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The case for a low dark matter density in dynamical dark energy model from local probes

T0 review · 3 major / 5 minor · reviewed 2026-08-10 · deepseek-v4-flash

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Pith's one-line read A low matter density keeps Lambda-CDM concordant with local probes when the BAO sound horizon is treated as a free parameter.

desk verdict Modest but honest follow-up: low Omega_M concordance in LambdaCDM works only after freeing r_s, and the paper never shows how much DESI actually contributes once that freedom is granted. read the letter →

arxiv 2501.08915 v1 pith:N4IHOYFC submitted 2025-01-15 astro-ph.CO

Ziad Sakr This is my paper · ORCID
classification astro-ph.CO
keywords matterdensitycosmologicaltensionsHubbleconstantsigma8baryonacousticoscillationssoundhorizondynamicaldarkenergyBayesiananalysis
topics Dark Energy
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 the well-known disagreements over the Hubble constant $H_0$ and the matter-fluctuation amplitude $\sigma_8$ can be resolved not by new physics but by the matter density $\Omega_{\rm M}$ simply being lower than the value inferred from the cosmic microwave background. It combines local probes, including cluster counts, gas fractions in clusters, cosmic chronometers, supernovae, and a direct mass-to-light estimate of $\Omega_{\rm M}$, in a Bayesian analysis that deliberately relaxes calibration parameters degenerate with the tensions. The central result is that within $\Lambda$CDM, a low $\Omega_{\rm M}$ around 0.22 to 0.26 is compatible with the locally measured $H_0$ and $\sigma_8$, even after including DESI baryon acoustic oscillation data and the Pantheon+ supernova sample, provided the sound-horizon scale $r_s$ in the BAO likelihood is promoted to a free parameter. Within the dynamical dark energy model $w_0w_a$CDM, the same relaxation can make the local values mutually compatible, but only at equation-of-state parameters far from $\Lambda$CDM, and adding high-redshift supernovae pushes $\sigma_8$ too low. The paper concludes that a low matter density preserves concordance in $\Lambda$CDM, while dynamical dark energy fails to solve all tensions at once under the low-density hypothesis.

What carries the argument

The load-bearing object is the sound drag scale $r_s$, the comoving size of the baryon-acoustic-oscillation ruler at recombination. In standard BAO analyses $r_s$ is computed from the early-universe model, which ties the distance ladder to assumptions about pre-recombination physics; this paper instead promotes $r_s$ to a free nuisance parameter in the DESI BAO likelihood, exactly as other calibration parameters are relaxed for cluster counts, supernova magnitudes, and gas fractions. The comparison between runs with $r_s$ fixed and $r_s$ free isolates how much of the apparent tension is carried by that calibration assumption, and the CPL parametrisation $w(a) = w_0 + w_a(1-a)$ supplies the dynamical dark energy alternative. The rest of the system is a Bayesian combination of probes specifically chosen to constrain $\Omega_{\rm M}$, $H_0$, and $\sigma_8$ without importing CMB values for the tension parameters.

What would settle it

Take the same DESI BAO likelihood and impose a tight prior on $r_s$ from an independent early-universe measurement, for example the Planck-calibrated value near 147 Mpc with sub-percent uncertainty; if the posterior no longer allows $\Omega_{\rm M} \approx 0.22$ to $0.26$ together with local $H_0$ and $\sigma_8$, the low-density concordance is an artifact of the freed $r_s$.

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Extended reading notes

Core claim

On the paper's own terms, the discovery is this: the standard cosmological model can host the locally preferred values of the Hubble constant and the matter-fluctuation amplitude if the matter density is lower than the CMB-preferred value, and the apparent obstruction from baryon acoustic oscillations disappears once the sound drag scale $r_s$ is no longer derived from the assumed cosmology but fitted as a free parameter. Within $\Lambda$CDM, this low-density concordance survives every combination of local probes tried, including the Pantheon+ sample that had previously spoiled it. Within $w_0w_a$CDM, relaxing $r_s$ does allow $\Omega_{\rm M}$, $H_0$, and $\sigma_8$ to sit at their local values simultaneously, but only with $(w_0,w_a)$ clearly away from $(-1,0)$, and adding Pantheon+ forces $\sigma_8$ to values far below local estimates. The paper's conclusion is therefore that the low-matter-density hypothesis rescues $\Lambda$CDM concordance but offers no rescue to dynamical dark energy.

Load-bearing premise

The whole result depends on the assumption that freeing the BAO ruler length does not drain the baryon acoustic oscillation data of their constraining power, so that any $\Omega_{\rm M}$, $H_0$, and $\sigma_8$ combination would fit just as well once $r_s$ is allowed to float.

Editorial extensions

If this is right

  • Within $\Lambda$CDM, the $H_0$ and $\sigma_8$ tensions no longer force a departure from the standard model if $\Omega_{\rm M}$ is allowed to be low and $r_s$ is freed; the concordance region survives the addition of DESI BAO and Pantheon+ data.
  • The apparent DESI BAO preference for dynamical dark energy is absorbed by the freed sound horizon, so those data alone do not constitute evidence against $\Lambda$CDM.
  • High-redshift supernova samples play a decisive role: adding Pantheon+ moves $\Omega_{\rm M}$ up and, under $w_0w_a$CDM, pushes $\sigma_8$ to locally implausible values, which is how the dynamical dark energy case fails.
  • Existing direct local measurements of $H_0$ and $\sigma_8$ can be accommodated without invoking early-universe or late-universe new physics, pointing instead to calibration of the BAO ruler as the decisive assumption.

Reading between the lines

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

  • A natural next test is to confront the freed $r_s$ posterior with an independent, model-minimal measurement of the sound horizon, for example from CMB lensing or standard-siren distances; agreement would elevate the low-density solution, while disagreement would mark it as a fitting artifact.
  • The same probe combination could be rerun with the full DESI clustering shape rather than compressed BAO distances; if the broad $r_s$ posterior persists, the calibration-relaxation strategy is robust, and if it narrows, the concordance may evaporate.
  • The contrast between Union II and Pantheon+ suggests the outcome hinges on the highest-redshift supernovae, making high-$z$ samples and their systematics the strategic control for future tests.
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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

3 major / 5 minor

Summary. The paper investigates whether a low matter density Omega_M, lower than the CMB-inferred value, can simultaneously accommodate the locally measured H0 and sigma8, within LambdaCDM and w0waCDM dark energy models, when combining galaxy cluster counts (SZ), gas mass fraction (fgas), cosmic chronometers, supernova samples (Union II or Pantheon+), and DESI year-one BAO measurements. The central claim is that within LambdaCDM, a low Omega_M can preserve concordance with local H0 and sigma8 values, provided the sound horizon at the drag epoch, r_s, is promoted to a free parameter, even when Pantheon+ is included. For w0waCDM, the paper reports that relaxing r_s allows accommodation of Omega_M, H0, and sigma8 simultaneously only without Pantheon+; adding Pantheon+ pushes sigma8 to low values and worsens concordance. The conclusion states that a low matter density helps preserve concordance within LambdaCDM while the dynamical dark energy model fails to solve all tensions at once.

Significance. If the central claim were established quantitatively, it would add an interesting data-combination result to the ongoing discussion of the H0 and sigma8 tensions: it would show that a local low-Omega_M solution remains viable even with DESI BAO data, provided the BAO calibration is treated as free. The paper's strength is its use of multiple independent local probes, public likelihoods in MontePython, and a clear comparison across dataset combinations. However, the significance is substantially limited by the absence of any diagnostic quantifying how much constraining power remains in the DESI BAO likelihood once r_s is free, and by the reliance on qualitative contour overlap rather than a tension statistic. As written, the paper shows that a low-Omega_M region is not excluded when many calibration parameters are simultaneously freed, but it does not demonstrate that this region is data-preferred over the CMB-anchored high-Omega_M region.

major comments (3)
  1. [Section 2 and Fig. 2] The paper promotes r_s to a free parameter in the DESI BAO likelihood, but it never quantifies the residual constraining power of the BAO data after this marginalization. DESI BAO observables are ratios of D_H(z)/r_s and D_M(z)/r_s; with r_s free, the absolute distance calibration is removed and only the redshift-dependent shape remains. Without a DESI-only (or DESI+core, without other geometric probes) run with r_s free, or a goodness-of-fit comparison (e.g., Delta chi-square or Bayesian evidence) between the r_s-fixed and r_s-free cases, the concordance seen in Fig. 2 could be a prior-volume artifact rather than a data-driven result. This is load-bearing: the central conclusion that 'low matter density preserves concordance... providing we promote rs to free parameter' depends on DESI BAO retaining meaningful constraining power.
  2. [Section 4 (and Figs. 1-6)] The claim of 'accommodation' is assessed exclusively by qualitative overlap of 68% and 95% confidence contours with the dashed lines representing local H0 and sigma8 values. No quantitative tension metric is used. Because the cluster-count likelihood has a free mass-calibration parameter (1-b) and the gas-mass-fraction likelihood has a free K(z), the combined constraints on Omega_M and sigma8 may be dominated by priors rather than data. The paper should report, for example, the change in best-fit chi-square when moving from the low-Omega_M region to the CMB-favored region, or compute a Bayesian tension statistic between the combined posterior and the local H0/sigma8 measurements. Absent that, the phrase 'accommodate' is not supported beyond the statement that certain contours overlap.
  3. [Section 3.2 and Fig. 6] The w0waCDM conclusion that 'the dynamical dark energy model ultimately fails to solve all tensions at once' is asserted based on the Pantheon+ cases in Fig. 6, where sigma8 is said to be 'much smaller' than local values. However, the figure shows that with r_s free and without cosmic chronometers, H0 is compatible with local values and sigma8 is only mildly low. The paper does not quantify the discrepancy or test whether the low-sigma8 shift is significant relative to the local measurement error. A quantitative comparison (e.g., 1-sigma or 2-sigma deviation in a combined parameter space) is needed before drawing the negative conclusion about w0waCDM.
minor comments (5)
  1. [Abstract and Section 2] The abstract states that BAO measurements are added 'in almost all of our Monte Carlo runs', while Section 2 says they are added 'to some of our MCMC runs'; please harmonize these descriptions.
  2. [Section 2] The text introduces r_s, M_B, (1-b), and K(z) as parameters but no equations are provided for the likelihoods or the model observables. Adding a small set of numbered equations would make the paper more self-contained and easier to referee.
  3. [Captions of Figs. 1-6] The captions say 'The 1D and 2D 68% and 95% confidence contours marginalized likelihood'; this should be 'marginalized posteriors' or 'marginalized likelihood contours'.
  4. [Introduction] The text 'Union 333 and DESY534 releases' and the reference to 'DESY5' appear to contain typos; reference [34] is the DES Collaboration, so the sample name should be consistently written (e.g., DES Y5) rather than DESY5.
  5. [Throughout] The symbol for the sound horizon is written as both r_s and rs (unsubscripted) in the same paragraphs; please use a consistent notation.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity; the paper's concordance claim is conditional on freeing nuisance parameters but is not equivalent to its inputs by construction.

full rationale

The paper's central claim is a Bayesian accommodation statement, not a prediction derived from a first-principles input. The conclusion that a low matter density can preserve concordance within LCDM is explicitly conditional on promoting the sound horizon r_s to a free parameter, and the text states that condition plainly ('providing we promote the sound drag r_s component in BAO calculations to a free parameter'). Freeing calibration parameters such as r_s, M_B, (1-b), and K(z) weakens the constraining power of individual probes, but the paper does not define the target outcome in terms of those parameters, and the MCMC posteriors in Figures 1-6 still show data-dependent shifts and finite widths. The low Omega_M value is fed into the analysis through local mass-to-light cluster measurements and cluster counts, which are external inputs rather than outputs of the model, so the accommodation is not manufactured by the likelihood alone. The reliance on the author's prior work ZS22 for the probe setup is a methodological citation, but the present chains are re-run with new DESI BAO data and new dark-energy models, so the self-citation is not load-bearing for the new conclusion. The skeptical concern that freeing r_s removes the absolute BAO calibration and that no Bayesian-evidence comparison is provided is a legitimate statistical-robustness critique, but it does not amount to a demonstration that any stated equation or fitted parameter has been renamed as a prediction. Under the specified circularity criteria, no quoted step reduces the conclusion to its inputs by construction.

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

The central result depends on the validity and informativeness of several public likelihoods, on the choice to free calibration parameters, and on the model space (LCDM or CPL). The most important assumptions and fitted parameters are listed above.

free parameters (5)
  • Sound horizon at drag epoch r_s = Varies across runs, roughly 100-170 Mpc in the posteriors shown in Figs. 2 and 4-6
    Promoted from a model-derived quantity to a free parameter to make DESI BAO data more model independent; central to the reported concordance.
  • Supernova absolute magnitude M_B = Approximately -19.4 to -19.1 mag in Pantheon+ panels of Figs. 2 and 6
    Left free to make supernova distances less model dependent; absorbs the calibration degeneracy with H0.
  • Cluster mass calibration (1-b) = Not reported numerically
    Relaxed for SZ cluster counts, weakening their Omega_M and sigma8 constraints and reducing dependence on hydrodynamical simulations.
  • Gas mass fraction calibration K(z) = Not reported numerically
    Relaxed for the fgas cluster probe because it is degenerate with sigma8.
  • Dark energy equation of state parameters w0, wa = Posteriors show w0 roughly -1.4 to -0.6 and wa roughly 0 to 2 depending on dataset
    Free parameters of the CPL model; the paper reports preference for values far from LambdaCDM in several configurations.
assumptions (4)
  • domain assumption FLRW background and the CPL dark energy parametrization w(a) = w0 + wa(1-a) hold for computing theoretical observables.
    Assumed throughout Section 2; this defines the model space of the analysis.
  • domain assumption The BBN prior omega_b,0 = 0.0226 +/- 0.00034 and the Planck priors on ns and As are correct external inputs.
    Used in the core combination to anchor baryon density and primordial amplitude independently of the Planck angular power spectrum.
  • domain assumption Cluster mass-observable scaling relations and hydrostatic equilibrium of the selected clusters provide unbiased cluster mass estimates after marginalizing (1-b) and K(z).
    Relied on for SZ cluster counts and fgas probes in Section 2.
  • domain assumption The DESI year-one BAO likelihood is correctly implemented in MontePython and remains valid when r_s is treated as a free parameter.
    Used in all runs with DESI; the validity of the likelihood with free r_s is the load-bearing premise of the concordance finding.

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Cite this review

Pith. "Pith review of The case for a low dark matter density in dynamical dark energy model from local probes." pith.science (2026). https://pith.science/paper/N4IHOYFC

@misc{pith2026250108915,
  author       = {Pith},
  title        = {Pith review of: The case for a low dark matter density in dynamical dark energy model from local probes},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/N4IHOYFC}},
  note         = {Machine review of arXiv:2501.08915}
}
abstract

In this work we investigate, through a Bayesian study, the ability of a local low matter density $\Omega_{\rm M}$, in discrepancy with the value usually inferred from the CMB angular power spectrum, to accommodate observations from local probes without being in tension with the local values of the Hubble constant $H_0$ or the matter fluctuation $\sigma_8$ parameters. For that, we combine multiple local probes, with the criteria that they either can constrain the matter density parameter independently from the CMB constraints, or can help in doing so after making their relevant observations more model independent by relaxing their relevant calibration parameters. We assume however, either a dynamical dark energy model, or the standard $\Lambda$CDM model, when computing the corresponding theoretical observables. We also add, in almost all of our Monte Carlo runs, the latest Baryonic acoustic oscillations (BAO) measurements from the DESI year one release to our core group. We found that, within $\Lambda$CDM model, for different combinations of our probes, we can accommodate a low matter density along with the $H_0$ and $\sigma_8$ values usually obtained from local probes, providing we promote the sound drag $r_s$ component in BAO calculations to a free parameter, and that even if we combine with the Pantheon+ Supernova sample. Assuming $w_0w_a$CDM, we also found that relaxing $r_s$ allow us to accommodate $\Omega_{\rm M}$, $H_0$ and $\sigma_8$ within their local values, with still however a preference for $w_0w_a$ values far from $\Lambda$CDM. However, when including Pantheon+ Supernova sample, we found that the latter preference for high matter density pushes $\sigma_8$ to much smaller values, mitigating by then a low matter density solution to the two common tensions. We conclude that a low matter density value, helps in preserving the concordance within $\Lambda$CDM model. (abridged)

Figures

Figures reproduced from arXiv: 2501.08915 by the authors.

Figure 1
Figure 1. The 1D and 2D 68% and 95% confidence contours marginalized likelihood for the mat [PITH_FULL_IMAGE:figures/full_fig_p005_1.png] view at source ↗
Figure 2
Figure 2. The 1D and 2D 68% and 95% confidence contours marginalized likelihood for the matter [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗
Figure 3
Figure 3. The 1D and 2D 68% and 95% confidence contours marginalized likelihood for the matter [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗
Figures from the paper (3 more)
Figure 4
Figure 4. Figure 4: The 1D and 2D 68% and 95% confidence contours marginalized likelihood for the matter [PITH_FULL_IMAGE:figures/full_fig_p008_4.png]
Figure 5
Figure 5. Figure 5: The 1D and 2D 68% and 95% confidence contours marginalized likelihood for the matter [PITH_FULL_IMAGE:figures/full_fig_p009_5.png]
Figure 6
Figure 6. Figure 6: The 1D and 2D 68% and 95% confidence contours marginalised likelihood for the matter [PITH_FULL_IMAGE:figures/full_fig_p010_6.png]

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Reviewed August 10, 2026 · model on record in the stance chip above.