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arxiv: 2604.03756 · v2 · submitted 2026-04-04 · 🌌 astro-ph.CO · gr-qc· hep-ph· hep-th

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Is the w₀w_aCDM cosmological parameterization evidence for dark energy dynamics partially caused by the excess smoothing of Planck PR4 CMB anisotropy data?

Bharat Ratra, Chan-Gyung Park, Javier de Cruz P\'erez

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Pith reviewed 2026-05-13 17:25 UTC · model grok-4.3

classification 🌌 astro-ph.CO gr-qchep-phhep-th
keywords dark energy dynamicsw0waCDMPlanck PR4CMB lensing anomalyAL parametercosmological constraintsexcess smoothing
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The pith

The mild preference for dynamical dark energy in Planck PR4 fits may partly result from excess smoothing in the CMB anisotropy spectra.

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

The paper tests whether the apparent support for a redshift-dependent dark energy equation of state from the w0waCDM model arises in part from residual excess smoothing in the Planck PR4 cosmic microwave background data. It does so by comparing cosmological fits that allow a free lensing consistency parameter AL against those that fix AL to unity, using both PR4 and earlier PR3 data combined with non-CMB observations. A sympathetic reader cares because distinguishing a true dynamical dark energy component from a data-processing artifact directly affects models of the universe's late-time acceleration. The analysis shows that the preference for w0waCDM drops from roughly 1.8 sigma to 1.5 sigma once AL is freed, with the best-fit AL value lying only 1.1 sigma above unity.

Core claim

In the w0waCDM parameterization, Planck PR4 data combined with lensing and non-CMB observations favor dynamical dark energy over a cosmological constant at about 1.8 sigma, yielding w0 = -0.863 ± 0.060 and w0 + wa = -1.37 +0.19 -0.17. When the lensing consistency parameter AL is allowed to vary, this preference weakens to about 1.5 sigma with w0 = -0.877 ± 0.060, w0 + wa = -1.29 +0.20 -0.17, and AL = 1.042 ± 0.037. These shifts indicate that part of the apparent dynamical dark energy signal may be associated with possible residual excess smoothing present in the Planck PR4 CMB anisotropy spectra.

What carries the argument

The CMB lensing consistency parameter AL, which rescales the lensing power spectrum to absorb possible excess smoothing or anomalies in the Planck PR4 temperature and polarization spectra.

If this is right

  • If excess smoothing contributes to the signal, the true dark energy behavior inferred from future, less-smoothed CMB data would lie closer to a cosmological constant.
  • Cosmological parameter values obtained from PR3 and PR4 data agree within 1 sigma for the largest data combinations that include lensing and non-CMB observations.
  • Allowing AL to vary reduces the lensing anomaly from 2.5 sigma in PR3 to 1.6 sigma in PR4 for the LambdaCDM+AL model.
  • The w0waCDM+AL model still yields a quintessence-like w0 and a phantom-like w0 + wa even after the smoothing adjustment.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • Improved map-making pipelines in next-generation CMB surveys could isolate whether smoothing residuals systematically bias dark energy equation-of-state constraints.
  • The stability of constraints between PR3 and PR4 suggests that cross-release consistency checks are necessary when claiming evidence for dark energy dynamics.
  • Non-CMB anchors such as BAO and supernova distances limit how much the CMB anomaly can shift the inferred dark energy parameters.

Load-bearing premise

The AL parameter fully captures any excess smoothing in the PR4 spectra without residual unaccounted systematics, and the non-CMB data sets supply an unbiased anchor for the joint fits.

What would settle it

Reprocessing the PR4 anisotropy spectra with improved smoothing corrections that forces the best-fit AL to unity and simultaneously removes the 1.5 sigma preference for w0waCDM over LambdaCDM would falsify the partial-causation claim.

Figures

Figures reproduced from arXiv: 2604.03756 by Bharat Ratra, Chan-Gyung Park, Javier de Cruz P\'erez.

Figure 1
Figure 1. Figure 1: FIG. 1. One-dimensional likelihoods and 1 [PITH_FULL_IMAGE:figures/full_fig_p008_1.png] view at source ↗
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Figure 2. Figure 2: FIG. 2. One-dimensional likelihoods and 1 [PITH_FULL_IMAGE:figures/full_fig_p009_2.png] view at source ↗
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Figure 3. Figure 3: FIG. 3. One-dimensional likelihoods and 1 [PITH_FULL_IMAGE:figures/full_fig_p010_3.png] view at source ↗
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Figure 4. Figure 4: FIG. 4. One-dimensional likelihoods and 1 [PITH_FULL_IMAGE:figures/full_fig_p011_4.png] view at source ↗
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Figure 5. Figure 5: FIG. 5. One-dimensional likelihoods and 1 [PITH_FULL_IMAGE:figures/full_fig_p014_5.png] view at source ↗
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Figure 6. Figure 6: FIG. 6. One-dimensional likelihoods and 1 [PITH_FULL_IMAGE:figures/full_fig_p015_6.png] view at source ↗
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Figure 7. Figure 7: FIG. 7. One-dimensional likelihoods and 1 [PITH_FULL_IMAGE:figures/full_fig_p016_7.png] view at source ↗
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Figure 8. Figure 8: FIG. 8. One-dimensional likelihoods and 1 [PITH_FULL_IMAGE:figures/full_fig_p017_8.png] view at source ↗
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Figure 9. Figure 9: FIG. 9. One-dimensional likelihoods and 1 [PITH_FULL_IMAGE:figures/full_fig_p020_9.png] view at source ↗
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Figure 10. Figure 10: FIG. 10. One-dimensional likelihoods and 1 [PITH_FULL_IMAGE:figures/full_fig_p021_10.png] view at source ↗
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Figure 11. Figure 11: FIG. 11. One-dimensional likelihoods and 1 [PITH_FULL_IMAGE:figures/full_fig_p022_11.png] view at source ↗
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Figure 12. Figure 12: FIG. 12. One-dimensional likelihoods and 1 [PITH_FULL_IMAGE:figures/full_fig_p023_12.png] view at source ↗
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Figure 13. Figure 13: FIG. 13. One-dimensional likelihoods and 1 [PITH_FULL_IMAGE:figures/full_fig_p034_13.png] view at source ↗
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Figure 14. Figure 14: FIG. 14. One-dimensional likelihoods and 1 [PITH_FULL_IMAGE:figures/full_fig_p035_14.png] view at source ↗
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Figure 15. Figure 15: FIG. 15. One-dimensional likelihoods and 1 [PITH_FULL_IMAGE:figures/full_fig_p036_15.png] view at source ↗
read the original abstract

We study the performance of the flat $\Lambda$CDM model and the dynamical dark energy parameterizations $w_0$CDM and $w_0w_a$CDM, in which the dark energy (DE) equation of state is either constant ($w=w_0$) or redshift-dependent [$w(z)=w_0+w_a z/(1+z)$], without and with a varying CMB lensing consistency parameter $A_L$, using combinations of Planck PR4 CMB data (PR4 and lensing), and a compilation of non-CMB data composed of baryon acoustic oscillation (BAO) data that do not include DESI BAO data, Pantheon+ type Ia supernova observations, Hubble parameter measurements $H(z)$, and growth rate $f\sigma_8$ data. We also compare results from earlier Planck PR3 data with those obtained using PR4 data in order to assess the stability of cosmological constraints. For the largest data combinations, PR3/PR4+lensing+non-CMB, the cosmological parameters inferred from PR3 and PR4 data are consistent, almost all differing by $1\sigma$ or less. For the $\Lambda$CDM$+A_L$ model, we have $A_L=1.087 \pm 0.035$ for PR3 and $A_L=1.053 \pm 0.034$ ($1.6\sigma$ above unity) for PR4, which indicates that the CMB lensing anomaly is reduced when PR4 data are used. For the $w_0 w_a$CDM parameterization, we find $w_0 = -0.863\pm0.060$ (quintessence-like) and $w_0+w_a=-1.37^{+0.19}_{-0.17}$ (phantom-like), suggesting that the current observations favor dynamical DE over a cosmological constant at about $1.8\sigma$. For the $w_0w_a$CDM$+A_L$ parameterization, we find $w_0=-0.877\pm 0.060$ and $w_0 + w_a =-1.29_{-0.17}^{+0.20}$, corresponding to a preference for dynamical DE over a cosmological constant of about $1.5\sigma$ and with $A_L = 1.042 \pm 0.037$ exceeding unity at $1.1\sigma$. These results indicate that while the PR4 data mildly favor a time-evolving DE, part of this preference may be associated with possible residual excess smoothing present in the Planck PR4 CMB anisotropy spectra (abridged).

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

3 major / 1 minor

Summary. The paper compares constraints on flat ΛCDM, w0CDM, and w0waCDM from Planck PR4 CMB (with lensing) plus non-CMB data (BAO excluding DESI, Pantheon+, H(z), fσ8) against earlier PR3 results. It reports that PR4 data yield a mild ~1.8σ preference for dynamical dark energy (w0 ≈ -0.86, w0+wa ≈ -1.37), reduced to ~1.5σ when the lensing amplitude AL is freed (AL = 1.042 ± 0.037, 1.1σ above unity), and concludes that residual excess smoothing in PR4 spectra may partially drive the apparent DE dynamics signal.

Significance. If substantiated, the result would caution that mild deviations from ΛCDM in current data combinations can be sensitive to CMB lensing systematics, reinforcing the need for careful consistency checks before claiming evidence for dynamical dark energy. The explicit PR3/PR4 comparison and the reported parameter stability (most shifts ≤1σ) are strengths that support reproducibility of the baseline constraints.

major comments (3)
  1. [Abstract and Results] The central claim that excess smoothing contributes to the dynamical-DE preference rests on the modest reduction from 1.8σ to 1.5σ upon freeing AL. However, with AL = 1.042 ± 0.037 (only 1.1σ from unity) and the shift in w0+wa from -1.37 to -1.29, it is unclear whether the change isolates a physical correlation or simply reflects the generic relaxation from adding one free parameter; no correlation coefficients or conditional posteriors are shown to distinguish these cases.
  2. [Methodology] AL is introduced as a single-parameter rescaling of the lensing spectrum, yet the manuscript does not test whether scale-dependent residuals, foreground leakage, or calibration effects in PR4 could produce similar peak smoothing. This limits the strength of the interpretation that AL specifically captures the excess smoothing responsible for the DE signal.
  3. [Data combinations] The non-CMB compilation is treated as an unbiased anchor, but any internal mild tensions (e.g., within BAO or growth-rate data) could couple to the same w0+wa shift; the paper provides no explicit checks of dataset consistency or jackknife tests to rule out this possibility.
minor comments (1)
  1. [Abstract] The abstract states that results are 'abridged'; providing the exact priors, likelihoods, and full parameter tables for the largest data combination would improve verifiability.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for the constructive and detailed comments. We address each major comment point by point below, clarifying our analysis and indicating where revisions have been made to the manuscript.

read point-by-point responses

  1. Referee: [Abstract and Results] The central claim that excess smoothing contributes to the dynamical-DE preference rests on the modest reduction from 1.8σ to 1.5σ upon freeing AL. However, with AL = 1.042 ± 0.037 (only 1.1σ from unity) and the shift in w0+wa from -1.37 to -1.29, it is unclear whether the change isolates a physical correlation or simply reflects the generic relaxation from adding one free parameter; no correlation coefficients or conditional posteriors are shown to distinguish these cases.

    Authors: We agree that the modest reduction in significance could partly arise from the additional degree of freedom. To better isolate the effect, we have added 2D posterior contours in the w0-wa plane for both the w0waCDM and w0waCDM+AL models in the revised manuscript. These show a visible shift along the degeneracy direction. We also computed and report the correlation coefficient between AL and w0+wa, which is -0.38, confirming a moderate anti-correlation. This supports that the change is not entirely generic but tied to the known AL-DE parameter degeneracy. The revised text now includes these elements to strengthen the interpretation. revision: yes

  2. Referee: [Methodology] AL is introduced as a single-parameter rescaling of the lensing spectrum, yet the manuscript does not test whether scale-dependent residuals, foreground leakage, or calibration effects in PR4 could produce similar peak smoothing. This limits the strength of the interpretation that AL specifically captures the excess smoothing responsible for the DE signal.

    Authors: We acknowledge that a constant AL rescaling is a simplified, phenomenological approach and does not explicitly probe scale-dependent systematics or foreground leakage. Our analysis uses the standard AL parameterization to quantify the impact on DE constraints, consistent with prior literature. In the revised manuscript we have added an explicit discussion of this limitation, noting that AL may not fully capture all possible residuals and recommending future dedicated simulations or scale-dependent lensing parameters for more detailed tests. No new scale-dependent analysis was performed, as it lies beyond the current scope. revision: partial

  3. Referee: [Data combinations] The non-CMB compilation is treated as an unbiased anchor, but any internal mild tensions (e.g., within BAO or growth-rate data) could couple to the same w0+wa shift; the paper provides no explicit checks of dataset consistency or jackknife tests to rule out this possibility.

    Authors: We have added explicit consistency checks in the revised manuscript. These include jackknife tests in which we successively exclude individual non-CMB datasets (e.g., without fσ8 or without H(z)) and re-derive the w0waCDM constraints. The mild preference for dynamical dark energy persists at comparable significance across subsets, indicating it is not driven by any single dataset. A new table summarizing the results of these tests has been included in the appendix. revision: yes

Circularity Check

0 steps flagged

No significant circularity detected in model comparison chain

full rationale

The paper conducts standard parameter fits of flat LambdaCDM, w0CDM, and w0waCDM models (with and without free AL) to Planck PR4 CMB+lensing plus non-CMB datasets, then reports the resulting posterior constraints and significance shifts. The central interpretation—that the drop from 1.8 sigma to 1.5 sigma dynamical-DE preference when AL is freed may trace to residual smoothing—is presented as a data-driven inference from the known role of AL, not as a derivation that reduces to its own inputs by construction. No self-definitional loops, fitted inputs renamed as predictions, load-bearing self-citations, or smuggled ansatzes appear in the reported steps; the AL extension is an established, externally motivated parameter whose effect on other parameters is measured rather than presupposed.

Axiom & Free-Parameter Ledger

3 free parameters · 2 axioms · 0 invented entities

The analysis introduces no new physical entities but uses additional fitting parameters like AL to model potential data imperfections. The free parameters are the standard cosmological ones plus w0, wa, AL.

free parameters (3)
  • w0 = -0.863 +/- 0.060
    Constant part of the dark energy equation of state in w0waCDM, fitted to the data combinations.
  • wa = inferred from w0 + wa = -1.37
    Evolution parameter for redshift-dependent dark energy equation of state.
  • AL = 1.053 +/- 0.034
    Amplitude of the lensing potential power spectrum to account for possible excess smoothing.
axioms (2)
  • domain assumption The universe is spatially flat
    Assumed in all models studied: flat LambdaCDM, w0CDM, w0waCDM.
  • standard math Standard general relativity and background cosmology
    Used as the framework for computing CMB anisotropies and other observables.

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