{"id":"778df192-9fe0-43d8-bdc4-118bb756ec82","arxiv_id":"2501.10323","paper_version":2,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":5.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":2,"one_line_summary":"A sign-switching dark-sector coupling, fitted to CMB, DESI BAO, and supernova data, can simultaneously raise H0 and lower S8, but the preference over LambdaCDM depends on using SH0ES-calibrated supernovae.","lead":"This paper proposes a dark matter and dark energy interaction model whose coupling switches direction at a late cosmic time, and tests it against Planck, DESI, and supernova data. The model can recover a high Hubble constant and a low S8 amplitude together, but only when supernovae are calibrated with Cepheid distances in the SH0ES sample.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Late-time branch after the sign flip violates the paper's own Step-2 stability condition, and no sound-speed or perturbation-growth check is provided; the reported H0/S8 relaxation could be an artifact of the perturbation implementation.","rationale":"The reader identified the same weakest assumption that I consider load-bearing. The paper's Step 2 explicitly ties numerical stability to the condition (1+wx) and ξ having opposite signs, but Step 3 guarantees that this product changes sign across aeq,dark. With wx frozen at -0.999 for the ξi<0 branch, the post-transition product is positive, so the late-time perturbation evolution is not protected by the paper's own stability criterion. The perturbation equations (7)-(8) have sign-dependent source terms, and the S8 posterior is sensitive to late-time growth, so if unstable modes are present the reported S8=0.772±0.013 and the inferred H0/S8 correlation do not constitute a valid test of the model. The paper's conclusion claims stability but provides no check. This concern does not justify rejection: it is a concrete computational/analytical issue that can be settled by inspecting CLASS transfer functions or computing c_s,eff^2. In other respects the paper is transparent about dataset dependence, acknowledges that positive evidence appears only with SH0ES-calibrated PantheonPlus or DESI-inclusive combinations, and reports convergence criteria for the MCMC runs, which are genuine supporting elements. Since the conditional verdict already captures the unresolved stability question, I would leave the verdict unchanged.","tokens_in":20904,"tokens_out":10971,"duration_ms":110440,"concrete_test":"At the CMB+PPS+DESI best fit of Table I, run the CLASS implementation and output the synchronous-gauge transfer functions δc, δx, and θx at k=0.01 h/Mpc between z=1 and z=0. Compare the late-time evolution with the ΛCDM best fit on the same background; if δx or θx grow exponentially or oscillate with growing amplitude after z≈zeq,dark≈0.25, the late branch is unstable and the S8 constraint is not physical. As a cross-check, evaluate the standard IDE effective sound speed for the late branch (ξ>0, wx=-0.999) using the expressions in Refs. [144,145]; a negative c_s,eff^2 for z<zeq,dark would confirm the instability.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central numerical claim is that a late transition from ξi<0 to ξi>0 raises H0 and lowers S8. That claim depends on the perturbation sector being well behaved after the transition. In Sec. II, Step 2, the authors impose the standard stability condition that (1+wx) and ξ have opposite signs, and they set wx=-0.999 for ξi<0. By Step 3, for ξi<0 the coupling becomes ξ=+ξi>0 for a>aeq,dark while 1+wx remains +0.001, so the same-sign configuration that Step 2 was designed to avoid holds throughout the late universe. The source terms in Eqs. (7a)-(7d) and (8a)-(8b) inherit this sign through sgn[aeq-a], and no effective sound-speed, c_s,eff^2, or perturbation-growth check is reported for this branch. The Sec. V statement that the numerical implementation 'ensures the stability of the system' is asserted rather than demonstrated. If the late branch develops growing modes, the headline values S8=0.772±0.013 and H0=70.29±0.58 from CMB+PPS+DESI are not a physical resolution of the two tensions but a numerical artifact of an unstable perturbation sector.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper proposes a phenomenological interacting dark energy (IDE) model in which the DM-DE coupling changes sign at the epoch when the two dark-sector densities are equal, with coupling kernel ξ(a)=ξ_i sgn(a_eq,dark−a). The authors implement the model in CLASS and MontePython, fitting Planck CMB, DESI BAO, and several supernova samples (PantheonPlus, PantheonPlus+SH0ES, Union3, DESY5). For CMB+PPS+DESI they report H0=70.29±0.58 km/s/Mpc and S8=0.772±0.013 at 68% CL, reducing the Hubble tension to 2.3σ while keeping S8 consistent with weak-lensing surveys. They find positive Bayesian evidence over ΛCDM only when the SH0ES-calibrated PPS sample is used; uncalibrated SN samples instead favor ξ_i>0 and do not relax the tensions. The paper's central claim is that this sign-switching interaction can potentially relax both tensions simultaneously.","tokens_in":21162,"tokens_out":6590,"duration_ms":69660,"significance":"If the numerical implementation is correct, this is a timely and potentially interesting one-parameter extension of ΛCDM that addresses both the H0 and S8 tensions using a single sign-switching coupling. The paper is commendably honest about the dataset dependence of the result, and it uses standard tension estimators, AIC, and Bayesian evidence. The main significance is conditional on the stability of the perturbation sector after the sign flip, which is asserted but not demonstrated. The work also builds on, rather than independently derives, the known correlations between the sign of ξ and H0/S8, so the simultaneous relaxation is partly an input of the model. With adequate stability validation and a corrected analytic background solution, the paper could be a useful contribution to the interacting dark energy literature.","major_comments":[{"comment":"The stability condition stated in Step 2 requires (1+w_x) and ξ to have opposite signs, and the authors set w_x=-0.999 for ξ_i<0 and w_x=-1.001 for ξ_i>0. However, after the sign switch at a_eq, the late-time branch has ξ=+ξ_i>0 for ξ_i<0 while 1+w_x remains +0.001, i.e. the same-sign configuration that Step 2 was designed to avoid; the analogous violation occurs for ξ_i>0. The paper provides no effective-sound-speed check, no perturbation growth test, and no convergence test for the post-transition epoch. The Sec. V statement that the numerical implementation 'ensures the stability of the system' is not supported by any shown diagnostic. Since the headline H0 and S8 values from CMB+PPS+DESI are derived from the perturbed CLASS output, the authors should report e.g. the time evolution of δ_c, δ_x, and θ_x across the transition, verify the absence of spurious growing modes, and describe how the sgn discontinuity at a_eq is handled in the Boltzmann solver.","section":"Sec. II, Step 2 and Step 3; Sec. V"},{"comment":"The expression for ρ_x in Eq. (5) appears to have a sign error in the transition factor. If ρ_x,0 is today's density and the coupling flips from ξ_i to -ξ_i at a_eq, continuity of ρ_x at a_eq requires a factor a_eq^{-2ξ_i} in the post-transition branch, but the printed formula shows a_eq^{+2ξ_i}. This affects not only the background evolution but also the derived quantity z_eq,dark through Eq. (6). Please correct the formula and verify that all subsequent equations and numerical results are consistent with the corrected branch.","section":"Eq. (5)"},{"comment":"The model is explicitly constructed so that the negative-coupling branch raises H0 and the positive-coupling branch lowers S8, using correlations reported in earlier work, and the transition time is fixed to the density-equality epoch rather than being determined by the data. Consequently, the reported simultaneous relaxation is partly by construction. A more informative test would treat the transition epoch (or a_eq) as a free parameter and report its posterior, or compare the sign-switching model against a constant-ξ model with the same number of parameters. Without such a test, the claim that the data support the sign-switching mechanism specifically is weaker than the headline ∆χ² and Bayes factors suggest.","section":"Sec. II, Steps 1-3; Eq. (6)"},{"comment":"The model assigns w_x=-0.999 for ξ_i<0 and w_x=-1.001 for ξ_i>0, but w_x is not sampled and is not a continuous function of ξ_i: at ξ_i=0 the assignment is discontinuous. This creates two distinct regimes in parameter space and may affect MCMC sampling near ξ_i=0 and the Bayesian evidence computation. Please clarify whether w_x is intended as a derived parameter, and discuss how the ξ_i=0 limit recovers ΛCDM continuously given that w_x flips between the two branches.","section":"Sec. II, Step 2"}],"minor_comments":[{"comment":"In the CMB+DESI column, log(10^10 A_s) is listed as 0.9681±0.0041, which is identical to the n_s entry and is not a valid amplitude value; this appears to be a copy-paste typo that should be corrected.","section":"Table I"},{"comment":"The text calls H the 'conformal Hubble rate' in the continuity equations, but the equations are written in the standard form with H as the physical Hubble rate. Please use \\(\\mathcal{H}\\) consistently if conformal time is intended, or clarify the notation.","section":"Sec. II, Eqs. (2)-(3)"},{"comment":"The caption says the left panel is based on 'CMB + DESI + PP and CMB + DESI + PPS data respectively,' but the text describes the analysis as CMB+PPS+DESI; please make the dataset combination in the caption consistent with the text.","section":"Fig. 3 caption"},{"comment":"The quadratic tension estimator is defined without specifying which subset of parameters enters the vectors x_i and x_j; please state whether the full covariance of the reported parameters or a subset is used.","section":"Sec. III-A, Eq. (9)"},{"comment":"The phrase 'reinforce by ∆AIC = ...' should read 'reinforced by ∆AIC = ...'; there are several similar grammatical slips throughout the text that should be corrected in a final revision.","section":"Sec. V"}],"recommendation":"major_revision","confidential_remarks":"The paper fits the scope of the journal and addresses a timely topic. The central issue is the missing stability validation for the post-transition perturbation branch; if the authors can provide concrete diagnostics (e.g., absence of growing modes, c_s,eff^2 positivity, resolution checks), the main claim may become defensible. The apparent sign error in Eq. (5) must also be fixed and checked against the numerics. I would not reject the paper outright, but the current evidence for the headline result is incomplete. The dependence of the positive Bayesian evidence on the SH0ES-calibrated PPS sample is acknowledged by the authors; editors may wish to ensure the abstract's phrasing ('can potentially relax') is not overinterpreted as a claim that the data already prefer the sign-switching mechanism independently of the local calibration."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"The paper is a serious, competent entry in the interacting-dark-energy literature. The new ingredient is a coupling whose sign flips at the epoch when dark matter and dark energy densities are equal. With the SH0ES-calibrated PantheonPlus sample plus DESI BAO, the model pulls H0 to 70.29 and S8 to 0.772, reducing the Hubble tension to 2.3 sigma and aligning S8 with weak lensing. What is genuinely good: the model is a clean one-parameter extension, the analysis covers CMB, DESI, and three different SN compilations, and the authors are transparent that positive Bayesian evidence appears only with the calibrated PantheonPlus data. That honesty is refreshing.\n\nThe soft spots are real, though. First, the printed analytic density solution in Eq. (5) has a suspicious sign in the a_eq^{2xi_i} factor; matching the post-transition branch at a_eq requires the opposite sign if rho_x0 is today's density. The numerical work is done in CLASS, so this may be a typo, but it needs fixing.\n\nSecond, and more important, the late-time branch violates the standard stability condition quoted in Step 2. For xi_i < 0, the early branch has xi < 0 and 1+w_x > 0, which is the stable configuration; after the flip, xi > 0 with the same 1+w_x > 0, which is the configuration the condition was designed to exclude. The paper asserts in the conclusions that the numerical implementation ensures stability, but provides no effective sound-speed or perturbation-growth check. The central result could in principle be an artifact of an unstable perturbation sector. That is not an accusation, it may well be fine, but the paper needs to demonstrate it.\n\nThird, the model is constructed to exploit the known xi-H0 and xi-S8 correlations, and the headline result disappears when other SN samples are used. The authors acknowledge this, so it is a limitation, not a hidden flaw.\n\nVerdict: worth a serious referee. The physics idea is legitimate, the data analysis is thorough, and the issues are addressable. A referee should ask for the analytic fix, a stability analysis of the late branch, and ideally a combined analysis that includes the other SN samples rather than just the one that favors the sign flip. If the stability check comes out clean, this becomes a useful addition to the tension-resolution toolbox.","headline":"A well-executed but conditional claim: the sign-switching IDE model relieves both tensions only with SH0ES-calibrated supernovae, and the late-time branch needs a stability check before the numbers can be trusted.","tokens_in":21738,"tokens_out":5588,"would_cite":false,"duration_ms":49793,"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 one-parameter dark-sector coupling that flips sign at the matter–dark-energy equality redshift can relax both the H0 and S8 tensions simultaneously.","keywords":["interacting dark energy","sign-switching coupling","dark matter–dark energy interaction","Hubble tension","S8 tension","DESI BAO","PantheonPlus","cosmological tensions"],"falsifier":"Rerun the joint analysis with the full DES or KiDS weak-lensing likelihoods rather than comparing the derived $S_8$; if the model's predicted lensing signal is rejected, the reported $S_8$ relaxation does not survive.","tokens_in":20633,"feed_emoji":"🌌","tokens_out":7346,"duration_ms":70774,"temperature":0.7,"pith_summary":"This paper argues that a single new parameter — the sign and size of a dark-matter–dark-energy coupling — can address the two most persistent discrepancies in ΛCDM cosmology at once. The coupling is allowed to flip direction exactly at the redshift where the two dark components have equal energy densities, so that whichever way energy flowed early, it flows the other way late. When the early-time coupling is negative, the model produces a higher H0 and a lower S8 than ΛCDM, and with Planck CMB, DESI BAO, and SH0ES-calibrated PantheonPlus data the Hubble tension falls to 2.3σ while S8 becomes consistent with weak-lensing measurements. The result matters because it is a minimal, testable modification of the standard model rather than a wholesale replacement. The paper also reports that the preference for the sign-switch model over ΛCDM depends on the supernova calibration and dataset combination.","feed_headline":"Sign-flipping dark interaction relaxes Hubble and S8 tensions","feed_subtitle":"One extra parameter gives H0 = 70.29 and S8 = 0.772, cutting the Hubble tension to 2.3 sigma.","key_machinery":"The central object is the signum-switching coupling $\\xi(a) = \\xi_i \\, \\mathrm{sgn}(a_{\\mathrm{eq,dark}} - a)$ inserted into the standard interacting-dark-energy continuity equations through $Q = \\xi(a)H\\rho_x$. The transition scale $a_{\\mathrm{eq,dark}}$ is defined by $\\Omega_m/\\Omega_x = 1$, tying the sign flip to the cosmic coincidence epoch; the density solutions acquire terms proportional to $a^{-3(w_x + \\xi_i/3)}$, and the linear perturbation equations carry sign-dependent source terms $\\Gamma = \\xi_i H (\\rho_x/\\rho_c) \\, \\mathrm{sgn}(a_{\\mathrm{eq,dark}} - a)$ and an analogous $\\Xi$. The machinery works by making the late-time coupling positive when the early-time coupling is negative, which reshapes the ratio $\\rho_c/\\rho_x$ and thereby pushes the expansion rate and the growth of matter perturbations in opposite directions.","core_discovery":"The paper proposes a one-parameter extension of ΛCDM in which dark matter and dark energy exchange energy at a rate $Q = \\xi(a)H\\rho_x$, with $\\xi(a) = \\xi_i \\, \\mathrm{sgn}(a_{\\mathrm{eq,dark}} - a)$. The sign of the coupling is fixed before the epoch where the two dark densities are equal and flips after it, reversing the direction of energy-momentum transfer. With an initially negative coupling ($\\xi_i < 0$, energy flowing from dark matter to dark energy) that turns positive at low redshift, the model simultaneously raises $H_0$ and lowers $S_8$ relative to ΛCDM; from Planck CMB, DESI BAO, and SH0ES-calibrated PantheonPlus data it reports $H_0 = 70.29 \\pm 0.58$ km/s/Mpc and $S_8 = 0.772 \\pm 0.013$, reducing the Hubble tension to 2.3σ and bringing $S_8$ into agreement with weak-lensing surveys. The model is preferred over ΛCDM only when the SH0ES Cepheid calibration is used or when DESI BAO data are included; with uncalibrated PantheonPlus, Union3, or DESY5 data the preferred coupling sign reverses and the tensions are not resolved.","pith_inferences":["A natural next test is to treat the supernova absolute magnitude $M_B$ as a free parameter in the same chains; if the $\\xi_i < 0$ preference vanishes under a free $M_B$, the sign-switch resolution is at least partly a restatement of the SH0ES calibration.","The model motivates a microphysical mechanism that changes the sign of the interaction at the coincidence epoch; without one, the transition is a phenomenological clock whose only theoretical anchor is the cosmic-coincidence coincidence itself.","Because the same $S_8$ shift could be mimicked by an imperfect treatment of perturbations after the sign flip, rerunning with a stable equation-of-state prescription or a coupled-quintessence model would show whether the growth suppression is real."],"forward_implications":["If the model is correct, the CMB + PPS + DESI combination implies $H_0 = 70.29 \\pm 0.58$ km/s/Mpc, bringing the early-universe inference within 2.3σ of the SH0ES distance-ladder value.","The same combination gives $S_8 = 0.772 \\pm 0.013$, removing the reported discrepancy with DES and KiDS weak-lensing estimates, pending a full lensing likelihood analysis.","DESI BAO data alone mildly prefer the sign-switch model over ΛCDM, so the effect shows up in the expansion history $H(z)/(1+z)$ as a systematically higher curve than ΛCDM.","The preferred transition sits at $z_{\\mathrm{eq,dark}} \\sim 0.25$; because this redshift correlates negatively with $H_0$ and positively with $S_8$, moving the transition epoch would shift the two tensions in opposite directions.","With uncalibrated PantheonPlus, Union3, or DESY5 supernova data the coupling is driven positive, yielding lower $H_0$ and higher $S_8$, so the claimed reconciliation is conditional on the SH0ES calibration."],"supporting_citations":[{"why":"Establishes that negative coupling eases $H_0$ and positive coupling eases $S_8$, the dual behavior the sign-switch model combines.","marker":"[133]"},{"why":"Provides the interaction kernel $Q = \\xi H \\rho_x$ that the model extends with a sign-changing coupling.","marker":"[108]"},{"why":"Gives the stability condition that $(1+w_x)$ and $\\xi$ must have opposite signs, used to set $w_x$ before the transition.","marker":"[144]"},{"why":"Shows DESI-era BAO data allow higher $H_0$ in interacting-dark-energy models, supporting the CMB+PPS+DESI preference for $\\xi_i < 0$.","marker":"[137]"},{"why":"Supplies the SH0ES Cepheid calibration used in the PPS supernova likelihood.","marker":"[7]"},{"why":"Provides the PantheonPlus supernova sample and its covariance, the basis of the PP and PPS analyses.","marker":"[157]"},{"why":"Supplies the DESI BAO measurements across $0.1 < z < 4.2$ used in the joint constraints.","marker":"[53]"},{"why":"Provides the Planck 2018 CMB temperature and polarization likelihoods used as the high-redshift anchor.","marker":"[2]"}],"fun_headline_variants":["Sign-flipping dark coupling eases Hubble and S8 tensions","Dark sector sign change relaxes both cosmic tensions","One dark parameter flip brings H0 and S8 into line","Reversing dark energy flow calms H0 and S8 tensions","Sign-switch in dark interaction relieves Hubble and S8"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The paper assumes the density fluctuations stay well-behaved after the coupling flips sign, even though the usual stability condition for interacting dark energy is violated then, and it provides no test of that late-time behavior.","fun_headline_variants_meta":{"raw":{"variants":["Sign-flipping dark coupling eases Hubble and S8 tensions","Dark sector sign change relaxes both cosmic tensions","One dark parameter flip brings H0 and S8 into line","Reversing dark energy flow calms H0 and S8 tensions","Sign-switch in dark interaction relieves Hubble and S8"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.001139,"raw_usage":{"total_tokens":4826,"prompt_tokens":1139,"completion_tokens":3687,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":755,"completion_tokens_details":{"reasoning_tokens":3602}},"tokens_in":755,"tokens_out":3687,"duration_ms":25895,"temperature":1.0,"reasoning_tokens":3602,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-10T19:13:29.427625+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Rerun the joint analysis with the full DES or KiDS weak-lensing likelihoods rather than comparing the derived $S_8$; if the model's predicted lensing signal is rejected, the reported $S_8$ relaxation does not survive.","supporting_citations":[],"review_version":1}