{"id":"1f04ead5-db35-47f7-b7ce-a947cc0acc06","arxiv_id":"2507.16147","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":4.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":2,"one_line_summary":"Using Planck plus DESI, Pantheon Plus and RSD data, the PEDE+wDM model gives 10^7 wdm = 4.0 (+2.5, -2.3) at 95% CL, yet LambdaCDM remains strongly favored by Bayesian evidence.","lead":"A new model treats dark matter as a barotropic fluid whose pressure equals its sound speed and dark energy as phenomenological emergent dark energy, then fits it to CMB, BAO, supernova and RSD data. The fit finds a small positive dark matter equation of state at 95% confidence, but Bayesian evidence still strongly prefers standard LambdaCDM.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The claimed positive DM EoS is not isolated from the assumed equality wdm = c_s^2; a two-parameter rerun is needed to test whether the signal is an EoS or a sound-speed effect.","rationale":"The paper's most defensible result is the per-dataset likelihood analysis, and the authors honestly report that LambdaCDM is strongly preferred (ln B = -25.14), which is independent evidence against the PEDE+wDM model. The statistical machinery is standard MCMC with MontePython and a modified CLASS; no machine-checked verification is provided, and the modified CLASS code is not released, so the perturbation implementation cannot be independently audited. The barotropic identification is the load-bearing assumption for the abstract's 'positive dark matter equation of state' claim: the observable signal is a suppression of sigma8/S8, which in this model is produced by the sound-speed term. Relaxing the equality wdm = c_s^2 would test whether the data really require a positive wdm or merely a positive c_s^2. The zero-truncated prior on wdm is a secondary but related issue; it removes the negative-wdm region and makes the reported one-sided interval prior-dependent. The concrete test proposed is a single MCMC rerun with two independent parameters and would directly settle whether the central claim survives. This concern does not change the reader's CONDITIONAL verdict, which already flags the barotropic assumption and the prior, so no adjustment is needed. The equation-number inconsistency between (4) and (5) is a typo-level issue that does not affect the claimed detection because the implemented PEDE EoS (5) is the standard one. Overall, the paper is a useful phenomenological constraint, and its main caveat is the model-dependent identification of wdm with c_s^2, not a fatal internal error.","tokens_in":13770,"tokens_out":15652,"duration_ms":160925,"concrete_test":"Rerun the MCMC analysis with two free dark-matter parameters: wdm allowed to take negative values (e.g., flat prior [-1e-4, 1e-4]) and c_s,dm^2 independent with flat prior [0, 1e-4], while keeping c_nad,dm = 0 and viscosity = 0. Compare the two-dimensional posterior for (wdm, c_s^2) on CMB+DESI+PP+RSD. If the positive signal appears only in c_s^2 and wdm is consistent with zero or negative, then the abstract's claim of a positive dark matter equation of state is unsupported and should be reframed as a constraint on the sound speed. If wdm remains positive with c_s^2 unconstrained, the barotropic identification is not the driver of the detection.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central claim in the abstract (10^7 wdm = 4.0^{+2.5}_{-2.3} at 95% CL) is a statement about the single parameter wdm, which the model forces to equal the rest-frame sound speed squared by setting c_nad,dm = 0 and viscosity to zero (Section 2). The authors themselves note in Section 4 that the effect on sigma8/S8 originates from the sound-speed term, not from the EoS term, because wdm ~ 10^-7 has negligible direct background effect. Therefore the data combination CMB+DESI+PP+RSD is essentially measuring a positive rest-frame sound speed, and only through the barotropic ansatz is this translated into a positive dark matter equation of state. If DM has any non-adiabatic pressure or viscosity, as allowed in generalized dark matter frameworks, the inferred wdm would absorb those components and the reported 'positive DM EoS' would not measure the EoS. In addition, the flat prior wdm >= 0 (Table 1) truncates the posterior at zero; for CMB, CMB+DESI, and CMB+DESI+PP the posterior is bounded at zero (0 < 10^7 wdm < 13.1/13.2/17.6), so the one-sided detection quoted for the RSD combination is shaped by this prior. A model with wdm ~ 0 but c_s^2 > 0 (e.g., warm or interacting DM) is physically distinct and currently degenerate with the claimed detection.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"This paper studies a cosmological model in which dark energy is described by phenomenological emergent dark energy (PEDE) and dark matter is treated as a barotropic fluid with a constant equation-of-state parameter wdm equal to the square of its rest-frame sound speed (c_s,dm^2 = wdm). The authors implement the model in CLASS/MontePython and fit it to Planck 2018 CMB, DESI BAO, Pantheon Plus, and Gold-2018 RSD data. For the combined CMB+DESI+PP+RSD dataset they report a positive wdm at 95% confidence (10^7 wdm = 4.0^{+2.5}_{-2.3}) and a Δχ^2 improvement of about 11 over PEDE, but Bayesian evidence strongly favors ΛCDM over PEDE+wDM (ln B = -25.14). The paper also compares PEDE and PEDE+wDM and discusses the effect of wdm on σ8 and S8.","tokens_in":14106,"tokens_out":7948,"duration_ms":77942,"significance":"If the reported signal were robust, it would indicate a small positive sound speed for dark matter, which suppresses small-scale matter fluctuations and is relevant to dark-matter microphysics. The study is a competent application of standard cosmological perturbation theory and MCMC techniques, using public codes and reporting Bayesian evidence, which is a strength. However, the physical interpretation is limited by the model's built-in identity wdm = c_s^2: the data are sensitive almost exclusively to the sound-speed term at perturbations, while the background EoS effect is negligible at wdm ~ 10^-7. The detection appears only after RSD data are added and is influenced by the prior truncation at wdm ≥ 0. Moreover, the model as a whole is very strongly disfavored relative to ΛCDM, so the significance is confined to a parameter within a non-preferred model. The paper's main value is as a phenomenological constraint, but the headline claim overstates what is actually measured.","major_comments":[{"comment":"The principal claim that the data measure a positive dark matter equation of state relies on the imposed identity c_s,dm^2 = wdm (with c_nad,dm = 0). The perturbation equations (10)-(11) show that the observable effect on the matter power spectrum enters through the k^2 wdm/(1+wdm) δdm term in the Euler equation, i.e., through the sound speed, while the background effect of wdm ~ 10^-7 in Eq. (1) is negligible. The authors themselves state in Section 4 that the reductions of σ8 and S8 \"mainly originate from the effects of a non-zero mean value of DM sound speed squared rather than directly from the effects of a DM EoS parameter.\" Therefore the abstract's wording \"statistically significant signal for positive dark matter equation of state and square of sound speed wdm = c_s^2\" overstates what is actually constrained: the data constrain c_s^2 under the barotropic ansatz, and the positive EoS conclusion is a restatement of the ansatz. To support the EoS claim, the authors should either fit wdm and c_s^2 as independent parameters (e.g., in the GDM framework) or explicitly rephrase the result as a constraint on the barotropic sound speed.","section":"Section 2 and Abstract"},{"comment":"The flat prior wdm ∈ [0, 100] × 10^-6 imposes a hard lower bound at zero. For the CMB, CMB+DESI, and CMB+DESI+PP datasets, the 95% intervals are 0 < 10^7 wdm < 13.1, 13.2, and 17.6, respectively, i.e., the posterior is cut at the prior boundary. The \"detection\" in the full CMB+DESI+PP+RSD combination (10^7 wdm = 4.0^{+2.5}_{-2.3}) arises only after including RSD, which favors smaller S8. Because the one-sided nature of the prior influences the posterior shape, the authors should quantify the sensitivity of the detection to the prior (e.g., by using a different lower bound or a prior that permits c_s^2 < 0 with a Jeans-type stabilization) and should interpret the result as a one-sided measurement rather than a two-sided detection. Without this, the statement \"statistically significant signal\" is not robust.","section":"Section 3 (Table 1) and Section 4"},{"comment":"The initial conditions for the dark matter perturbations are set by assuming a \"density-infinitesimal CDM component\" with zero velocity divergence. This is an ad hoc prescription; the paper does not show that these are the growing-mode adiabatic initial conditions for a fluid with wdm ≠ 0 in the synchronous gauge. Since the claimed signal is driven by the perturbation-level sound-speed term, the analysis should validate this choice (e.g., by comparing with a full multi-fluid initial-condition solver or by testing the sensitivity of the wdm posterior to alternative initial conditions). At minimum, the caveat should be stated.","section":"Section 2, Eqs. (14)-(15)"}],"minor_comments":[{"comment":"Equation (4) is missing a factor 1/3: from Eq. (3) the correct relation is wde = -1 + (1/3)(1+z) d ln Ωde/dz. As written, Eq. (4) is inconsistent with Eq. (5), which is the standard PEDE expression. Please correct Eq. (4).","section":"Section 2, Eq. (4)"},{"comment":"There are several typos and grammatical errors, including \"signifiant\" (twice), \"increasd\", \"vaules\", and \"ofwdm\"; a careful proofread is needed.","section":"Section 4"},{"comment":"The phrase \"seemingly opposite\" is imprecise: the previous paper (Yao et al. 2024) fixed c_s^2 = 0, so the difference in results is expected given the different model assumptions. The authors should clarify this point more directly.","section":"Section 4"},{"comment":"The RSD likelihood description states that k is fixed at 0.1 Mpc for f σ8; please clarify whether this is the same convention as the Gold-2018 public likelihood and whether the scale dependence of f in Eq. (17) is consistently evaluated.","section":"Section 3"},{"comment":"The large asymmetric errors on σ8 and S8 for PEDE+wDM (e.g., σ8 = 0.776^{+0.077}_{-0.029}) reflect the truncated wdm posterior; reporting the posterior mode or median in addition to the mean would help interpret the non-Gaussian distributions.","section":"Tables 3 and 4"}],"recommendation":"major_revision","confidential_remarks":"The paper is a routine parameter-constraint study whose central quantitative result (the wdm detection) is physically interpretable only as a sound-speed constraint under a barotropic ansatz. The referee recommends requiring a two-parameter fit (wdm and c_s^2 separately) or a clear reframing, plus a robustness check on the wdm ≥ 0 prior. The Bayesian evidence strongly disfavors the model, which further tempers the claimed significance. The scope is appropriate for a journal like RAA, but the abstract should be adjusted to avoid overstating the EoS measurement."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Short version: this is a standard MCMC constraint update, not a new mechanism. The model takes dark matter as a barotropic fluid with wdm = c_s^2 (zero non-adiabatic sound speed and viscosity), places it on a PEDE background, and fits Planck 2018 + DESI BAO + Pantheon Plus + Gold18 RSD. The new content relative to Yao et al. 2024 is that the DM sound speed is no longer fixed to zero, plus a more modern data set. That is a genuine, if incremental, step.\n\nWhat it does well: the analysis is standard and transparent enough to follow. The authors honestly report that LambdaCDM is preferred with very strong evidence for the full data combination (ln B = -25.14). They also explicitly note that the S8 reduction comes from the sound-speed term, not from the EoS, because wdm ~ 1e-7 has negligible background effect. That is the right kind of honesty.\n\nThe soft spots are real but not fatal. First, Eq. (4) is inconsistent with Eq. (5) by a missing factor 1/3 and a wrong (1+z) placement; Eq. (5) is the correct known PEDE expression, so the results likely rest on the right formula, but the typo must be fixed. Second, the flat prior wdm >= 0 truncates the posterior at zero. For the CMB, CMB+DESI, and CMB+DESI+PP combinations, the posteriors are upper limits touching zero; the quoted 95% interval for the RSD combination is one-sided in shape. The bound is motivated by avoiding imaginary sound speeds, but the authors should show how much of the detection is prior-driven. Third, and most important for interpretation: with c_nad,dm = 0, the sound speed is locked to the EoS. The data combination is essentially measuring a small positive rest-frame sound speed; calling it a positive dark matter equation of state is a statement about the ansatz, not an independent measurement. Separating wdm from c_s^2 would require a two-parameter GDM fit. The authors themselves almost admit this in Section 4, so they are not hiding the issue. Fourth, the modified CLASS code is not released, so the perturbation implementation is not independently checkable.\n\nBottom line: the central statistical result is plausible, the model is clearly disfavored, and the paper is a useful constraint rather than an overclaim. It deserves a serious referee. I would send it to review, with requests to fix Eq. (4), release the code, and discuss the prior and the wdm = c_s^2 identification more explicitly.","headline":"A workmanlike constraint update: the claimed positive DM EoS is really a positive sound speed under the barotropic ansatz, and the model still loses badly to LambdaCDM on Bayesian evidence.","tokens_in":14723,"tokens_out":3759,"would_cite":false,"duration_ms":35154,"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":"The paper reports a statistically significant positive dark matter equation of state, implying a small positive sound speed, when dark matter is modeled as a barotropic fluid and dark energy as phenomenological emergent dark energy.","keywords":["dark matter equation of state","barotropic dark matter","phenomenological emergent dark energy","generalized dark matter","cosmological parameter constraints","redshift space distortions","Bayesian evidence","small-scale structure"],"falsifier":"Measure the dark-matter-induced matter power spectrum or $f\\sigma_8$ at several wavenumbers and check whether the suppression has the scale dependence predicted by a constant barotropic sound speed $c_s^2\\approx4\\times10^{-7}$; alternatively, fit the same data with a generalized dark matter model that allows a free non-adiabatic sound speed and viscosity and see whether the positive $w_{\\rm dm}$ signal survives.","tokens_in":13525,"feed_emoji":"🔭","tokens_out":7409,"duration_ms":71131,"temperature":0.7,"pith_summary":"This paper tests the assumption that dark matter is perfectly cold by replacing it with a barotropic fluid whose constant equation-of-state parameter also sets its sound speed, and by replacing the cosmological constant with phenomenological emergent dark energy. Using Planck CMB, DESI BAO, Pantheon Plus supernovae, and Gold 2018 redshift-space distortion data, the authors report a statistically significant positive dark matter equation of state at 95% confidence for the full data combination. A positive sound speed suppresses small-scale structure growth and lowers the inferred values of sigma_8 and S_8, offering a possible route toward addressing the small-scale problems of cold dark matter. However, Bayesian evidence strongly favors the LambdaCDM model over this new model, so the detection is a feature within a model that is overall disfavored.","feed_headline":"Tiny positive dark-matter pressure found in combined data","feed_subtitle":"The signal lowers small-scale clustering and S8, but the model still loses strongly to LambdaCDM.","key_machinery":"The load-bearing piece is the identification of dark matter as a barotropic fluid with a single number controlling both pressure and perturbations: $w_{\\rm dm}=c_{s,\\rm dm}^2=c_{ad,\\rm dm}^2$, with non-adiabatic sound speed and viscosity set to zero. In the perturbed FRW equations this puts a term $w_{\\rm dm} k^2 \\delta_{\\rm dm}/(1+w_{\\rm dm})$ into the DM velocity-divergence equation, so a positive $w_{\\rm dm}$ acts as a pressure gradient that resists gravitational collapse and suppresses the small-scale matter power spectrum. The dark energy side is the PEDE parameterization $\\Omega_{\\rm de}(z)=\\Omega_{\\rm de0}[1-\\tanh(\\log_{10}(1+z))]$, whose equation of state approaches $-1$ in the future but is phantom-like today; PEDE has the same number of free parameters as flat $\\Lambda$CDM, which keeps the model comparison clean.","core_discovery":"The central claim is that current cosmological data, when the dark energy sector is taken to be phenomenological emergent dark energy, prefer a dark matter sector that is not perfectly cold: a barotropic DM fluid with constant equation of state $w_{\\rm dm}$ whose rest-frame sound-speed squared equals it, $c_{s,\\rm dm}^2 = c_{ad,\\rm dm}^2 = w_{\\rm dm}$, with zero non-adiabatic sound speed and zero viscosity. For the data combination CMB+DESI+PP+RSD the posterior is $10^7 w_{\\rm dm} = 4.0^{+2.5}_{-2.3}$ at 95% confidence, so $w_{\\rm dm}$ is positive at roughly $4\\times10^{-7}$. This positive barotropic pressure suppresses the matter power spectrum at small scales and lowers $\\sigma_8$ and $S_8$ compared with the same model at $w_{\\rm dm}=0$; the redshift-space distortion data are what drive the detection, since they prefer a lower $S_8$ than CMB alone. At the same time, the model comparison gives $\\ln B = -25.14$ relative to $\\Lambda$CDM, which the paper reads as very strong evidence against the PEDE+$w_{\\rm DM}$ model despite the within-model signal.","pith_inferences":["If dark matter has any non-adiabatic pressure, viscosity, or a redshift-dependent equation of state, the inferred positive $w_{\\rm dm}$ would soak up those effects; fitting a generalized dark matter model with separate non-adiabatic sound speed and viscosity to the same data is the direct test of the barotropic assumption.","The sign flip from a negative dark-matter equation of state in an earlier zero-sound-speed analysis to a positive one here suggests that the constraint is model-dependent, and future datasets that sharpen $S_8$ will determine whether the positive pressure is preferred.","A barotropic sound speed of order $10^{-7}$ suppresses structure over a specific range of scales; high-resolution small-scale probes such as Lyman-$\\alpha$ forest or galaxy clustering at high $k$ could confirm or falsify that scale dependence.","The Bayesian penalty against the model comes from both the extra parameter and the worse fit; if future data keep the $S_8$ deficit, the balance could shift."],"forward_implications":["If the positive signal is real, cold dark matter is not exactly pressureless: a barotropic sound speed near $4\\times10^{-7}$ suppresses low-mass structure formation, offering a physical route to address small-scale problems without invoking warm or interacting dark matter.","The addition of RSD data is what turns an upper limit into a detection: with CMB, CMB+DESI, and CMB+DESI+PP alone the 95% interval for $10^7w_{\\rm dm}$ is consistent with zero, while including Gold2018 $f\\sigma_8$ data gives the positive value.","Within this model, a positive equation of state lowers $\\sigma_8$ and $S_8$: for CMB+DESI+PP+RSD the fit gives $\\sigma_8=0.778\\pm0.021$ and $S_8=0.758\\pm0.021$ versus $\\sigma_8=0.8532\\pm0.0060$ and $S_8=0.8261\\pm0.0094$ for PEDE with cold dark matter.","Bayesian evidence still prefers $\\Lambda$CDM very strongly over PEDE+$w_{\\rm DM}$ for the datasets that include Pantheon Plus, so the detection is a feature within a model that is overall disfavored."],"supporting_citations":[{"why":"Introduces the PEDE parameterization used for the dark-energy sector.","marker":"Li & Shafieloo 2019"},{"why":"The earlier PEDE+cold-DM-with-EoS analysis this paper extends and compares against.","marker":"Yao et al. 2024"},{"why":"Provides the generalized dark matter framework with equation of state, sound speed, and viscosity.","marker":"Hu 1998"},{"why":"Derives the perturbation equations the paper uses for dark matter and dark energy.","marker":"Kumar et al. 2019"},{"why":"Supplies the Planck 2018 CMB temperature and polarization likelihoods.","marker":"Aghanim et al. 2020b"},{"why":"Provides the DESI first-year BAO measurements.","marker":"Adame et al. 2024c"},{"why":"Supplies the Pantheon Plus supernova compilation.","marker":"Scolnic et al. 2022"},{"why":"Provides the Gold 2018 RSD $f\\sigma_8$ dataset whose inclusion drives the positive $w_{\\rm dm}$ detection.","marker":"Sagredo et al. 2018"},{"why":"Implements the Bayesian evidence computation used in model comparison.","marker":"Heavens et al. 2017a,b"}],"fun_headline_variants":["Tiny DM pressure found, but LambdaCDM wins on evidence","Dark matter may have slight pressure, yet LambdaCDM persists","Positive DM pressure hinted, but model loses to LambdaCDM","Small DM pressure seen, but standard model still favored"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The detection hinges on treating dark matter as exactly barotropic, with zero non-adiabatic sound speed and zero viscosity, so that every small-scale suppression is attributed to a positive equation-of-state parameter; if dark matter has any entropy pressure or viscosity, the inferred $w_{\\rm dm}$ would not isolate the equation of state.","fun_headline_variants_meta":{"raw":{"variants":["Tiny DM pressure found, but LambdaCDM wins on evidence","Dark matter may have slight pressure, yet LambdaCDM persists","Positive DM pressure hinted, but model loses to LambdaCDM","Small DM pressure seen, but standard model still favored"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.0003,"raw_usage":{"total_tokens":1795,"prompt_tokens":1074,"completion_tokens":721,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":690,"completion_tokens_details":{"reasoning_tokens":651}},"tokens_in":690,"tokens_out":721,"duration_ms":7145,"temperature":1.0,"reasoning_tokens":651,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-06T15:17:09.883786+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Measure the dark-matter-induced matter power spectrum or $f\\sigma_8$ at several wavenumbers and check whether the suppression has the scale dependence predicted by a constant barotropic sound speed $c_s^2\\approx4\\times10^{-7}$; alternatively, fit the same data with a generalized dark matter model that allows a free non-adiabatic sound speed and viscosity and see whether the positive $w_{\\rm dm}$ signal survives.","supporting_citations":[{"cited_title":"2024, Physical Review D, 109, 063502 2, 8, 11","cited_arxiv_id":null,"evidence_quote":"The earlier PEDE+cold-DM-with-EoS analysis this paper extends and compares against."},{"cited_title":"C., & Yadav, S","cited_arxiv_id":null,"evidence_quote":"Derives the perturbation equations the paper uses for dark matter and dark energy."},{"cited_title":"2022, The Astrophysical Journal, 938, 113 6","cited_arxiv_id":null,"evidence_quote":"Supplies the Pantheon Plus supernova compilation."},{"cited_title":"2018, Physical Review D, 98, 083543 6","cited_arxiv_id":null,"evidence_quote":"Provides the Gold 2018 RSD $f\\sigma_8$ dataset whose inclusion drives the positive $w_{\\rm dm}$ detection."}],"review_version":1}