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Exploring non-cold dark matter in a scenario of dynamical dark energy with DESI DR2 data

T0 review · 2 major / 5 minor · reviewed 2026-08-06 · deepseek-v4-flash

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Pith's one-line read This paper claims that Planck, DESI DR2, and supernova data contain a 3.3σ hint that dark matter has a small positive equation of state, but only when dark energy's equation of state is held constant; allowing dark energy to evolve…

desk verdict Solid constraints, but the headline wdm preference rests on a missing nested model comparison and should be read as a hint, not a detection. read the letter →

arxiv 2507.07798 v1 pith:22MPN5VZ submitted 2025-07-10 astro-ph.CO gr-qchep-ph

Tian-Nuo Li , Peng-Ju Wu , Guo-Hong Du , Yan-Hong Yao , Jing-Fei Zhang , Xin Zhang This is my paper
classification astro-ph.COgr-qchep-ph
keywords darkmatterequationofstatenon-colddynamicalenergyDESIDR2BAOcosmicmicrowavebackgroundtypeIasupernovaeBayesianevidencew0waparametrization
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

The paper asks whether dark matter is genuinely cold, and whether the answer depends on how dark energy is modeled. Fitting a free dark-matter equation of state $w_{\rm dm}$ to Planck CMB, DESI DR2 BAO, and two type Ia supernova catalogs, it finds a $2.8\sigma$–$3.3\sigma$ preference for a small positive $w_{\rm dm}$ when dark energy is assumed to have a constant equation of state. When dark energy is allowed to evolve as $w(a)=w_0+w_a(1-a)$, that preference drops to $0.8\sigma$–$1.1\sigma$. The central message is that the apparent warmth of dark matter is entangled with the dark-energy parametrization, so the nonzero-$w_{\rm dm}$ hint is not yet a standalone discovery. The paper also finds that freeing $w_{\rm dm}$ pulls $w_0$ and $w_a$ closer to the $\Lambda$CDM values and, for one dataset combination, makes the evolving-dark-energy model statistically comparable to $\Lambda$CDM.

What carries the argument

The load-bearing object is the dark-sector perturbation system: the continuity and Euler equations for density and velocity perturbations of dark matter and dark energy, with the equation-of-state and sound-speed assignments $w_{\rm dm}$ free, $c^2_{s,\rm dm}=0$, $c^2_{s,\rm de}=1$. In the background, a nonzero $w_{\rm dm}$ changes the dark-matter density evolution from $a^{-3}$ to $a^{-3(1+w_{\rm dm})}$; in the perturbations, it changes the source terms that shape CMB anisotropies and lensing. This machinery is what lets the same Planck, DESI, and supernova data act as a ruler for the dark-matter equation of state, and it is also where the model's assumptions enter.

What would settle it

Repeat the Planck + DESI DR2 + DESY5 likelihood analysis with dark matter represented by a warm-dark-matter distribution function or by a fluid with a scale-dependent sound speed; if the $w_{\rm dm}>0$ preference remains above $3\sigma$, the perfect-fluid parameterization is not creating the signal, and if it drops, the reported preference is an artifact of that parameterization.

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Extended reading notes

Core claim

Treating dark matter as a perfect fluid with a free, constant equation of state $w_{\rm dm}$ and zero sound speed, and scanning three dark-energy models ($\Lambda$CDM, constant $w$, and $w_0w_a$CDM), the authors use Planck CMB (including PR4 lensing), DESI DR2 BAO, and DESY5 or PantheonPlus supernovae to constrain $w_{\rm dm}$. In the constant-$w$ model, the data give $w_{\rm dm}=0.00147\pm0.00045$ and $w=-0.916\pm0.026$, a $3.3\sigma$ deviation from cold dark matter; in the evolving-$w$ model, the same data give $w_{\rm dm}=0.00040^{+0.00050}_{-0.00057}$ (DESY5) and $w_{\rm dm}=0.00058^{+0.00059}_{-0.00052}$ (PantheonPlus), below $1.1\sigma$. The authors conclude that the evidence for non-cold dark matter is strong only when dark energy's equation of state is held constant, because $w$ and $w_{\rm dm}$ are positively correlated, and that adding $w_{\rm dm}$ makes dynamical dark energy look less extreme relative to $\Lambda$CDM.

Load-bearing premise

The paper treats dark matter as a single perfect fluid with a constant equation of state and exactly zero sound speed; if the real dark matter has a velocity distribution, a scale-dependent sound speed, or viscosity, the inferred positive $w_{\rm dm}$ would not be a measurement of its true equation of state.

Editorial extensions

If this is right

  • If the constant-$w$ result is taken at face value, dark matter carries a small positive pressure, $w_{\rm dm}\sim1.5\times10^{-3}$, meaning it is not perfectly cold but is far from relativistic.
  • The positive $w$–$w_{\rm dm}$ correlation implies that any claim about dark energy from DESI BAO should be accompanied by a simultaneous fit for the dark-matter equation of state, or the two signals can be confused.
  • The weakening to $0.8\sigma$–$1.1\sigma$ in the $w_0w_a$ model means current data cannot jointly establish both evolving dark energy and non-cold dark matter; one of the two must take priority.
  • The Bayes factor of $-0.97$ for the $w_0w_a$nCDM model with CMB+DESI+DESY5 means the extra $w_{\rm dm}$ parameter does not penalize the model enough to rule it out against $\Lambda$CDM.
  • Freeing $w_{\rm dm}$ shifts the best-fit $w_0$ and $w_a$ toward $(-1,0)$, so a small dark-matter pressure absorbs part of what otherwise looks like dark-energy dynamics.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • A testable extension: rerunning the same likelihood analysis with dark matter modeled as a thermal warm-dark-matter distribution instead of a zero-sound-speed fluid would show whether the $3.3\sigma$ preference survives a more physical perturbation treatment; this paper does not perform that test.
  • The same degeneracy likely contaminates other recent DESI-based dark-energy results: any change in the background expansion can be partially traded against a small dark-matter pressure, so future DESI analyses should report $w_{\rm dm}$ alongside $w_0$ and $w_a$.
  • Measurements that separate expansion from growth, such as redshift-space distortions or tomographic cosmic-shear data, could break the $w$–$w_{\rm dm}$ correlation in a way the current CMB+BAO+SN combination cannot.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

2 major / 5 minor

Summary. This paper constrains a constant dark-matter equation-of-state parameter wdm in three dark-energy frameworks (ΛnCDM, wnCDM, and w0wanCDM) using Planck CMB data (including PR4 lensing), DESI DR2 BAO, and DESY5 or PantheonPlus supernova samples. The analysis uses a modified CLASS code with Cobaya, reports marginalized 1σ constraints, posterior contour plots, and Bayesian evidence relative to ΛCDM. The central finding is that CMB+DESI+DESY5 gives wdm = 0.00147 ± 0.00045 in the wnCDM model, quoted as a 3.3σ preference for wdm > 0, while the preference drops to 0.8σ–1.1σ when the dark-energy equation of state is allowed to evolve as w(a) = w0 + wa(1−a). The paper also discusses how letting wdm vary shifts the inferred w0 and wa toward ΛCDM expectations.

Significance. If the preference for wdm > 0 is robust, the result is an interesting hint of non-cold dark matter and a useful illustration of the strong dependence of such hints on the assumed dark-energy parametrization. The paper deserves credit for using a standard, publicly available pipeline, reporting priors and convergence criteria, and presenting Bayesian evidence alongside parameter constraints. However, the headline significance is not backed by the model comparison that would establish a preference for non-cold DM over ordinary cold DM, and the physical interpretation is contingent on a single-fluid, constant-equation-of-state, zero-sound-speed modeling ansatz. The study is incremental but publishable after the missing nested model comparison is supplied and the claims are moderated accordingly.

major comments (2)
  1. [Sec. III, Table III] The headline 3.3σ preference for a non-zero wdm is a marginalized posterior exclusion of wdm = 0 within the wnCDM model, not a model comparison between wnCDM and wCDM. Because w and wdm are positively correlated, the wCDM model can partially absorb the signal by shifting w: for CMB+DESI+DESY5, w moves from −0.969 ± 0.020 (wCDM) to −0.916 ± 0.026 (wnCDM) in Table II. The paper must report the nested Bayes factors ln B(wnCDM/wCDM), ln B(w0wanCDM/w0waCDM), and, ideally, ln B(ΛnCDM/ΛCDM). Table III only gives evidence relative to ΛCDM; it does not answer whether the extra wdm parameter is favored once the Occam penalty is applied. A rough Savage–Dickey estimate using the reported posterior width (0.00045) and the prior width (0.2) gives ln B(wnCDM/wCDM) of order −0.1 to +1, i.e., inconclusive, despite the 3.3σ. The authors should either compute these nested evidences or explicitly temper the language from 'preference' to 'parameter-space hint with unknown evidence weight.'
  2. [Sec. II.A, Eqs. (4)-(5)] The physical interpretation of wdm as the dark-matter equation of state is contingent on the perfect-fluid assumption with constant wdm and zero sound speed, c_s,dm^2 = 0, as fixed after Eq. (5). A real non-cold dark-matter component with a distribution function or viscosity would generally have a scale-dependent sound speed and anisotropic stress, and the CMB response to wdm could be substantially different. The inferred wdm > 0 might then absorb other microphysical effects rather than measuring the true equation of state. The paper should add an explicit caveat that the 3.3σ result is a statement within this specific phenomenological model, and ideally test the sensitivity to nonzero c_s,dm^2 or to an adiabatic sound-speed choice before claiming evidence for non-cold dark matter.
minor comments (5)
  1. [Abstract] The phrase 'within the content of a constant DE EoS' should read 'within the context of a constant DE EoS.'
  2. [Throughout] The capitalization of the supernova sample is inconsistent: 'PantheonPlus' in the text but 'pantheonPlus' in Figs. 1–3 and Table II; please standardize.
  3. [Sec. I] There are minor grammatical issues, e.g., 'Observational evidence suggest' should be 'Observational evidence suggests', and 'Although the ΛCDM model has been successful' would read more smoothly.
  4. [Sec. III, Fig. 4 and text] The statement that w0wanCDM yields w0 and wa 'closer to the ΛCDM expectations' should note that the shifts are within the 1σ uncertainties and are not statistically significant on their own.
  5. [Sec. IV, Conclusion] The sentence 'the Bayesian evidence indicates that the w0wanCDM model is comparably favored to the ΛCDM model' should specify that this holds only for the CMB+DESI+DESY5 data combination, since Table III gives ln B = −0.97 for that case and moderate-to-strong evidence against w0wanCDM for the other combinations.

Circularity Check

0 steps flagged · score 2.0 of 10

No significant circularity: the paper reports standard MCMC parameter estimation, not a derivation that reduces to its own inputs.

full rationale

The paper makes no first-principles derivation claim; it performs Markov Chain Monte Carlo parameter estimation and reports marginalized posterior constraints. The wdm value and its quoted sigma are fitted outputs from the same likelihood that is used to report the preference, which is ordinary statistical inference rather than circular reasoning. The model is defined explicitly in Eqs. (1)-(5), where wdm enters the background and perturbation equations as a free parameter, and no equation is asserted to follow from another claim of the paper. Citations to the authors' prior works, such as Refs. [28], [33], [37], and [70], are contextual literature references and are not used as evidence to establish the present constraint; they therefore are not load-bearing. The stated simplifications (c_s,de^2 = 1 and c_s,dm^2 = 0) are modeling assumptions, not circular reductions. The absence of a nested Bayesian comparison of wnCDM versus wCDM is a model-selection limitation and a correctness concern, not a circularity: the 3.3 sigma statement is explicitly a marginal-posterior exclusion of wdm = 0, not a fitted parameter disguised as an independent prediction. On the supplied text, the central claim has independent empirical content and the circularity score is low.

Assumptions & free parameters 4 free parameters · 5 assumptions · 0 invented entities

The model adds one phenomenological parameter, wdm, to otherwise standard dark-sector fluids. The paper does not provide a microphysical origin or an independent probe for wdm; the preference is a fit to the same data used to constrain the dark energy parameters, so the significance is not a standalone detection.

free parameters (4)
  • wdm (dark matter equation of state) = 0.00084 +/- 0.00035 (Lambda nCDM, CMB+DESI); 0.00147 +/- 0.00045 (w nCDM, CMB+DESI+DESY5); 0.00058 +/- 0.00059 (w0wa…
    Central free parameter of the paper, constrained from the same CMB/BAO/SN data. The headline significances are the sigma distances of this fitted value from zero.
  • w (constant dark energy equation of state) = e.g., -0.916 +/- 0.026 for w nCDM with CMB+DESI+DESY5; -1.050 +/- 0.039 for wCDM with CMB+DESI
    Standard extension parameter fitted jointly with wdm; its positive correlation with wdm drives the stronger preference in the w nCDM model.
  • w0 and wa (time-varying dark energy equation of state) = e.g., w0 = -0.862 +/- 0.056, wa = -0.43 +/- 0.32 for w0wa nCDM with CMB+DESI+PantheonPlus
    Chevallier-Polarski-Linder parameters fitted in the w0wa-nCDM model; when freed, the wdm preference weakens to 0.8-1.1 sigma.
  • Standard Lambda-CDM base parameters (omega_b, omega_dm, theta_s, tau_reio, ln(10^10 A_s), n_s) = not tabulated individually in the paper beyond priors in Table I
    Fitted base parameters in all models; not central to the dark sector claim but required for the likelihood evaluation.
assumptions (5)
  • standard math The universe is spatially flat, homogeneous, isotropic, and described by the FRW metric with General Relativity (Eq. (1)).
    Background expansion model under test; standard cosmology.
  • domain assumption Dark matter and dark energy are minimally coupled perfect fluids with no non-gravitational interactions.
    Section II.A states this; if interactions exist, the constraints would change.
  • ad hoc to paper Non-cold dark matter has a constant equation of state wdm and zero sound speed c_s,dm^2 = 0 in the perturbation equations.
    Phenomenological model introduced at Section II.A after Eq. (5); the central claim depends on this fluid description.
  • domain assumption Dark energy sound speed is fixed to c_s,de^2 = 1.
    Standard choice for smooth dark energy, stated in Section II.A; a different sound speed would alter perturbation constraints.
  • domain assumption External likelihoods (Planck CamSpec/Commander/SimAll and PR4 lensing, DESI DR2 BAO, DESY5, PantheonPlus) are correctly calibrated and independent.
    All results inherit the systematics of these public data products; the paper does not assess cross-dataset systematics.

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Cite this review

Pith. "Pith review of Exploring non-cold dark matter in a scenario of dynamical dark energy with DESI DR2 data." pith.science (2026). https://pith.science/paper/22MPN5VZ

@misc{pith2026250707798,
  author       = {Pith},
  title        = {Pith review of: Exploring non-cold dark matter in a scenario of dynamical dark energy with DESI DR2 data},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/22MPN5VZ}},
  note         = {Machine review of arXiv:2507.07798}
}
abstract

Recent observations of DESI hint that dark matter (DM) may not be cold but have a non-zero equation of state (EoS) parameter, and that dark energy (DE) may not be a cosmological constant. In this work, we explore the possibility of a non-zero DM EoS parameter within the framework of dynamical DE. We perform analysis by using the latest baryon acoustic oscillation (BAO) data from DESI DR2, the cosmic microwave background (CMB) data from Planck, and the type Ia supernova (SN) data from DESY5 and PantheonPlus. When using the combination of CMB, BAO, and SN data, our results indicate a preference for a non-zero DM EoS parameter at the $2.8\sigma$ and $3.3\sigma$ level within the content of a constant DE EoS. In contrast, for a time-evolving DE EoS parameterized by $w_0$ and $w_a$, this preference decreases to $0.8\sigma$ and $1.1\sigma$. Furthermore, allowing a non-zero DM EoS yields best-fit values of $w_0$ and $w_a$ that exhibit smaller deviations from the $\Lambda$CDM expectations, and Bayesian evidence analysis shows a comparable preference for this model relative to $\Lambda$CDM. The overall results of this work indicate that a non-zero DM EoS parameter warrants further exploration and investigation.

Figures

Figures reproduced from arXiv: 2507.07798 by the authors.

Figure 1
Figure 1. FIG. 1. The 1D marginalized posterior constraints [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2. Constraints on the cosmological parameters using the CMB, DESI, DESY5, and PantheonPlus data in the [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3. Constraints on the cosmological param [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗
Figures from the paper (2 more)
Figure 4
Figure 4. Figure 4: FIG. 4. Comparison of the constraints on [PITH_FULL_IMAGE:figures/full_fig_p006_4.png]
Figure 5
Figure 5. Figure 5: FIG. 5. The evolution of DE EoS [PITH_FULL_IMAGE:figures/full_fig_p006_5.png]

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