{"id":"3cd0ee9d-ce21-476a-93b7-975588c8535b","arxiv_id":"2504.21110","paper_version":2,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":4,"one_line_summary":"A dark sector interaction that acts only on perturbations leaves the background expansion untouched while changing the integrated Sachs-Wolfe effect, matter clustering, fσ8, and S8 predictions.","lead":"This paper proposes a new way for dark matter and dark energy to exchange energy only when the universe is disturbed, leaving the overall expansion history identical to the standard model. A generalist should read it because it shows how such a hidden interaction could change galaxy clustering and the cosmic microwave background in ways future surveys can test.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The ISW and fσ8 claims are not isolated from the wCDM background offset; re-baselining against wx-identical Σ=0 wCDM is required before the interaction signature is established.","rationale":"The reader's weakest_assumption is the HALOFIT calibration for scale-dependent growth, which is a valid concern for the nonlinear P(k) part. My independent reading surfaces a more upstream issue: the reference model for all quoted deviations is ΛCDM, while the model's own background is wCDM with wx ≠ -1. The paper's own text acknowledges that a large part of the CMB difference from ΛCDM comes from wx alone; the same decomposition is missing for the ISW, P(k), and fσ8 claims. This does not make the construction wrong—the modified CLASS implementation, explicit initial conditions, and stability checks are coherent—but it means the central phenomenological claim is not yet cleanly demonstrated. Re-baselining with the same modified CLASS code is straightforward and would settle the issue. The HALOFIT concern remains valid but affects only the nonlinear P(k) portion, whereas the re-baselining concern affects the ISW, fσ8, and S8 headline claims. Both concerns justify a CONDITIONAL verdict rather than acceptance, so I recommend keeping the reader's verdict unchanged.","tokens_in":54056,"tokens_out":4331,"duration_ms":42630,"concrete_test":"Recompute Figs. 4-7 and 9-12 with Σ=0 at each adopted wx (the wCDM reference) and quote all percentage deviations relative to that baseline. If the Σ-induced ISW, P(k), and fσ8 deviations remain at the claimed 10-15% level, the interaction signature is genuine; if they drop to a few percent or below, the headline claims are dominated by the wx choice and must be restated. This requires only rerunning the same modified CLASS code with Σ=0.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central claim is that the perturbation-only interaction of Eq. (36) leaves the wCDM background untouched while producing observable ISW, P(k), and fσ8 signatures. The paper's headline percentage differences, however, are all quoted relative to ΛCDM, not relative to the wCDM model with the same wx and Σ=0 that the frozen model is designed to preserve. The paper itself notes (Sec. VI.C.1) that ~20% of the CMB TT/EE difference from ΛCDM arises solely from the difference in wx, independently of the value taken by Σ. The ISW section then quotes enhancements by more than 10% and around 50% for strong coupling, and fσ8 deviations up to 15%, all relative to ΛCDM, without decomposing the wx-driven offset from the Σ-driven change. Since the frozen model's background is wCDM, the interaction's genuine fingerprint is the difference between the frozen model and the wx-identical Σ=0 baseline. Without that baseline, the central hidden-from-geometry, visible-in-growth claim is not demonstrated: the reported 10-50% effects could be dominated by the wx choice rather than by the dark-sector interaction.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper proposes a 'frozen vanilla model' in which dark matter and dark energy exchange energy only at the level of cosmological perturbations, through δQ_x = -Σ(3Hρ̄_x)(K+δ_x) with K = (h'/2 + θ_T)/(3H), while the wCDM background is left unchanged. The authors derive the coupled perturbation equations and radiation-era initial conditions, implement them in a modified CLASS code, and explore four sign branches of (1+w_x) and Σ. They report that the interaction modifies the late ISW amplitude, the nonlinear matter power spectrum, fσ8(z), and S8(z) by up to about 15% relative to ΛCDM, and that curvature and dark-energy pressure perturbations remain bounded, suggesting the absence of large-scale instabilities. The central claim is that the interaction is hidden from geometric and background probes while leaving observable growth and ISW signatures.","tokens_in":54385,"tokens_out":7098,"duration_ms":79223,"significance":"If the findings hold, the model provides a concrete way for dark-sector energy exchange to escape background and geometric constraints while producing late-time ISW, P(k), fσ8, and S8 signatures, and it offers a possible route to alleviating the S8 tension. The linear perturbation derivation in Secs. III-V is internally consistent, the parameter choices are explicit, and the numerical results are forward predictions rather than fits to target observables. The use of a modified public CLASS code aids reproducibility, and the distinction from momentum-transfer models is clearly stated: here the continuity equations are modified while the Euler equations remain unchanged. The main quantitative claims, however, rest on two load-bearing assumptions: the choice of ΛCDM as the reference baseline and the transfer of HALOFIT calibration to a model with scale-dependent growth. Both need to be addressed before the central claim can be regarded as established.","major_comments":[{"comment":"All reported ISW enhancements and fσ8 deviations are quoted relative to ΛCDM, not relative to the wCDM model with the same w_x and Σ=0 that the frozen model is designed to preserve. The manuscript itself notes in Sec. VI.C.1 that approximately 20% of the CMB TT/EE difference from ΛCDM arises solely from the difference in w_x, independently of Σ. Since the frozen model's background is wCDM, the genuine interaction fingerprint is the difference between the frozen model and the w_x-identical, Σ=0 baseline. Without that decomposition, the reported 'more than 10%' ISW enhancement and 'up to 15%' fσ8 changes cannot be attributed to the dark-sector interaction. Please recompute the percentage differences against the Σ=0 wCDM baseline and state explicitly which part of each deviation is due to w_x and which to Σ.","section":"Sec. VI.C.2, Sec. VI.C.4, Figs. 5 and 7"},{"comment":"The nonlinear matter power spectrum at z=0 is computed with the HALOFIT routine, which is calibrated to standard ΛCDM N-body simulations. The frozen model exhibits scale-dependent growth and a scale-dependent interaction in Eq. (36), and the paper provides no N-body or mock-calibration test showing that the halo-model parameters transfer to this scenario. Therefore the claimed small-scale P(k) deviations of about 10%, and any conclusions drawn from them about nonlinear structure formation, are unsupported. I recommend either restricting the P(k) claims to the linear regime or validating the nonlinear prescription with N-body simulations before presenting these deviations as model predictions.","section":"Sec. VI.C.3, Fig. 6"},{"comment":"Appendix A sketches a Lagrangian Lδ−EFT but does not derive δQ_x = -Σ(3Hρ̄_x)(K+δ_x); it states only that mixed terms involving u^μ and ∇_μ δφ_A should be included and that a full Lagrangian model will appear in future work. Thus Eq. (36) is currently a phenomenological ansatz rather than a derived effective-theory operator. This is a limitation rather than an internal inconsistency, but it should be acknowledged in the abstract or introduction, and the strength of the 'new mechanism' claim should be calibrated accordingly.","section":"Appendix A"}],"minor_comments":[{"comment":"Equation (46) writes the ISW temperature shift as proportional to (2/c^2)∫dτ Ψ̇, but the text and figures refer to the derivative of (Ψ+Φ); the standard linear ISW contribution in the Newtonian gauge involves both metric potentials. Please correct the formula.","section":"Eq. (46)"},{"comment":"The text labels the dark-energy pressure perturbation as 'δpx (24)', but Eq. (24) is the density-contrast equation; the pressure perturbation is defined in Eq. (56). Please correct the cross-reference.","section":"Sec. VI.C.5"},{"comment":"The caption of Fig. 9 lists repeated parameter combinations (for example, w_x=-1.06 with the same Σ value appears three times), and the text in Sec. VI.D states that Σ=0.1 is impossible for w_x=-1.06. The legend should be cleaned and made consistent with the stability statement.","section":"Fig. 9 and Sec. VI.D"},{"comment":"The phrase 'we have numerically proven' overstates what is a numerical observation; please replace it with 'we find' or 'we observe numerically'.","section":"Sec. VI.B"},{"comment":"The model naming is inconsistent across figures and text: 'frozen-branch-I', 'Frozen-branch-I', and 'Branch I' are all used. Please unify the terminology.","section":"Throughout"}],"recommendation":"major_revision","confidential_remarks":"The paper is exploratory and the central quantitative claims need two repairs: re-baselining against the w_x-identical Σ=0 wCDM model, and either removing or validating the nonlinear HALOFIT predictions. Both are fixable within the manuscript's scope, and I do not see a fatal internal inconsistency in the linear perturbation derivation. The phenomenological status of Eq. (36) should also be stated more prominently."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"The frozen vanilla model is a genuinely new perturbation-only dark-sector interaction: Eq. (36) adds δQ_x = -Σ(3Hρ̄_x)(K + δ_x) to the continuity equations while leaving Euler equations and the background untouched. That is a real ansatz, not a rehash of momentum-transfer models, and the paper works through its linear consequences carefully. The initial-condition analysis in Sec. V and the four-branch stability picture are useful. If you work on interacting dark sectors, this is worth reading.\n\nThe central claim—geometry stays wCDM while growth changes—is plausible but not yet demonstrated at the headline level. The ISW and fσ8 numbers (10–50% and up to 15%) are quoted relative to ΛCDM, not relative to the wx-identical Σ=0 wCDM model that the frozen model is designed to preserve. The paper itself notes in Sec. VI.C.1 that ~20% of the TT/EE difference comes from wx alone, but the ISW section never decomposes the wx-driven offset from the Σ-driven change. Without that baseline, the interaction's unique fingerprint could be significantly smaller than advertised. This is fixable: rerun the same plots against the wCDM model with the same wx and Σ=0.\n\nThe other soft spot is the nonlinear P(k). The paper feeds a model with scale-dependent growth into HALOFIT, which is calibrated to ΛCDM N-body simulations. The authors flag this, but they do not test whether the halo-model calibration transfers. The small-scale deviations they quote are therefore suggestive, not established. Linear spectra and fσ8 are on firmer ground.\n\nMinor points: no code or likelihood is shipped (they say an MCMC is coming), and the relation to the concurrent work in Ref. [121] is acknowledged but not examined. Neither is disqualifying for an exploratory paper.\n\nSummary: this is a solid phenomenological proposal with a clear new mechanism and internally consistent linear theory. The headline observational claims need re-baselining before they can be taken at face value; the nonlinear claims need a calibration check. A serious referee would have a clear job to do.\n\nRecommendation: send it to peer review. It deserves referee time, but the revision should re-plot against the wx-identical Σ=0 baseline and temper the ISW/fσ8 percentages accordingly.","headline":"A clean perturbation-only dark-sector interaction, but the headline ISW and fσ8 numbers need re-baselining against the wCDM model they claim to preserve.","tokens_in":54862,"tokens_out":2287,"would_cite":true,"duration_ms":24269,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":["83F05","85A40"],"pacs":[],"model":"deepseek-v4-flash","headline":"A perturbation-only dark-sector interaction can shift structure growth while leaving the vanilla background untouched.","keywords":["dark sector interactions","perturbation-level coupling","frozen vanilla model","integrated Sachs-Wolfe effect","fσ8 growth estimator","S8 tension","matter power spectrum","wCDM background"],"falsifier":"Run N-body simulations with the frozen model's modified continuity equations, keeping the same background and scale-dependent $\\delta Q$, and compare the $z=0$ nonlinear matter power spectrum at $0.1 < k < 10\\ h/{\\rm Mpc}$ with the HALOFIT-based predictions; discrepancies beyond the expected percent-level would invalidate the small-scale claims.","tokens_in":53887,"feed_emoji":"🌌","tokens_out":6904,"duration_ms":74560,"temperature":0.7,"pith_summary":"This paper proposes a new way to couple dark matter and dark energy: the energy exchange is switched off in the smooth background and activated only in the perturbations, so the expansion history stays identical to the vanilla wCDM model. The authors argue that this frozen mechanism still leaves measurable imprints: it can enhance or suppress the late integrated Sachs-Wolfe effect, alter the nonlinear matter power spectrum, and shift the growth estimator $f\\sigma_8(z)$ by up to roughly 15 percent at low redshift, which in some branches lowers $S_8$ and eases the reported $S_8$ tension. A sympathetic reader would care because the model offers a concrete route by which dark-sector interactions could hide from geometric probes while revealing themselves in structure formation, without triggering the large-scale instabilities that plague many interacting dark-energy models.","feed_headline":"Dark-sector energy swap hides from expansion, bends structure growth","feed_subtitle":"The frozen vanilla model keeps the background wCDM while shifting ISW, galaxy clustering, and fσ8 at late times.","key_machinery":"The load-bearing object is the perturbative delta-effective interaction of Eq. (36): $\\delta Q_x = -\\Sigma(3H \\bar{\\rho}_x)(K + \\delta_x)$ with $K = h'/2 + \\theta_T/(3H)$, together with the compensating $\\delta Q_{\\rm dm} = -\\delta Q_x$. It acts only in the continuity equations for dark matter and dark energy, while the Euler equations remain unchanged and the dark-matter frame can still have zero initial velocity. Scale dependence enters through $\\delta_x$, $h'$, and $\\theta_x$, making the coupling efficient at small scales during matter domination and at intermediate scales only near dark-energy domination. The paper pairs this with $c^2_{sx}=1$ and $c^2_{ax}=w_x$, classifies models into four branches by the signs of $(1+w_x)$ and $\\Sigma$, and evolves the system with a modified Boltzmann code.","core_discovery":"The central discovery is a covariant interaction vector confined to the perturbative sector, specified in the synchronous gauge by $\\delta Q_x = -\\Sigma(3H \\bar{\\rho}_x)(K + \\delta_x)$, with $K = h'/2 + \\theta_T/(3H)$, and the compensating source $\\delta Q_{\\rm dm} = -\\delta Q_x$. Because the background energy-momentum conservation is untouched, the Friedmann expansion is fixed to the vanilla/CPL model with a constant equation of state $w_x$. The paper claims this mechanism is stable, with dark-energy pressure perturbations that remain bounded, a curvature perturbation $\\zeta$ conserved on super-Hubble scales, and the usual background-level \"doom factor\" instability absent, while still generating distinctive late-time signatures: the ISW amplitude can change by tens of percent, the matter power spectrum is suppressed or enhanced depending on the sign of $\\Sigma$, and $f\\sigma_8(z)$ changes by up to 15 percent at low redshift, with $\\sigma_8(z=0)$ in branch I falling in $[0.771, 0.800]$ and thereby alleviating the $S_8$ tension.","pith_inferences":["If the frozen mechanism is correct, the $S_8$ tension can be addressed without changing the expansion history or early-universe parameters, isolating the discrepancy to late-time growth and giving surveys a sharper target than models that alter both.","The scale dependence of the interaction implies a weakly scale-dependent growth rate in the observable window $0