{"id":"628185fd-2261-4016-9503-038a7cebbbac","arxiv_id":"2603.24331","paper_version":3,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":5.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":5,"one_line_summary":"Late-time dark-sector decay producing sub-0.1 GeV dark matter is ruled out by Lyman-alpha forest and BBN constraints.","lead":"This paper calculates how dark matter produced by the late decay of a heavy dark-sector particle would suppress small-scale structure, and compares that to Lyman-alpha forest observations. It finds that in this decay model, dark matter lighter than about 0.1 times the proton mass is excluded when existing bounds are combined, making small-scale cosmic structure a sharper test of non-thermal dark matter.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Two-moment WDM mapping validated only on a handful of benchmarks; the exclusion boundary mχ≈0.08 GeV lies outside the tested region.","rationale":"The reader's weakest assumption correctly identifies the two-moment WDM mapping as the load-bearing premise. The paper provides spot checks but not a systematic validation across the parameter region that determines the headline exclusion. The transfer-function fitting method in §4.2 is an independent cross-check, but it still assumes the shape of the non-thermal transfer function is well described by the thermal-WDM fitting formula with fixed μ=1.12; this itself is only validated on the same small set of benchmarks. The concern is not internal inconsistency but a generalization gap: the paper claims broad 2% validity without showing the supporting calculations, and the exclusion boundary lies near mχ=0.08 GeV, which is not among the displayed validation points. This warrants a conditional acceptance: the physical argument is coherent, but the central constraint should be confirmed by publishing or performing the broader validation. No fatal flaw was found; the manuscript's own text flags the missing support in §3.2. The verdict should remain CONDITIONAL as the reader stated, hence UNCHANGED.","tokens_in":18204,"tokens_out":4719,"duration_ms":48318,"concrete_test":"Evaluate the boundary point mχ = 0.08 GeV, mϕ = 1000 GeV, mN = 1 GeV, and the yDS value that saturates the meff = 5.7 keV contour (approximately yDS = 2×10^-12). Solve the full Boltzmann equations (2.15)–(2.16) without the zero-momentum approximation, feed the resulting phase-space distribution into CLASS, and compute the transfer function. Then (i) fit T(k) with both α and μ free, and check whether μ deviates from 1.12 by more than 5%; (ii) extract α and compare the half-mode wavenumber to that of the equivalent thermal WDM obtained from eq. (3.3). If the half-mode scale differs by more than 2%, the mapping is not uniformly valid and the claimed exclusion changes. Repeat at the analogous boundaries for mϕ = 100 and 10 GeV.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The paper's central exclusion mχ≲0.08 GeV rests on the equivalence mapping in §3.1: the non-thermal χ distribution is replaced by a thermal WDM distribution matched through number density and mean squared comoving momentum (eqs. 3.2–3.3), and the resulting meff is compared to published Lyα bounds. This two-moment matching is reasonable only if the full phase-space shape—especially the high-momentum tail—affects the free-streaming cutoff in the same way as a Fermi-Dirac distribution. The paper's own validation is limited to five benchmark points: mχ = 0.01, 1, 10 GeV (Table 1) and mχ = 0.62, 1.33 GeV (Table 2), all with mϕ = 1000 GeV, yDS = 10^-12, mN = 1 GeV. The key exclusion contour at mχ ≈ 0.08 GeV is not among these benchmarks. The text asserts that analogous calculations across a broader parameter space remain within 2% relative error, but the calculation is not exhibited. If the mapping error grows at smaller mχ (where the distribution shifts to larger q/mχ) or for different mϕ or mN/mϕ ratios, the meff boundary could shift enough to move the 0.08 GeV exclusion. The claimed 2% agreement in α is not a guarantee of 2% agreement in the exclusion contour, because α and meff are nonlinearly related and the shape parameter μ is fixed at 1.12 in the fitting.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper studies a non-thermal dark matter model in which the DM particle χ is produced by the late decay of a frozen-out dark scalar ϕ → N χ. The authors solve the Boltzmann equations for the phase-space distribution of χ, including a zero-momentum approximation for the decaying parent, and derive the resulting linear matter power spectrum. They then map the non-thermal χ distribution to an equivalent thermal WDM distribution by matching number density and mean squared comoving momentum (Eqs. 3.2–3.3), obtaining an effective WDM mass m_eff. This m_eff is compared to recent Lyman-α forest lower bounds on thermal WDM mass, and the results are combined with BBN lifetime limits. The main claim is that for the decay production scenario, DM masses m_χ ≲ 0.08 GeV are excluded, with even conservative limits excluding m_χ ≲ 0.01 GeV.","tokens_in":18561,"tokens_out":17453,"duration_ms":187059,"significance":"If the main result holds, the paper provides a strong and phenomenologically useful constraint on a well-motivated class of non-thermal dark matter models, showing that small-scale structure probes are complementary to BBN and can exclude sub-GeV DM from dark-sector decay. The paper has notable strengths: the Boltzmann collision terms are derived carefully, the comoving number conservation is checked explicitly, and the mapping to thermal WDM is cross-validated against CLASS transfer functions at several benchmark points. The two independent routes to the effective mass—velocity-dispersion matching and transfer-function fitting—agree at the displayed benchmarks, which is a good internal consistency check. The analysis is not circular: the Lyman-α and BBN limits are external observables. The main weakness is that the mapping is explicitly validated only for a handful of benchmark points, while the headline exclusion boundary lies outside those points; the asserted 2% accuracy across the parameter space is not exhibited.","major_comments":[{"comment":"The central claim rests on the equivalence mapping between the non-thermal χ distribution and a thermal WDM distribution. The CLASS validations are limited to m_ϕ = 1000 GeV, y_DS = 10^-12, m_N = 1 GeV, with m_χ = 0.01, 1, 10 GeV (Table 1) and m_χ = 0.62, 1.33 GeV (Table 2). The headline exclusion m_χ ≲ 0.08 GeV (Figs. 7–9) is not tested, and the text's statement that 'analogous calculations across a broader parameter space' remain within 2% is not supported by any displayed calculation. Since the boundary is precisely where the mapping error matters, please provide explicit α_χ vs α_WDM comparisons for points on the m_eff = 5.7 keV and 3.2 keV exclusion curves, including different m_ϕ and y_DS, or a dense scan of the relative error. Without this, the 0.08 GeV bound is an extrapolation.","section":"§3.2, Tables 1–2"},{"comment":"The abstract states unconditionally that 'masses lighter than ~10^-1 GeV are excluded', but §5 correctly qualifies this as applying to the decay production scenario. The model also has a freeze-in production component, which becomes non-negligible for y_DS ≳ 2×10^-12 and is colder than the decay component. For larger y_DS the Lyα constraint is therefore weaker, and the full model may admit lighter m_χ. The abstract and conclusions should carry the y_DS ≲ 2×10^-12 qualification so that the headline does not overstate the scope of the bound.","section":"Abstract and §5"},{"comment":"The BBN constraints are imposed as upper limits on the ϕ lifetime (τ ≤ 0.7 s or 0.07 s), but the decay chain is ϕ → N χ, and the energy that affects BBN is injected when N decays to SM particles through the seesaw Yukawa, not necessarily at the time of ϕ decay. The paper does not specify the N lifetime or the relevant Yukawa couplings, nor does it justify that the adopted τ limits are conservative with respect to the additional delay. Since the combined exclusion around m_χ ≈ 0.08 GeV uses these BBN lines, please clarify that the bounds are correctly applied or cite the analysis in Ref. [8] where this is established.","section":"§4, BBN limits"}],"minor_comments":[{"comment":"The kinematic integration limits p_ϕ± are not written explicitly in the main text. Please state them in §2 or refer to Appendix A at first use, as the reader currently has to reconstruct them from the appendix.","section":"Eq. (2.12)"},{"comment":"The quantity ⟨v²⟩ is called the comoving pseudo-velocity dispersion but is defined as ⟨q²⟩_χ/m_χ². It would help to state explicitly that the physical velocity dispersion at scale factor a is a^{-2}⟨q²⟩_χ/m_χ² and that this is why comoving matching is sufficient.","section":"§3.1 / Appendix B.2"},{"comment":"The fitting exponent µ = 1.12 is used without explanation. Please note that this is the standard value for a fermionic thermal relic and cite the original determination, as this matters for the interpretation of α and m_eff.","section":"§3.2, Eq. (3.5)"},{"comment":"Table 3 lists several observational limits (Milky Way satellite counts, stellar streams) that are not used in the analysis. It would improve clarity to state explicitly in the text that only the Lyman-α and UV luminosity function limits are used in the figures.","section":"Table 3"},{"comment":"Figure 4 includes y_DS = 10^-11, which is outside the decay-production regime as defined in the paper. The caption notes this, but the main text could repeat it to avoid readers interpreting this benchmark as one that can be constrained by the presented BBN/Lyα bounds.","section":"§3, Fig. 4"}],"recommendation":"major_revision","confidential_remarks":"This is a solid constraint study with careful derivations and sensible internal consistency checks. The main issue is that the headline exclusion boundary m_χ ≈ 0.08 GeV is not covered by the displayed CLASS validation of the equivalence mapping; the 'within 2% across broader parameter space' claim needs to be substantiated with explicit calculations at the boundary. I also think the abstract overstates the applicability of the bound by omitting the decay-production condition. If the authors add the requested validation and qualify the abstract, I would be willing to support acceptance."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Quick take: this is a competent and mostly convincing application of the established thermal-WDM mapping to the Cheng-Liao dark-sector decay model. The new result—a combined Ly-alpha + BBN bound that excludes m_chi <~ 0.08 GeV in much of the decay-production parameter space—is plausible and worth taking seriously. The paper does a good job on the basics: the Boltzmann collision terms are derived cleanly, the comoving number conservation check is a nice sign of care, and the two mapping routes (velocity dispersion vs. transfer-function fitting) agree to ~2% at the benchmarks shown. The m_chi = 0.01 GeV benchmark is actually a more extreme case than the 0.08 GeV boundary, so the mapping does not obviously fail where it matters most.\n\nThe soft spots are real but not fatal. The validation of the equivalence mapping is shown for only five benchmark points, all with m_phi = 1000 GeV and yDS = 1e-12. The text claims the 2% accuracy holds 'across a broader parameter space' without exhibiting that calculation. Since the exclusion contours in Figs. 7-12 are computed with the velocity-dispersion method across a grid of m_phi, m_chi, m_N, yDS, the reader cannot independently verify the mapping's accuracy near the actual boundary. The stress-test concern is pointed, but the m_chi = 0.01 GeV point gives me some confidence. Still, the authors should be asked to show the error map or release the code. No data or code is provided, which is a legitimate complaint for a numerical constraints paper.\n\nI also think the abstract's '~10^-1 GeV' is an over-compression—the actual bound depends on yDS and m_phi (e.g., m_phi = 10 GeV allows down to ~0.07 GeV, while m_phi = 1000 GeV with yDS ~ 2e-12 pushes to ~0.1 GeV). That's a presentation issue, not an error.\n\nNo circular reasoning: the Ly-alpha and BBN limits are external, and the mapping is checked against CLASS.\n\nThis paper is for people who want the current status of this specific model and a template for applying WDM bounds to late-decay DM. With a modest revision adding validation coverage and code release, it would be a solid JCAP paper. Send to a good referee—the phenomenological claim is sharp and the calculation deserves scrutiny. I'd cite it if I work in this area.","headline":"Careful, useful constraint on a dark-sector decay model; the thermal-WDM mapping is credible, but the paper should show validation across its actual parameter grid.","tokens_in":19074,"tokens_out":4534,"would_cite":true,"duration_ms":45781,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":["83F05","85A40"],"pacs":["95.35.+d","98.80.-k"],"model":"deepseek-v4-flash","headline":"Dark matter produced by late dark-sector decay must be heavier than about 0.1 GeV; combining Lyman-alpha forest and Big Bang nucleosynthesis bounds rules out lighter candidates.","keywords":["dark matter","Lyman-alpha forest","warm dark matter","non-thermal dark matter","dark sector decay","sub-GeV dark matter","Big Bang nucleosynthesis","matter power spectrum"],"falsifier":"Compute the exact linear matter power spectrum for the full non-thermal distribution at parameter points just inside and outside the exclusion boundary—for example mχ = 0.08 GeV, m_φ = 1000 GeV, m_N = 1 GeV, y_DS near 2×10^-12—and compare the half-mode scale (or the full T(k)) with the equivalent-WDM prediction. If the two disagree by more than the quoted ~2%, the exclusion boundary would shift and the central claim would need revision.","tokens_in":18078,"feed_emoji":"🌌","tokens_out":4920,"duration_ms":46729,"temperature":0.7,"pith_summary":"This paper argues that a specific non-thermal dark matter production mechanism—dark matter generated by the late-time decay of a heavier dark-sector particle—is almost fully closed off for sub-GeV candidates. By computing the momentum distribution of the decay-produced particles and mapping it to an equivalent thermal warm dark matter model, the authors translate existing Lyman-alpha forest limits into a direct constraint on the dark matter mass. Combined with Big Bang nucleosynthesis bounds on the parent particle's lifetime, they conclude that dark matter below roughly 0.1 GeV is excluded, and that even 0.01 GeV is ruled out under conservative assumptions. A reader should care because non-thermal production is a common way to evade WIMP search limits, and this paper shows small-scale structure can test it.","feed_headline":"Sub-GeV dark matter excluded by Lyman-alpha forest and BBN","feed_subtitle":"Lyman-alpha forest plus Big Bang nucleosynthesis closes the window on late-decay sub-GeV dark matter.","key_machinery":"The equivalent thermal warm dark matter (WDM) approximation is the load-bearing tool. The non-thermal decay distribution F(q) is replaced by a Fermi-Dirac distribution with the same comoving number density and the same mean squared comoving momentum; solving the two matching equations yields an effective temperature T_eff and effective mass m_eff. Because the Lyman-alpha forest has published lower bounds on thermal WDM mass, m_eff can be tested directly. A second, independent route fits the numerical transfer function to the standard WDM fitting form and inverts the mass–break-scale relation, giving consistent boundaries.","core_discovery":"The paper's central claim is that in the dark sector decay model, where a WIMP-like scalar φ freezes out and then decays through a right-handed neutrino into the dark matter particle χ, the resulting non-thermal χ particles are too hot to be the dominant dark matter if they are light. Using Boltzmann equations to evolve the phase-space distribution through the decay, the authors find that the distribution is single-peaked and can be matched to a thermal warm dark matter distribution by equating comoving number density and mean squared comoving momentum. The effective warm dark matter mass obtained this way is compared against the latest Lyman-alpha forest bound; the fiducial 5.7 keV limit ex","pith_inferences":["The same two-moment mapping could be applied to other late-decay production models (for instance, gravitino or axino superWIMPs), provided their distributions stay single-peaked; the paper's benchmark checks do not cover all those cases.","Because the paper fixes χ to account for all dark matter, a subdominant χ component would evade the mass bound; the exclusion should be viewed as applying to the dominant-DM interpretation.","Tighter future Lyman-alpha bounds (or 21-cm observations of the epoch of reionization) would push the lower mass limit upward approximately as m_eff ∝ ⟨v²⟩^{-3/8}, so the threshold scales slowly and substantial improvement requires significantly stronger limits.","A full test of the mapping near the boundary using a non-linear or N-body method, rather than the linear transfer function, would strengthen the claim; the five benchmark points do not exhaust parameter space."],"forward_implications":["Dark matter from this decay scenario cannot be the dominant component below ~0.1 GeV: the strongest Lyman-alpha bound excludes mχ ≲ 0.08 GeV, and even the weakest excludes mχ ≲ 0.01 GeV.","The joint Lyman-alpha plus BBN constraints require the decay coupling y_DS to be at least about 10^-12 for sub-GeV dark matter, because the parent must decay early enough to redshift the hot daughters.","Lyman-alpha data place an upper limit on the parent mass m_φ; for example, for mχ = 0.1 GeV the ceiling drops to about 500 GeV, and for mχ = 0.01 GeV the allowed window closes.","Highly degenerate parent–neutrino spectra (m_N/m_φ close to 1) are excluded by BBN for m_φ = 1000, 100, and 10 GeV once the ratio exceeds thresholds of 0.945, 0.810, and 0.001, respectively.","The mapping method is generic: any single-peaked non-thermal DM distribution can be translated into an effective WDM mass and constrained by the same published Lyman-alpha limits."],"fun_headline_variants":["Lyman-alpha forest kills sub-0.1 GeV dark matter from decays","Lyman-alpha forest rules out hot sub-0.1 GeV dark matter from decays","Lyman-alpha + BBN exclude sub-0.1 GeV dark matter from late decays","Dark sector decay dark matter: masses under 0.1 GeV excluded by Lyman-alpha + BBN","Sub-0.1 GeV dark matter from decays is dead: Lyman-alpha + BBN prove it"],"cache_read_input_tokens":2304,"weakest_assumption_plain":"The load-bearing premise is that matching only the number density and mean squared comoving momentum of the non-thermal distribution to a thermal warm dark matter distribution reproduces the small-scale power suppression everywhere; this was spot-checked for only a handful of parameter points.","fun_headline_variants_meta":{"raw":{"variants":["Lyman-alpha forest kills sub-0.1 GeV dark matter from decays","Lyman-alpha forest rules out hot sub-0.1 GeV dark matter from decays","Lyman-alpha + BBN exclude sub-0.1 GeV dark matter from late decays","Dark sector decay dark matter: masses under 0.1 GeV excluded by Lyman-alpha + BBN","Sub-0.1 GeV dark matter from decays is dead: Lyman-alpha + BBN prove it"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.001412,"raw_usage":{"total_tokens":5517,"prompt_tokens":698,"completion_tokens":4819,"prompt_tokens_details":{"cached_tokens":256},"prompt_cache_hit_tokens":256,"prompt_cache_miss_tokens":442,"completion_tokens_details":{"reasoning_tokens":4701}},"tokens_in":442,"tokens_out":4819,"duration_ms":30784,"temperature":1.0,"reasoning_tokens":4701,"cache_read_input_tokens":256,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-02T17:29:47.593902+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Compute the exact linear matter power spectrum for the full non-thermal distribution at parameter points just inside and outside the exclusion boundary—for example mχ = 0.08 GeV, m_φ = 1000 GeV, m_N = 1 GeV, y_DS near 2×10^-12—and compare the half-mode scale (or the full T(k)) with the equivalent-WDM prediction. If the two disagree by more than the quoted ~2%, the exclusion boundary would shift and the central claim would need revision.","supporting_citations":[],"review_version":1}