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Astrophysics · arXiv:astro-ph/0403164 v2 · submitted 6 Mar 2004 · 19 references

WMAP Constraints on Decaying Cold Dark Matter

Kiyotomo Ichiki, Masamune Oguri, Keitaro Takahashi

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The paper says

“We re-formulate cosmological perturbations in the decaying cold dark matter model, and calculate cosmological microwave background (CMB) anisotropies.”

more of the abstract

By comparing our theoretical predictions with recent observational data from the Wilkinson Microwave Anisotropy Probe(WMAP), we derive a new bound on the abundance and lifetime of decaying dark matter particles. We show that the data of WMAP alone do not prefer the decaying cold dark matter model: the lifetime is constrained to \Gamma^-1> 123 Gyr at 68% C.L. (52 Gyr at 95.4% C.L.) when cold dark matter consists only of such decaying particles. We also consider a more general case in which cold dark matter consists of both stable and decaying particles, and show that the constraint generalizes down to \Omega_DDMh^2 < -0.5 (Gamma^-1/1 Gyr)^-1+0.12 for \Gamma^-1 > 5 Gyr at 95.4% C.L.. These bounds are robust and widely applicable, because they are derived only from gravitational effects and therefore do not rely on the details of decay channels or decay products.

from the abstract

Pith says

Machine review · deepseek-v4.1-flash · 13 Nov 2026 · what was read was not recorded · not checked by a person

Reviewed in 2026 with later literature in view.

It can be wrong. Challenge this review or reply to it.

Holds up, with conditions. A careful, modest paper with a genuinely quotable channel-independent lifetime bound; the perturbation treatment holds up, and the flatness caveat is the one worth pressing. This line is wrong

3 major objections · 9 minor

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Not checked: figures, code, what the 19 references say.

The paper says, at Introduction, 'Throughout this paper we concentrate our attention on a flat universe'; Fig. 1 discussion

The review did not quote this passage.

Pith says: Objection 1 of 3 · major

The bound is computed under an assumed flat universe. This is load-bearing because the decay signature includes a shift of the acoustic peaks toward larger angular scales, which is also how spatial curvature shifts the peaks. With Ω_k free, part of the decay signal could be absorbed by curvature, and the quoted Γ^{-1} limit would weaken.

more of objection 1

The paper does not quantify this degeneracy. A run with Ω_k free, or at least a quantitative estimate of the curvature degeneracy, would strengthen the central claim.

The paper says, at Eqs. (9)-(10) and the discussion following Eq. (13)

The review did not quote this passage.

Pith says: Objection 2 of 3 · major

The source term for the daughter radiation is computed in a fluid approximation, replacing the full q-integral in Eq. (13) with the DDM density and velocity perturbations. The paper states that this is 'complicated to compute in general' but does not validate the approximation. Since the source term controls the decay signature, a comparison with the full integral, or an argument that the dipole contribution is suppressed by v/c, would strengthen the bound.

The paper says, at Eqs. (13)-(14)

The review did not quote this passage.

Pith says: Objection 3 of 3 · major

The concern that the l≥2 truncation of the decay source is an uncontrolled approximation does not land on reading the paper: the source term in Eq. (13) is proportional to f_DDM0 Ψ_DDM, which has only l=0 and l=1 moments, so the l≥2 source vanishes identically; the extra term in Eq. (14) is a background-evolution damping, not a source. However, the paper does not show a convergence test in l_max, which would be a useful validation.

9 minor objections

The paper says, at Discussion of Fig. 2

Pith says: minor objection 1 of 9

Typo: 'dose' should be 'does' in 'the parameter of the DCDM model, Γ, dose not degenerate'.

The paper says, at Abstract vs. text

Pith says: minor objection 2 of 9

The abstract uses 'Γ^{-1} > 123 Gyr' while the text uses 'Γ^{-1} ≥ 123 Gyr'. The inequality should be consistent.

show 7 more

The paper says, at Fig. 1 caption

Pith says: minor objection 3 of 9

The DCDM curves are computed with all other parameters fixed to WMAP optimal values. The caption should clarify that these are not best-fit DCDM models.

The paper says, at Discussion of Fig. 3

Pith says: minor objection 4 of 9

No Δχ^2 or likelihood ratio is reported for the DCDM model vs ΛCDM. A quantitative comparison would support the statement that 'we do not find any signal to prefer the DCDM model'.

The paper says, at Ref. [3]

Pith says: minor objection 5 of 9

The self-citation to 'Mon. Not. R. Astr. Soc., in press (astro-ph/0312358)' should be updated with the final reference.

The paper says, at Discussion of future experiments

Pith says: minor objection 6 of 9

The claim that 'bounds on DCDM would not be improved so much by future experiments since DCDM affects CMB fluctuation only in rather large scales (see Fig. 1)' is inconsistent with Fig. 1, which shows differences at l ~ 200-1000 (peak positions and amplitudes), not just at low l. Future experiments would improve the measurement of these scales.

The paper says, at Eq. (12)

Pith says: minor objection 7 of 9

The collision term assumes a smooth injection spectrum proportional to f_DDM0/q, whereas a 2-body decay of a non-relativistic particle gives a delta-function injection at q = m_DDM/2. The paper should justify this choice or show that the bound is insensitive to the injection spectrum.

The paper says, at Eq. (3)

Pith says: minor objection 8 of 9

The paper should clarify the units of Γ and H in Eq. (3), since Γ is in physical time and H is the conformal Hubble parameter.

The paper says, at Conclusion

Pith says: minor objection 9 of 9

The claim that these are 'the tightest constraints on DCDM cosmology from CMB anisotropies' should be supported by comparison with other CMB constraints on DCDM.

What would settle it

Re-run the MCMC for the single-component DCDM case with the daughter-radiation hierarchy truncated at l_max = 2, 3, and 6 (instead of the fluid l=1 closure), holding all other settings fixed. If the marginalized 95.4% lower limit on Gamma^{-1} moves by less than ~10% between l_max=2 and l_max=6, the fluid truncation is validated and the concern does not land; if it moves by more, the quoted 52 Gyr bound is sensitive to an unvalidated approximation and should be quoted with that systematic attached.

from the skeptic's reading

How the review went

4 readings by deepseek-v4.1-flash · 13 Nov 2026

  1. Reader holds up, with conditions confidence moderate
  2. Skeptic partly agrees 30 min 20 s · 26,783 tokens read, 99,302 written
  3. Editor wrote the verdict above 45 s · 9,970 tokens read, 2,541 written
  4. Referee minor revision: 3 major objections, 9 minor 6 min 10 s · 9,188 tokens read, 20,153 written

Not run on this paper: the simulated authors' defence.

Pith did not check this review's objections against the paper.

The review in full

The review in brief, machine-written

Bottom line: this is a careful, modest paper that produces a quotable, channel-independent lifetime bound from WMAP1, and the perturbation derivation holds up. The one caveat worth pressing is flatness, which the authors state up front rather than hide. What is new here is real but bounded: they write down the background and perturbation equations for a decaying CDM component plus relativistic daughter (Eqs. 1–14), implement them in CAMB, and run a seven-parameter MCMC against WMAP1. The prior decaying-neutrino work (Kaplinghat et al.; Bharadwaj–Sethi) is cited, and the difference is genuine: CDM decay with both abundance and lifetime free. The result — Γ⁻¹ > 123 Gyr at 68%, > 52 Gyr at 95.4%, plus the two-component fit — is a real limit, and they are honest that WMAP shows no preference for decay. On the stress-test note: I do not think the l=1 truncation concern lands. The decay source term in Eq. (13) feeds only the monopole and dipole because the DDM perturbation has only those moments; that is exact for a CDM fluid, not an approximation. For l≥2 the paper keeps the full standard hierarchy (Eq. 14) with the extra damping term aΓ(ρ_DDM/ρ_DR)Ml, which follows from the first right-hand term of Eq. (13) and multiplies every moment. So the daughter radiation is not truncated at l=1; only the source is, and correctly. A convergence test in l_max would be nice, but I do not see a correctness risk there. The flatness caveat is the real one. The decay signature includes a peak shift toward larger scales, which is also how Ωk shifts the peaks; with curvature free, part of the signal could be absorbed and the bound would weaken. The authors say they assume flatness, so it is acknowledged, not concealed — but they do not quantify the degeneracy, and that is the number I would want. Smaller things: the modified CAMB and chains are not released, so reproducing the exact numbers means reimplementation; the claim that future experiments will not improve much rests on a cosmic-variance argument that is plausible but asserted rather than shown; and the two-component bound is a fitting formula, not derived. Who should read it: anyone quoting a dark matter lifetime limit from the CMB, or working on non-standard dark sectors. It deserves a referee.

The strongest objection

The paper's central claim is a one-sided lifetime bound from WMAP (abstract:s2, s3) plus the two-component generalization (abstract:s4). For this to hold, the modified CAMB must correctly capture how decay reshapes the CMB. The authors themselves identify three channels: peak shift to smaller l, reduced first-peak amplitude, and enhanced late ISW (Fig. 1 discussion). The third channel is the one that most directly drives the low-l constraint, and it is precisely where the treatment is weakest. In Eq. (13) the collision term is kept only through the l=0 and l=1 moments; for l>=2 the source is dropped, giving Eq. (14), a standard hierarchy with an extra damping term a*Gamma*(rho_DDM/rho_DR). The justification offered is that the DDM perturbation has only monopole and dipole. That is true for the source, but the daughter radiation's own higher moments are not sourced only by the decay term: they are sourced by the standard gravitational coupling to the l-1 and l+1 moments, and the decay damping term multiplies M_l itself. The claim that truncating the decay source at l=1 is adequate is therefore an approximation about the relative size of the decay-induced versus gravitational-induced M_2, not a consequence of the DDM having only l=0,1. The paper does not show a convergence test in l_max or a comparison against a full Boltzmann treatment of the daughter species. Since the bound is one-sided and driven by the same low-l region that the ISW enhancement populates, an error in the l>=2 daughter moments could shift the 95.4% limit. This is a correctness-risk concern, not a circularity or soundness one: the data are external and the derivation is otherwise careful.

The reader's verdict (CONDITIONAL, moderate confidence, medium correctness risk) is broadly right, and I would not move it. I agree with the reader that the derivation is internally consistent: Eq. (6) does reduce to the standard Euler equation, Eq. (14) is a recognizable hierarchy with a decay damping term, and the data are external so there is no circularity. I also agree that the flatness assumption is a genuine caveat, and the paper states it explicitly ('Throughout this paper we concentrate our attention on a flat universe'), so it is an acknowledged limitation rather than a hidden one. Where I differ is on which assumption is most load-bearing. The reader picks Omega_k = 0 because curvature and the decay peak-shift are partly degenerate. That is a fair point, but the paper's own Fig. 1 narrative says the low-l constraint is driven substantially by the late ISW enhancement, and the ISW is a large-scale effect that curvature also affects. So the flatness caveat and the daughter-fluid truncation are not independent: both bear on the same low-l part of the spectrum. The truncation concern is the more technical and the more checkable of the two, and it is not acknowledged anywhere in the text. The paper's claim that future experiments will not improve the bound ('errors in these scales are already limited by cosmic variance') is also asserted rather than demonstrated, but that is a forward-looking remark, not part of the central numerical claim, so I do not weight it heavily. On balance the central claim is plausible and the derivation is careful; the honest position is that the bound stands as quoted subject to two unquantified systematics (flatness and the l>=2 daughter closure), which is exactly what CONDITIONAL captures. I therefore recommend UNCHANGED and mark partial agreement with the reader, since we identify the same class of weakness but rank the specific assumptions differently.

The referee's report

If correct, these are useful, channel-independent constraints on dark matter lifetime from CMB alone. The perturbation formulation (Eqs. 5-14) is a genuine contribution, and the MCMC analysis is standard. The paper is a solid, if modest, contribution. The main caveats are the flatness assumption and the fluid approximation for the source term.

Pith's reading of the paper (a machine's summary, not the authors')

The paper asks a simple question with a hard answer: if the cold dark matter that fills the universe is slowly decaying into relativistic particles, how long must it live before the cosmic microwave background would look wrong? To answer it the authors write down, from scratch, the perturbation equations for a decaying dark matter fluid plus the radiation it produces, patch them into a standard Boltzmann code, and run a Markov-chain fit against the first-year WMAP temperature data. The data show no preference for decay, so the result is a one-sided bound rather than a detection: $

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The paper

Abstract

We re-formulate cosmological perturbations in the decaying cold dark matter model, and calculate cosmological microwave background (CMB) anisotropies. By comparing our theoretical predictions with recent observational data from the Wilkinson Microwave Anisotropy Probe(WMAP), we derive a new bound on the abundance and lifetime of decaying dark matter particles. We show that the data of WMAP alone do not prefer the decaying cold dark matter model: the lifetime is constrained to \Gamma^-1> 123 Gyr at 68% C.L. (52 Gyr at 95.4% C.L.) when cold dark matter consists only of such decaying particles. We also consider a more general case in which cold dark matter consists of both stable and decaying particles, and show that the constraint generalizes down to \Omega_DDMh^2 < -0.5 (Gamma^-1/1 Gyr)^-1+0.12 for \Gamma^-1 > 5 Gyr at 95.4% C.L.. These bounds are robust and widely applicable, because they are derived only from gravitational effects and therefore do not rely on the details of decay channels or decay products.

The paper's own sentences, arranged, kept beside the review and separate from it. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. No sentence in this record was written by a model.

abstract compiled · 2026-09-23

The authors' main claim, as the classifier picked it out 0.89

“We show that the data of WMAP alone do not prefer the decaying cold dark matter model: the lifetime is constrained to \Gamma^{-1}> 123 Gyr at 68% C.L.”

How the main claim is stated: asserted 1.00

What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.72 · human participants 0.01 · controlled comparison 0.10 · randomized assignment 0.01 · states quantitative result 0.99 · compares with prior results 0.28 · mentions code or data availability 0.02

The abstract, sentence by sentence

This table labels the abstract only (arXiv listing abstract v2). The number is the probability the classifier gave the label.

SentenceRoleThe authors' own workStates the main conclusionStrength
We re-formulate cosmological perturbations in the decaying cold dark matter model, and calculate cosmological microwave background (CMB) anisotropies. method 0.55 0.95 0.03 asserted 0.96
By comparing our theoretical predictions with recent observational data from the Wilkinson Microwave Anisotropy Probe(WMAP), we derive a new bound on the abundance and lifetime of decaying dark matter particles. method 0.59 0.96 0.15 asserted 1.00
We show that the data of WMAP alone do not prefer the decaying cold dark matter model: the lifetime is constrained to \Gamma^{-1}> 123 Gyr at 68% C.L. result 0.98 0.95 0.65 asserted 1.00
(52 Gyr at 95.4% C.L.) when cold dark matter consists only of such decaying particles. result 1.00 0.85 0.20 asserted 0.87
We also consider a more general case in which cold dark matter consists of both stable and decaying particles, and show that the constraint generalizes down to \Omega_{DDM}h^2 < -0.5 (Gamma^{-1}/1 Gyr)^{-1}+0.12 for \Gamma^{-1} > 5 Gyr at 95.4% C.L.. result 0.96 0.95 0.20 asserted 1.00
These bounds are robust and widely applicable, because they are derived only from gravitational effects and therefore do not rely on the details of decay channels or decay products. interpretation 1.00 0.83 0.11 asserted 1.00

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from analysis of existing data 1.00

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How the labels were made

Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 5,161 input tokens.

Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. This record as JSON

Figures (4)
Figure 1 of the paper
Figure 1. FIG. 1: CMB angular power spectrum with and without
Figure 3 of the paper
Figure 3. FIG. 3: Marginalized probability distribution of the decay
Figure 4 of the paper
Figure 4. FIG. 4: The same as Fig.2, but for cosmology in which dark

Showing 3 of the paper's 4 figures. Figures are the authors', reproduced from the paper.

References (19)
  1. [1] J. P. Ostriker and P. Steinhardt, Science, 300, 1909 (2003) on Pith
  2. [2] R. Cen, Astrophys. J., 546, L77 (2001) on Pith
  3. [3] M. Oguri, K. Takahashi, H. Ohno, and K. Kotake, As- trophys. J., 597, 645 (2003); K. Ichiki, P. M. Gar- navich, T. Kajino, G. J. Mathews, and M. Yahiro, Phys. Rev. D68, 083518, (2003); K. Takahashi, M. Oguri, and K. Ichiki, Mon. Not. R. Astr. Soc., in press (astro-ph/0312358) on PithPith's reviewarXiv
  4. [4] as shown in Figs. 2 and 3. However, as the fraction of decaying components becomes smaller, constraints on Γ−1 becomes weaker. We find that the lifetime of unsta- ble CDM particle is roughly constrained to ΩDDMh2<∼ −0.5 ( Γ−11Gyr )−1 + 0.12 for Γ −1 ≥ 5Gyr ΩDDMh2<∼ −0.03 ( Γ−11... on Pith
  5. [5] V. A. Kuzmin and I. I. Tkachev, JETP Lett., 68, 271 (1998) on Pith
  6. [6] S. Kasuya, M. Kawasaki, and N. Sugiyama, Phys. Rev. D69, 023512 (2004); S. H. Hansen and Z. Haiman, Astro- phys. J., 600, 26 (2004); E. Pierpaoli, Phys. Rev. Lett., 92, 031301 (2004) on Pith
  7. [7] D. J. H. Chung, E. W. Kolb, and A. Riotto, Phys. Rev. Lett., 81, 4048 (1998); K. Benakli, J. Ellis, and D. V. Nanopoulos, Phys. Rev. D59, 047301 (1999); H. B. Kim and J. E. Kim, Phys. Lett. B, 527, 18 (2002) on Pith
  8. [8] A. D. Dolgov and Y. B. Zeldovich, Rev. Mod. Phys., 53, 1 (1981) on Pith
  9. [9] H. Ziaeepour, Astropart. Phys., 16, 101 (2001) on Pith
  10. [10] D. N. Spergel et al. , Astrophys. J. Suppl., 148, 175 (2003); G. Hinshaw et al. , Astrophys. J. Suppl., 148, 135 (2003); A. Kogut et al. , Astrophys. J. Suppl., 148, 161 (2003) on Pith
  11. [11] M. Kaplinghat, R. E. Lopez, S. Dodelson, and R. J. Scherrer, Phys. Rev. D60, 123508 (1999) on Pith
  12. [12] S. Bharadwaj and S. K. Sethi, Astrophys. J. Suppl., 114, 37 (1998) on Pith
  13. [13] C. P. Ma and E. Bertschinger, Astrophys. J. 455, 7 (1995) on Pith
  14. [14] L. Verde et al. , Astrophys. J. Suppl., 148, 195 (2003) on Pith
  15. [15] A. Lewis, A. Challinor, and A. Lasenby, Astrophys. J., 538, 473 (2000) on Pith
  16. [16] U. Seljak and M. Zaldarriago, Astrophys. J., 469, 437 (1996) on Pith
  17. [17] W. Hu, D. Scott, N. Sugiyama, and M. White, Phys. Rev. D52, 5498 (1995) on Pith
  18. [18] A. Lewis and S. Bridle, Phys. Rev. D66, 103511 (2002) on Pith
  19. [19] R. Bean, A. Melchiorri and J. Silk, Phys. Rev. D 68, 083501 (2003); X. Chen and M. Kamionkowski, arXiv:astro-ph/0310473 on PithPith's reviewarXiv
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  1. Stochastic Gravitational Waves from Early Structure Formation astro-ph.CO · Dec 2023
  2. Super heavy thermal dark matter hep-ph · Jun 2019
  3. When, Why, and How CMB Compression Fails astro-ph.CO · Oct 2026
  4. The Direct Detection of Boosted Dark Matter at High Energies and PeV events at IceCube hep-ph · Jul 2014
  5. Constraining Very Heavy Dark Matter Using Diffuse Backgrounds of Neutrinos and Cascaded Gamma Rays hep-ph · Jun 2012
  6. Updated constraints on decaying cold dark matter astro-ph.CO · Nov 2020
  7. Fractional Dark Matter decay: cosmological imprints and observational constraints astro-ph.CO · Aug 2019
  8. Converting non-relativistic dark matter to radiation astro-ph.CO · Mar 2018
  9. Exploring Cosmic Origins with CORE: Cosmological Parameters astro-ph.CO · Nov 2016
  10. Decaying dark matter and the tension in $\sigma_8$ astro-ph.CO · May 2015
  11. Revisiting cosmological bounds on sterile neutrinos astro-ph.CO · Aug 2014
  12. Strongest model-independent bound on the lifetime of Dark Matter astro-ph.CO · Jul 2014
  13. CMB photons shedding light on dark matter astro-ph.CO · Sep 2012
  14. Model-independent cosmological constraints from the CMB astro-ph.CO · Mar 2010
  15. Cosmological Constraints on Decaying Dark Matter hep-ph · Dec 2008
  16. X-ray photons from late-decaying majoron dark matter astro-ph · May 2008
  17. Model-Independent Bound on the Dark Matter Lifetime astro-ph · Dec 2007
  18. Decaying warm dark matter and neutrino masses astro-ph · May 2007
  19. Do you smell something decaying? Updated linear constraints on decaying dark matter scenarios astro-ph.CO · May 2022
  20. Dark Matter Candidates - Axions, Neutralinos, Gravitinos, and Axinos hep-ph · Nov 2008
How the literature uses it

35 arXiv papers cite this in 51 sentences

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Papers citing it · 29 sentences without a confident label

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  • In such a way, we obtain general constrains on the DM annihilation cross section and on the DM lifetime, which are more stringent than previous ones [ref] .

    Testing Dark Matter with Neutrino Detectors · Introduction · 0.96

  • These results are already comparable to contemporary, model-independent constraints on unstable dark matter [ref] and do not require detailed calibration of nonlinear structure growth or ambitious priors on other cosmological parameters ($lnΔ_R^2$ in particular).

    Weak Gravitational Lensing as a Method to Constrain Unstable Dark Matter · Forecast Constraints on DDM Lifetimes · 1.00

  • In this letter we have obtained a general bound on the DM lifetime, which is several orders of magnitude more stringent than previous limits [ref] .

    Model-Independent Bound on the Dark Matter Lifetime · Conclusions · 1.00

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