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ACT DR6 Leads to Stronger Evidence for Dynamical Dark Matter

T0 review · 5 major / 4 minor · reviewed 2026-08-06 · deepseek-v4-flash

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Pith's one-line read Combining ACT DR6, DESI DR2, and DESY5 data, the paper reports 3.4σ evidence that dark matter has an evolving equation of state, with pressure proportional to the cosmic scale factor.

desk verdict Careful ACT DR6 constraint work on a CPL-like dark-matter EoS, but the headline 3.4σ detection is contradicted by the paper's own single-parameter SDDM null and by dataset-dependent significance shifts. read the letter →

arxiv 2506.23029 v1 pith:OMNU4YVG submitted 2025-06-28 astro-ph.CO astro-ph.HEgr-qc

Deng Wang , Kazuharu Bamba This is my paper
classification astro-ph.COastro-ph.HEgr-qc
keywords dynamicaldarkmatterequationofstateACTDR6DESIDR2DESY5cosmicmicrowavebackgroundbaryonacousticoscillationslarge-scalestructure
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 tries to establish that dark matter is not the pressureless, time-independent fluid assumed by standard cosmology, but has an equation of state that changes with the expansion of the universe. Using ACT DR6 cosmic microwave background data together with DESI DR2 baryon acoustic oscillations and DESY5 supernovae, it finds a 3.4σ preference for a nonzero evolution parameter ωdma=0.088±0.030. It also claims that ACT alone, without Planck, confirms the linear relation ωdma=−ωdm0, so that the dark-matter equation of state is directly proportional to the scale factor. If this is right, the dark sector contains an evolving dark-matter component, and structure growth, cosmic acceleration, and the fate of the universe would all need to be reconsidered.

What carries the argument

The central object is the CPL-style dark-matter equation of state ωdm(a)=ωdm0+ωdma(1−a), inserted into the Friedmann equations through ΩDM(a)=Ωdm $a^{{-3(1+ωdm0+ωdma)}}$ $e^{{3ωdma(a−1)}}$. The paper develops DDMCAMB, a modified version of the CAMB Boltzmann code, to compute background and perturbation evolution for arbitrary dark-matter equation-of-state models, and fits three models—full DDM, single-parameter proportional SDDM, and DDME with a CPL dark-energy component—to ACT DR6, DESI DR2, DESY5, and Planck data with MCMC. The load-bearing identity is the linear relation ωdma=−ωdm0, which reduces the two free parameters to one and makes the dark-matter pressure track the scale factor directly.

What would settle it

Re-run the ACT+DESI+DESY5 fit with the comoving sound horizon treated as a free parameter or calibrated by a local distance ladder; if ωdma drops to within about 1σ of zero, the 3.4σ is a calibration artefact. A second check is to compute the model-selection evidence for DDM against ΛCDM, since the single-parameter proportional model already returns ωdm=0.006±0.015.

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Extended reading notes

Core claim

The central discovery is that a dark-matter equation of state of the form ωdm(a)=ωdm0+ωdma(1−a) is preferred over pressureless cold dark matter at the 3.4σ level when ACT DR6 CMB data are combined with DESI DR2 BAO and DESY5 supernovae. The best-fit values ωdma=0.088±0.030 and ωdm0=−0.084±0.029 are consistent with the linear relation ωdma=−ωdm0, implying that the dark-matter equation of state is proportional to the scale factor a. ACT data alone independently support that same relation, matching the earlier Planck-based result. The paper also finds that adding Planck lowers the significance to 2.98σ and adding DESY1 large-scale-structure data lowers it to 1.50σ, while the proportional relation remains. The broader claim is that the dark sector is likely dynamical dark matter plus dynamical dark energy rather than cold dark matter plus a cosmological constant.

Load-bearing premise

The 3.4σ result rests on the assumption that the ACT+DESI+DESY5 combination measures the dark-matter evolution parameter without a systematic bias; the paper itself notes that combining CMB and DESI data produces a larger Hubble constant through the CMB's sound-horizon calibration, and if that bias mimics the signal, the evidence would vanish.

Editorial extensions

If this is right

  • Dark matter would not be cold and pressureless: its equation of state evolves with the scale factor, with negative pressure today if ωdm0<0.
  • Because the relation ωdma=−ωdm0 is confirmed by ACT independently of Planck, the dark-matter equation of state can be described by a single parameter proportional to a.
  • The same data combinations show roughly 2σ evidence for coexisting dynamical dark matter and dynamical dark energy, supporting the replacement of cold dark matter plus a cosmological constant by an evolving dark sector.
  • The DDM parameter space allowed by the tight ACT+DESI+DESY5 constraints produces measurable changes in the matter power spectrum, CMB lensing potential, velocity spectra, and lensing-galaxy correlations, so future surveys can test the model.
  • Adding Planck or DESY1 lowers the significance to about 3σ or 1.5σ, so the strength of the evidence depends on which datasets are combined.

Reading between the lines

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

  • Beyond the paper: a 3.4σ parameter significance in a two-parameter extension is not automatically model-selection evidence; the paper's own single-parameter SDDM fit shows no preference (ωdm=0.006±0.015), so a Bayesian comparison of DDM against ΛCDM could be considerably weaker.
  • Beyond the paper: the rd-induced Hubble-constant bias the authors flag implies a clean test—re-fit with rd calibrated from the local distance ladder or left free—and if ωdma then returns to zero, the headline signal is a distance-scale artefact.
  • Beyond the paper: the negative today's pressure implied by ωdm0≈−0.08 predicts suppressed small-scale structure growth (lower S8) relative to ΛCDM, a signature that DESI and next-generation lensing surveys should be able to check within a few years.
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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

5 major / 4 minor

Summary. The paper introduces a CPL-like parameterization for the dark matter equation of state, ωdm(a)=ωdm0+ωdma(1−a), and constrains it with ACT DR6 CMB anisotropy and lensing, DESI DR2 BAO, and DESY5 supernova data. It claims a 3.4σ detection of nonzero ωdma and states that ACT independently confirms the linear relation ωdma=−ωdm0, so that the DM EoS is proportional to the scale factor. The paper also constrains a one-parameter 'proportional' DDM model and a model with dynamical DE, and it presents forecasts for LSS observables. The central claim is that dark matter is not cold and pressureless over cosmic time.

Significance. If the 3.4σ detection were real, the paper would provide an important observational challenge to the standard CDM paradigm and would motivate new particle and modified-gravity scenarios. The work expands the parameter space explored in the authors' earlier study and uses an independent ACT DR6 likelihood, which is a useful cross-check. However, the evidence as presented is not robust: the quoted 1σ error gives only 2.9σ, the one-parameter SDDM version of the same model shows no preference for evolving DM from the same data (ωdm=0.006±0.015 in Table I), and adding DESY1 reduces the significance to 1.5σ. These internal checks, together with the authors' own warning about rd/H0 bias in CMB+DESI combinations, mean the central claim is not sustained.

major comments (5)
  1. [DDM evidence induced by ACT; Table I] The 3.4σ number in the abstract is not supported by the quoted errors. Table I lists ωdma=0.088±0.030 for ADS, which is 2.9σ from zero, and ωdm0=−0.084±0.029, also 2.9σ. If the 3.4σ significance is computed from a joint marginalized statistic or a profile likelihood, the paper should state the statistic and its definition; as written, the reader cannot reproduce the headline significance.
  2. [Table I and SDDM discussion] The SDDM result in Table I is internally inconsistent with the claim that ACT confirms the proportional relation. SDDM is the same model restricted to ωdma=−ωdm0, so its single parameter should track the DDM best fit along that line. Yet for ADS, SDDM gives ωdm=0.006±0.015, i.e., no preference for a non-zero DM EoS, whereas the DDM best fit lies at ωdm0=−0.084 and ωdma=0.088. This means the apparent DDM signal is not a robust preference along the claimed proportionality direction; it emerges only when the second EoS parameter is added. The paper does not reconcile this contradiction.
  3. [DDM versus LSS] The dataset-dependence of the result is not described accurately. Adding DESY1 changes ωdma from 0.088±0.030 to 0.039±0.026, a 1.5σ effect, and adding Planck to ADS lowers it to 0.063±0.025, below the 3σ threshold. The paper then excludes DESY1 on the grounds that it introduces inconsistencies. Because the exclusion is motivated by the effect it has on the result, the quoted 3.4σ should be treated as a selection-dependent finding rather than a robust detection.
  4. [Discussions and conclusions] The paper itself states that the combination of CMB and DESI gives biased constraints because the CMB-derived rd induces a larger H0, and it invokes this bias to explain the anomalous positive ωdm in SDDM for the AD data. Since the same mechanism could plausibly bias ωdma upward, the paper should verify with a concrete test, such as marginalizing over rd or comparing with a free sound-horizon calibration, that the ADS preference for ωdma>0 is not a propagation of this known bias. Without such a test, the unbiasedness assumption behind the headline claim is unsupported.
  5. [DDM evidence induced by ACT; Fig. 1] The 'confirmation' of the linear relation ωdma=−ωdm0 is a post-hoc reading of the posterior degeneracy. The one-dimensional constraints in Fig. 2 and the SDDM row in Table I show that the data do not independently prefer this line. The paper should report a model comparison, such as Δχ² or Bayesian evidence, for DDM, SDDM, and ΛCDM before treating the relation as a confirmed physical property.
minor comments (4)
  1. [Discussions and conclusions] The sentence 'we propose a conjecture that DM obeys the directly proportional DM EoS ωdma = ωdma emerged on cosmic scales' is not grammatical and should read ωdm(a)=ωdm a; as printed, it is meaningless.
  2. [Introduction and Supplementary A] The authors refer to their previous DDM work as 'Ref. [1]', but in the bibliography Ref. [1] is Penzias and Wilson (1965); the previous DDM paper is Ref. [69]. This makes it difficult to follow the line of reasoning.
  3. [Data and methodology] No statement of code or data availability is given; since the analysis uses a custom modification of CAMB (DDMCAMB), a public release or a clear statement of availability is needed for reproducibility.
  4. [Table I] The paper does not define how the 2σ upper limits in Table I are computed, whether marginal or profile; adding a footnote would remove ambiguity.

Circularity Check

1 steps flagged · score 6.0 of 10

The claimed ACT 'confirmation' of the proportional DM EoS is read off the same two-parameter fit that produced the relation, and the paper's own SDDM null shows the 3.4σ signal is not a stable, independent prediction.

  1. fitted input called prediction [Abstract; Section 'DDM evidence induced by ACT'; Table I]
    "Interestingly, ADS gives ωdma = 0.088 ± 0.030 indicating a 3.40 σ evidence of DDM ... ADS and APDS further help confirm the proportional DM EoS (see Fig. 1)."

    The '3.4σ evidence' is a marginalized parameter estimate of the two-parameter DDM fit, and the proportional relation ωdma = −ωdm0 is then read off the very same posterior (Fig. 1) and elevated to a 'confirmation.' That is a fitted input called a prediction. The paper's own Table I shows the single-parameter SDDM model, which imposes exactly that relation, gives ωdm = 0.006 ± 0.015 for the same ADS data — no DDM preference and inconsistent with the DDM best-fit on the line (ωdm0 ≈ −0.084). Thus the confirmation reduces to a degeneracy of the fitted two-parameter model, and the headline significance is not robust to restricting the model to the claimed relation.

full rationale

The new data (ACT DR6, DESI DR2, DESY5) are external and the MCMC pipeline is standard, so the numerical constraints are not circular in themselves. However, the central interpretative claim — that ACT independently confirms the linear relation ωdma = −ωdm0 and hence a directly proportional DM EoS — is a posterior degeneracy of the same fit presented as an independent confirmation. The SDDM model, which is exactly the proportional relation, yields no preference from the same ADS data (ωdm = 0.006 ± 0.015), demonstrating that the 3.4σ signal is driven by the extra freedom in ωdm0 rather than by data preference for the proportional model. The paper's own discussion of rd-induced H0 bias provides a plausible spurious-signal mechanism, and the arithmetic (0.088/0.030 ≈ 2.9σ) does not match the quoted 3.4σ. These are correctness risks; the circular element is specifically the use of the fitted posterior to 'confirm' the relation it was used to infer. Because the underlying data are external and the model is not defined in terms of the measured parameters, the partial circularity score is 6 rather than higher.

Assumptions & free parameters 6 free parameters · 5 assumptions · 0 invented entities

The central claim depends on two ad hoc EoS parameters fitted to the data, a CPL-like parametrization chosen without microphysical justification, and an unstated treatment of DM perturbative quantities in the fits. The linear relation is inferred from the posterior and then offered as a conjecture.

free parameters (6)
  • ωdm0 (today's DM equation of state) = -0.084 ± 0.029 (ADS, DDM)
    Fitted to ACT+DESI+DESY5; the 'negative pressure' side of the DDM signal.
  • ωdma (evolution amplitude) = 0.088 ± 0.030 (ADS, DDM)
    Fitted; its distance from zero is the 3.4σ claim.
  • ωdm (single-parameter proportional EoS) = 0.006 ± 0.015 (ADS, SDDM)
    Fitted; shows no DDM evidence, undercutting the DDM signal.
  • ω0, ωa (DE EoS parameters in DDME) = ω0 ≈ -0.758 ± 0.072, ωa ≈ -1.10 ± 0.50 (APDS)
    Fitted only in the DDME model; not central to the headline claim.
  • c_s,eff (DM effective sound speed) = scanned up to 3e-5 in LSS plots; presumably 0 in MCMC
    Not constrained; influences small-scale power spectrum.
  • σdm (DM shear) = scanned O(1e-3) in LSS plots; presumably 0 in MCMC
    Not constrained; affects small-scale clustering.
assumptions (5)
  • standard math Friedmann equations and GR background evolution
    Basics section, Eqs. (1) and the two Friedmann equations.
  • ad hoc to paper Dark matter is a perfect fluid with CPL-like EoS ωdm(a)=ωdm0+ωdma(1−a)
    Basics section; no microphysical derivation, adopted from the author's prior paper.
  • domain assumption DM perturbation equations with effective sound speed and shear (Eqs. 1-2 of Supplementary)
    Used in the code; the fitted analysis does not state the values of c_s,eff and σdm, so the perturbation sector is under-specified.
  • ad hoc to paper The linear relation ωdma = -ωdm0 is a physical property rather than a degeneracy direction
    Proposed as a conjecture in the Discussions after being read off the 2D posterior.
  • domain assumption Sroll2 likelihood provides an unbiased τ prior
    A Planck measurement used in all ACT-only analyses, so 'independent of Planck' is not strict.

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Cite this review

Pith. "Pith review of ACT DR6 Leads to Stronger Evidence for Dynamical Dark Matter." pith.science (2026). https://pith.science/paper/OMNU4YVG

@misc{pith2026250623029,
  author       = {Pith},
  title        = {Pith review of: ACT DR6 Leads to Stronger Evidence for Dynamical Dark Matter},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/OMNU4YVG}},
  note         = {Machine review of arXiv:2506.23029}
}
abstract

Dark matter is fundamental to the composition, structure, and evolution of the universe. Combining the ACT's cosmic microwave background, DESI's baryon acoustic oscillations with DESY5 type Ia supernova observations, we find a $3.4\,\sigma$ evidence for dynamical dark matter (DDM) with an equation of state, $\omega_{dm}(a)=\omega_{dm0}+\omega_{dma}(1-a)$. Independent of the Planck measurements, the ACT data confirms the linear relation $\omega_{dma}=-\omega_{dm0}$, inducing that the equation of state of dark matter is directly proportional to the scale factor $a$. Furthermore, the effects of DDM on the large-scale structure observables are thoroughly studied. Our findings are of great significance for understanding cosmic acceleration, structure growth, and the fate of the universe.

Figures

Figures reproduced from arXiv: 2506.23029 by the authors.

Figure 2
Figure 2. FIG. 2: One-dimensional marginalized posterior distribu [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3: One-dimensional and two-dimensional marginalized [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figure 1
Figure 1. FIG. 1: Two-dimensional marginalized posterior distributions of the DM EoS parameters from the ACT and Planck CMB [PITH_FULL_IMAGE:figures/full_fig_p008_1.png] view at source ↗
Figures from the paper (9 more)
Figure 2
Figure 2. Figure 2: FIG. 2: One-dimensional marginalized posterior distributions of the parameter [PITH_FULL_IMAGE:figures/full_fig_p009_2.png]
Figure 3
Figure 3. Figure 3: FIG. 3: The matter power spectra derived from different values of [PITH_FULL_IMAGE:figures/full_fig_p009_3.png]
Figure 4
Figure 4. Figure 4: FIG. 4: The CMB temperature, E-mode polarization, and temperature-E-mode polarization power spectra derived from dif [PITH_FULL_IMAGE:figures/full_fig_p010_4.png]
Figure 5
Figure 5. Figure 5: FIG. 5: The Weyl potential power spectra derived from different values of [PITH_FULL_IMAGE:figures/full_fig_p011_5.png]
Figure 6
Figure 6. Figure 6: FIG. 6: The CMB lensing potential power spectra derived from different values of [PITH_FULL_IMAGE:figures/full_fig_p012_6.png]
Figure 7
Figure 7. Figure 7: FIG. 7: The velocity power spectra derived from different values of [PITH_FULL_IMAGE:figures/full_fig_p012_7.png]
Figure 8
Figure 8. Figure 8: FIG. 8: The density-velocity cross power spectra derived from different values of [PITH_FULL_IMAGE:figures/full_fig_p013_8.png]
Figure 9
Figure 9. Figure 9: FIG. 9: The power spectra of the relative baryon-DM velocity derived from different values of [PITH_FULL_IMAGE:figures/full_fig_p014_9.png]
Figure 10
Figure 10. Figure 10: FIG. 10: The angular correlation coefficient between the CMB lensing and the simulated galaxy number counts observations [PITH_FULL_IMAGE:figures/full_fig_p015_10.png]

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