^a) with w^a = (4/π^2)v_i δ z^a, producing the effective acceleration A = -(4/π^2)Γδ√(2ϵ).
Sec. II B, Eqs. (2)-(4). This is the load-bearing phenomenological input; no derivation from fundamental interactions is provided.
domain assumption The evolution equations (5)-(11) and the LRS covariant decomposition are taken from the authors' previous paper [26].
Sec. II C. The current paper does not re-derive the system, so errors there would propagate into all forecasts.
domain assumption Voids are isolated, spherically symmetric, with uniform bang time tB=0 and mass profile Eq. (12) initialized at zi=150.
Sec. II D. Real voids are aspherical and interact with their environment; this simple profile is used to generate the lensing templates.
domain assumption Linearized weak lensing with convergence κ=Σ/ΣC and shear γ=(Σ̄-Σ)/ΣC applies, and Doppler magnification is neglected.
Sec. II F. The small-deflection Born approximation and the neglect of source-observer velocity effects are assumed; the authors flag this as a simplification.
domain assumption The HSW profile, Eq. (18), is a universal description of cosmic void density profiles.
Sec. II G. The empirical form from N-body simulations is used to calibrate the model and generate mock voids.

invented entities (1)

Massive daughter dark matter fluid with injection velocity V^a relative to the mother fluid independent evidence
purpose: Produces the 'flooding' of voids that makes density profiles shallower and suppresses weak-lensing convergence and shear.
Postulated as the decay product in a two-body DDM scenario. The paper provides a falsifiable handle through the predicted lensing deficit at roughly 2% precision, though no concrete particle model is specified.

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Cite this review

Pith. "Pith review of Constraining decaying dark matter models with gravitational lensing and cosmic voids." pith.science (2026). https://pith.science/paper/CNK2KLU7

@misc{pith2026250708275,
  author       = {Pith},
  title        = {Pith review of: Constraining decaying dark matter models with gravitational lensing and cosmic voids},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/CNK2KLU7}},
  note         = {Machine review of arXiv:2507.08275}
}

read the original abstract

Despite overwhelming observational evidence for dark matter, we still have no evidence of direct detection. Consequently, our knowledge about dark matter is limited, for example, we do not know if dark matter is a stable particle or if it decays. Without a theoretical particle model, the parameter space of possible decay models is highly variable, and astrophysical or cosmological means of indirectly constraining the phenomenological models are required. This paper investigates a scenario in which a dark matter decays and the dark daughter particle moves with respect to the comoving mother particle. The model is parameterised by the decay rate and the injection velocity of the dark matter particles, which can be converted to the mass ratio. In previous work, a simpler model was used to investigate the evolution of cosmic voids typified as regions with low content of galaxies and non-baryonic matter. It was found that the growth of S-type voids is modified by the dark matter decay, leading to imprints at the present day. Here we extend our study and improve the method used to model the decay. We also study the gravitational weak-lensing signal that will be able to detect or constrain the parameter space of decaying dark matter. The results of this study suggest that future weak lensing surveys may provide unique probes of the phenomological parameters of dark matter.

Figures

Figures reproduced from arXiv: 2507.08275 by the authors.

**Figure 2.** FIG. 2: The void size function with the 68 % and 95 % bands for three cases of increasing injection velocity, [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗

**Figure 3.** FIG. 3: Weak lensing convergence (upper panels) and shear (lower panels) of a void located at [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗

Figures from the paper (5 more)

**Figure 4.** Figure 4: FIG. 4: The distribution of values of maximal amplitude of weak lensing convergence and maximum value of weak [PITH_FULL_IMAGE:figures/full_fig_p007_4.png]

**Figure 5.** Figure 5: FIG. 5: The distribution of values of maximal amplitude of weak lensing convergence and maximum value of weak [PITH_FULL_IMAGE:figures/full_fig_p008_5.png]

**Figure 6.** Figure 6: FIG. 6: The distribution of values of maximal amplitude of weak lensing convergence and maximum value of weak [PITH_FULL_IMAGE:figures/full_fig_p009_6.png]

**Figure 7.** Figure 7: FIG. 7: The distribution of values of maximal amplitude of weak lensing convergence and maximum value of weak [PITH_FULL_IMAGE:figures/full_fig_p010_7.png]

**Figure 8.** Figure 8: FIG. 8: The distribution of values of maximal amplitude of weak lensing convergence and maximum value of weak [PITH_FULL_IMAGE:figures/full_fig_p010_8.png]

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Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

Why Cosmic Voids Matter: Pristine Evolution
astro-ph.CO 2025-09 conditional novelty 7.0 of 10

Cosmic voids traced by halos become stable at late times, and the matter around them evolves linearly, supporting their use as clean dark-energy probes.

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