{"id":"799116e0-132f-4cd1-9563-9138841bd941","arxiv_id":"2508.19109","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":4.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":2,"one_line_summary":"With DESI DR2 data, one interacting dark sector model with a time-dependent coupling shows a nonzero coupling at more than 95% CL, but Bayesian evidence still favors Lambda-CDM.","lead":"This paper tests whether the strength of a possible interaction between dark energy and dark matter changes over cosmic time, using Planck, DESI BAO, and three supernova datasets. In one of four model variants the data favor a nonzero, time-varying coupling at better than 95% confidence, though the simpler Lambda-CDM model remains preferred overall.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"IVS1a detection depends on unverified stability of the perturbed-fluid implementation for negative ξ0; a stability check or vacuum-perturbation comparison is required.","rationale":"The reader's weakest assumption correctly identifies the missing stability check as the load-bearing issue: the IVS1a detection is only as trustworthy as the perturbation equations coded into the modified CAMB, and the paper provides neither those equations nor a stability analysis. I agree that this is the right concern, which is why I do not move the reader's CONDITIONAL verdict. I mark agreement as partial rather than full because the paper explicitly states that DE is the cosmological constant (w=−1); in the standard CAMB treatment a vacuum component has no perturbations, in which case the Valiviita instability does not directly apply. The manuscript, however, never confirms that this is what the modified code does, and the unavailability of the code prevents an independent check. Thus the central claim is conditional on the perturbation implementation being the stable interacting-vacuum version. The Bayesian-evidence tension noted by the reader is real but not the deciding issue: a parameter-level credible interval can exclude zero even when a model with more parameters is disfavored by the evidence. The concrete test above would settle whether the stability concern actually lands, and if it does not, the CONDITIONAL verdict could be upgraded.","tokens_in":26759,"tokens_out":11921,"duration_ms":139946,"concrete_test":"Release the modified CAMB perturbation equations, or run this check: take the IVS1a MAP point (ξ0≈−0.146, ξ_a≈0.34) and integrate the linear perturbation equations from a=10^-8 to a=1 for k=10^-3, 10^-2, 10^-1 h/Mpc, monitoring δ_x and the Weyl potential. If any mode grows without bound, or if applying the Valiviita et al. stability criterion to Eqs. (6)–(9) with w_x=−1 flags an instability, rerun the CMB+DESI+PantheonPlus analysis with DE perturbations forced to zero (homogeneous vacuum). If the resulting ξ0 posterior no longer excludes zero at 95% CL, the headline claim is an artifact of the perturbation scheme.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The paper's only >95% claim is the IVS1a posterior with ξ0≈−0.15, ξa≈0.34 (Table II). This posterior is produced by MCMC calling a modified CAMB, but the paper never displays the perturbed conservation equations corresponding to Eqs. (6)–(7) with ξ(a) from Eqs. (9)/(11), nor does it apply a stability criterion. This is not a cosmetic omission: for Q=3ξ(a)Hρ_x with w_x=−1, the behavior of DE perturbations is not fixed by the background equations. If the code evolves δρ_x and θ_x with an effective sound speed, negative ξ0 can excite exponentially growing modes of the kind discussed in Valiviita et al. [11]; if DE is instead treated as a homogeneous vacuum (δρ_x=θ_x=0), the model is a standard interacting-vacuum model and the concern disappears. The manuscript cites [11] but never states which treatment is implemented, and the modified code is not released. If the preferred negative-ξ0 samples lie in an unstable branch, the likelihood—and therefore the claimed exclusion of ξ0=0—would be dominated by the perturbation implementation rather than by the CMB+DESI+SN data. The Bayesian evidence tension is secondary; the stability assumption is what the central claim actually rests on.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper constrains four interacting dark-energy (DE) / dark-matter (DM) models with time-dependent coupling ξ(a) using Planck 2018 CMB, DESI DR2 BAO, and three Type Ia supernova compilations (PantheonPlus, Union3, DESY5). The models combine two interaction functions, Q = 3ξ(a)Hρ_x (IVS1) and Q = 3ξ(a)H ρ_cρ_x/(ρ_c+ρ_x) (IVS2), with two coupling parametrizations, ξ(a)=ξ0+ξa(1−a) (IVS1a/IVS2a) and ξ(a)=ξ0[1+(1−a)/(a^2+(1−a)^2)] (IVS1b/IVS2b). The central result is that for IVS1a the combination CMB+DESI plus any of the three SN samples excludes ξ0=0 at more than 95% confidence (e.g., ξ0 = −0.146, 95% interval [−0.256, −0.016] for CMB+DESI+PantheonPlus), while the other cases show at most mild evidence. The paper also reports that Bayesian model comparison always favors ΛCDM over the interacting models, with log Bayes factors lnB_ij typically between −4 and −12.","tokens_in":27203,"tokens_out":5283,"duration_ms":56317,"significance":"If the perturbation treatment is valid, the IVS1a result is a nontrivial constraint on an interesting class of varying-coupling interacting dark sector models, and the paper usefully documents the dataset and model dependence of such constraints. The analysis uses modern external datasets and a nested null model, and it reports both parameter constraints and Bayesian evidences. However, the headline claim is currently overstated: the 95% credible interval excludes zero within a model that is itself strongly disfavored relative to ΛCDM by the paper's own evidence calculation. In addition, the paper does not demonstrate that the perturbed-fluid implementation is stable in the negative-ξ0 region that drives the IVS1a claim. Both issues need to be addressed before the result can be taken as evidence for a nonzero dark-sector interaction.","major_comments":[{"comment":"The central >95% claim depends on the perturbed-fluid implementation in the modified CAMB, but the manuscript never states the perturbed conservation equations for DE when Q=3ξ(a)Hρ_x and w_x=−1, nor does it apply a stability criterion. For negative ξ0, which is the preferred IVS1a region (e.g., ξ0=−0.146 for CMB+DESI+PantheonPlus in Table II), the DE perturbation sector can develop instabilities of the type discussed in Valiviita et al. [11]. If the code instead treats DE as a homogeneous vacuum (δρ_x=θ_x=0), the model is different and the concern disappears. The text cites [11] but does not state which treatment is used, and the modified code is not released. Please report the perturbed conservation equations, provide stability conditions for Eqs. (6)–(7) with ξ(a) from Eqs. (9) and (11), and verify that the posterior samples lie in the stable region, or compare with the vacuum-interac","section":"II (Eqs. (6)–(7)), III (methodology), Table II"},{"comment":"The abstract and conclusions describe the IVS1a result as 'evidence for a non-zero interaction at more than 95% CL'. However, Table II reports lnBij=−5.8 for CMB+DESI+PantheonPlus (and −5.5 and −4.0 for the other SN combinations), which is strong evidence against IVS1a relative to ΛCDM on the revised Jeffreys scale stated in Section III. A 95% credible interval that excludes ξ0=0 inside a strongly disfavored model is not evidence for an interaction over ΛCDM; it is a parameter constraint within that model. Please rephrase the abstract and conclusions to separate these two statements, e.g., 'within IVS1a the data exclude ξ0=0 at >95% CL, but the model as a whole is disfavored relative to ΛCDM'.","section":"Abstract; Section IV.A; Table II (lnBij row)"},{"comment":"The conclusion that the coupling is 'dynamical' is partly built into the parametrizations and is not an independent prediction of the data. For IVS1a, ξ(a)=ξ0+ξa(1−a) has a time-dependent term by construction, so finding ξa≠0 is a fit of the assumed functional form rather than a discovery of time variation. The paper should be explicit that it is testing the viability of specific parametrizations, not reconstructing the time dependence of ξ in a model-independent way. This does not invalidate the parameter constraints, but it should frame the robustness claim.","section":"Section II, Eqs. (9) and (11); Section V"}],"minor_comments":[{"comment":"In the CMB+DESI+Union3 column, the reported Ω_bh^2 value is '0.00246+0.00014...' which appears to be a typo for 0.02246. Please correct.","section":"Table II"},{"comment":"The caption notes that the dotted zero line is 'not clearly visible' in the right panel. Please use a different line style or add a small legend so the reader can identify the no-interaction case.","section":"Figure 7 caption"},{"comment":"The modified CAMB code is not released. Releasing the code or providing a public repository would substantially improve reproducibility, especially since the perturbation treatment is a key part of the central claim.","section":"Section III"},{"comment":"Equation (5) uses κ^2 without explicitly defining it as 8πG. Defining it would make the paper more self-contained.","section":"Section II"}],"recommendation":"major_revision","confidential_remarks":"The missing stability analysis is the key technical issue. The authors are experienced in this area and likely have the tools to provide the required perturbed equations and stability test; the paper should not be accepted without it. The abstract's 'evidence' wording also needs to be reconciled with the paper's own Bayesian evidence values. If the authors address these points, the paper could be a useful contribution to the DESI DR2 interacting-DE literature."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Short version: this is a solid, workmanlike constraints paper on interacting dark energy with time-dependent couplings, and its headline result — >95% exclusion of ξ0=0 in the IVS1a model — is internally consistent with Table II. The thing to know before trusting it: the exclusion is load-bearing on an unverified perturbation treatment for negative couplings, and the abstract's \"evidence\" language is in tension with the paper's own Bayes factors, which strongly favor ΛCDM.\n\nWhat's new: specific posterior constraints on four variable-coupling models (IVS1a/b, IVS2a/b) using Planck 2018, DESI DR2 BAO, and three SN compilations. I don't see those exact combinations in the cited literature. The analysis is standard: modified CAMB, Cobaya MCMC, Gelman-Rubin convergence, and MCEvidence for model comparison. The tables are comprehensive and they report both parameter constraints and Bayes factors. Credit is due for that.\n\nSoft spots, in order of size. First, the stability question. They cite Valiviita et al. on instabilities but never state the perturbed equations for Q=3ξ(a)Hρ_x with w_x=-1, and never apply a stability criterion. If their code evolves δρ_x and θ_x with an effective sound speed, negative ξ0 can excite exponential instabilities, and the posterior — including the claimed exclusion of zero — could be an artifact of the implementation. If instead they treat DE as a homogeneous vacuum (δρ_x=θ_x=0), the concern evaporates, but they don't say which it is. Modified code is not released. This is the load-bearing gap.\n\nSecond, interpretation. The \"evidence\" claim is a posterior exclusion within a model whose overall Bayes factor is lnBij ≈ -5.8, i.e., strong evidence against the model on the very Jeffreys scale they cite. That doesn't make the posterior exclusion wrong, but it makes the abstract's phrasing misleading. A non-zero coupling in a strongly disfavored model is not the same as evidence for the interaction.\n\nThird, minor: Table II has a typo (Ω_b h^2 = 0.00246 under Union3, should be 0.02246). The parametrizations are self-cited from 2019; that's fine, but it means the \"time-dependent coupling\" conclusion is inherited from the assumed functional form, not independently predicted.\n\nWho this is for: anyone compiling DESI DR2 interacting-dark-energy constraints. It's a useful update, not a breakthrough. Worth citing with a caveat, not as a detection.\n\nRecommendation: send to peer review, but require (1) a stability analysis or explicit statement of the vacuum treatment, (2) code release, (3) an abstract that doesn't overclaim relative to the Bayes factors.","headline":"Competent DESI DR2 update on variable dark-sector couplings; the headline IVS1a detection is internally consistent but rests on an unverified perturbation stability treatment and is oversold relative to the paper's own Bayes factors.","tokens_in":27594,"tokens_out":3902,"would_cite":false,"duration_ms":39024,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"A time-varying dark-energy–dark-matter coupling is preferred over no coupling at more than 95% confidence in one of four interacting models, with energy flowing from dark energy into dark matter.","keywords":["interacting dark energy","dark matter","dark energy coupling","time-dependent coupling","DESI DR2 BAO","cosmological tensions","Bayesian evidence","MCMC parameter estimation"],"falsifier":"Run the cited interacting-fluid stability check for IVS1a at the best-fit values ξ0≈-0.15 and ξa≈0.34: if the criterion flags a negative effective sound speed squared in that region, the posterior is sampling an unstable fluid and the >95% evidence is not physical. A dataset-level falsifier is to repeat the CMB+DESI+supernova fit with an independent high-resolution CMB likelihood; if the negative-ξ0 posterior disappears, the signal is tied to the Planck likelihood.","tokens_in":26736,"feed_emoji":"🌌","tokens_out":12424,"duration_ms":96589,"temperature":0.7,"pith_summary":"Most interacting dark-sector models treat the coupling between dark energy and dark matter as a constant. This paper relaxes that assumption: it lets the coupling vary with the scale factor in two functional forms and constrains the resulting models with Planck CMB data, DESI DR2 baryon-acoustic-oscillation measurements, and three independent supernova samples. The central result is that one of the four scenarios—an interaction proportional to the dark-energy density with a coupling that changes linearly with (1−a)—shows evidence for a nonzero present-day coupling at more than 95% confidence when CMB+DESI is combined with any of the three supernova catalogs. The preferred sign means energy flows from dark energy into dark matter, raising the inferred matter density and lowering the clustering parameter S8 relative to the standard model; the other three scenarios give at most mild or inconclusive evidence, and ΛCDM remains preferred by Bayesian evidence in all cases.","feed_headline":"Data hint dark energy feeds dark matter at 95% confidence","feed_subtitle":"One variable-coupling model survives CMB, DESI DR2 BAO, and three supernova samples; the rest do not.","key_machinery":"The central object is a time-dependent dark-sector coupling ξ(a) inserted into two interaction rates: Q=3ξ(a)Hρ_x, proportional to the dark-energy density, and Q=3ξ(a)Hρ_cρ_x/(ρ_c+ρ_x), proportional to the product of the two dark densities divided by their sum. Two parametrizations are used: a two-parameter Taylor form ξ(a)=ξ0+ξa(1−a), and a one-parameter, divergence-free form ξ(a)=ξ0[1+(1−a)/(a^2+(1−a)^2)] adapted from a dark-energy equation-of-state parametrization. These functions change the energy flow between the dark sectors at both background and perturbation level, altering the CMB temperature spectrum (acoustic peak heights and the low-multipole integrated Sachs-Wolfe region) and th","core_discovery":"The paper's central claim is that, after the DESI DR2 BAO data are added to Planck CMB and Type Ia supernova samples, the interacting model IVS1a—defined by Q=3ξ(a)Hρ_x with ξ(a)=ξ0+ξa(1−a)—produces a present-day coupling ξ0 that is negative at more than 95% confidence (for example ξ0=-0.146 with 68% uncertainties +0.045/-0.074 for CMB+DESI+PantheonPlus), while the time-variation parameter ξa is nonzero at more than 68% confidence and at more than 95% for the DESY5 sample. In the authors' reading, this points to genuine energy exchange between dark energy and dark matter, with a coupling that changes with cosmic time, and the sign of the effect is robust across the three supernova compilatio","pith_inferences":["My inference: the same negative-coupling preference should be tested in models where the dark-energy equation of state is also time-dependent, since the DESI DR2 BAO data independently favour dynamical dark energy; the two effects could reinforce or cancel.","My inference: the Bayesian penalty from two extra parameters is the main reason ΛCDM stays preferred; a theoretically motivated one-parameter coupling that reproduces IVS1a's late-time behaviour would be a sharper test of the interaction.","My inference: because the >95% result emerges when any of the three supernova compilations is added, a single re-analysis with one unified supernova likelihood plus low-redshift growth data would either consolidate or challenge the signal."],"forward_implications":["If the IVS1a result holds, dark energy and dark matter are not separately conserved: energy flows from dark energy into dark matter today, at a rate set by ξ0 about -0.15.","The same data combination raises the inferred matter density (Ωm≈0.35) and lowers the clustering amplitude (S8≈0.76), easing the S8 tension relative to Planck-ΛCDM while keeping H0 near 68 km/s/Mpc.","The sign of the coupling flips from positive in CMB-only fits to negative in CMB+DESI fits, indicating that the DESI BAO measurements are driving the >95% evidence.","The result is parametrization-dependent: only the two-parameter linear-in-(1−a) coupling reaches >95% confidence; the one-parameter divergence-free form does not cross that threshold.","In none of the five data combinations does the Bayesian evidence prefer an interacting model over ΛCDM, so the paper's claim is a preference inside a restricted model family, not a decisive detection."],"supporting_citations":[{"why":"Introduces the two interaction rates and the ξ(a)=ξ0+ξa(1−a) parametrization that define the models under test.","marker":"[122]"},{"why":"Supplies the instability conditions for interacting dark-sector perturbations that motivate the stability caveat.","marker":"[11]"},{"why":"Supplies the Planck 2018 CMB power-spectrum likelihood used in all five data combinations.","marker":"[124]"},{"why":"Supplies the DESI DR2 BAO measurements whose addition flips the sign of ξ0 and drives the >95% evidence.","marker":"[126]"},{"why":"PantheonPlus supernova catalogue, one of the three SNIa samples giving ξ0<0 at >95% CL in IVS1a.","marker":"[127]"},{"why":"Union3 supernova catalogue, the second independent SNIa sample yielding the same >95% result.","marker":"[128]"},{"why":"DESY5 supernova catalogue, the third SNIa sample, and the one that also makes ξa nonzero at >95% CL.","marker":"[129]"},{"why":"Supplies the numerical CMB solver that the authors modified to compute power spectra for the interacting models.","marker":"[130]"},{"why":"Supplies the Bayesian-evidence method used to compare the interacting models with ΛCDM.","marker":"[134]"}],"fun_headline_variants":["Dark energy and matter may interact—one model passes at 95%","Variable dark coupling gets a boost from DESI DR2 BAO data","Data favor time-changing dark energy-matter interaction (95% CL)","Dark sector handshake? New BAO data hints at coupling variability","One variable coupling model beats others with DESI DR2 BAO"],"cache_read_input_tokens":2688,"weakest_assumption_plain":"The result depends on the assumption that the model's equations stay stable at the negative couplings the data prefer; if that assumption fails, the detected signal is an artifact.","fun_headline_variants_meta":{"raw":{"variants":["Dark energy and matter may interact—one model passes at 95%","Variable dark coupling gets a boost from DESI DR2 BAO data","Data favor time-changing dark energy-matter interaction (95% CL)","Dark sector handshake? New BAO data hints at coupling variability","One variable coupling model beats others with DESI DR2 BAO"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.001264,"raw_usage":{"total_tokens":5051,"prompt_tokens":821,"completion_tokens":4230,"prompt_tokens_details":{"cached_tokens":256},"prompt_cache_hit_tokens":256,"prompt_cache_miss_tokens":565,"completion_tokens_details":{"reasoning_tokens":4137}},"tokens_in":565,"tokens_out":4230,"duration_ms":26072,"temperature":1.0,"reasoning_tokens":4137,"cache_read_input_tokens":256,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-05T15:56:00.978266+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Run the cited interacting-fluid stability check for IVS1a at the best-fit values ξ0≈-0.15 and ξa≈0.34: if the criterion flags a negative effective sound speed squared in that region, the posterior is sampling an unstable fluid and the >95% evidence is not physical. A dataset-level falsifier is to repeat the CMB+DESI+supernova fit with an independent high-resolution CMB likelihood; if the negative-ξ0 posterior disappears, the signal is tied to the Planck likelihood.","supporting_citations":[],"review_version":1}