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arxiv: 2606.31977 · v1 · pith:L3F7XI5Cnew · submitted 2026-06-30 · 🌌 astro-ph.CO

Constraining dark energy with complementary probes of large-scale structure

Neel Shah , Kazuya Koyama , Johannes Noller , Lanyang Yi This is my paper

Pith reviewed 2026-07-01 03:33 UTC · model grok-4.3

classification 🌌 astro-ph.CO
keywords dark energyEFTofDElarge-scale structureredshift space distortionsintegrated Sachs-WolfeDESIDES
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The pith

Supplementing CMB+BAO+SNe data with DESI RSD, DES 3x2pt and ISW cross-correlations improves the figure of merit for EFTofDE perturbation parameters {c_B, c_M} by a factor of 2.69.

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

The paper constrains dark energy perturbations in the Effective Field Theory of Dark Energy framework by jointly modeling background expansion and perturbations, then fitting the combined theory space to multiple datasets. Adding redshift space distortions from DESI DR1, 3x2pt measurements from DES Y3, and integrated Sachs-Wolfe cross-correlations between CMB temperature and galaxy counts to standard CMB+BAO+SNe probes produces markedly tighter bounds on the perturbation parameters. The most constraining combination raises the figure of merit for {c_B, c_M} by a factor of 2.69 and for the mapped functions {μ(z), Σ(z)} by 3.37. The analysis also reveals interdependence between background parameters {w0, wa} and perturbation parameters caused by the gradient stability prior, and reports a 2.9σ deviation from ΛCDM for the EFTofDE model with the baseline datasets.

Core claim

By supplementing CMB+BAO+SNe probes with DESI DR1 RSD, DES Y3 3×2pt and ISW cross-correlations between CMB temperature and galaxy counts, the constraints on the dark energy perturbation parameters {c_B, c_M} in the EFTofDE framework achieve a 2.69 times higher figure of merit. The same data combination improves the figure of merit for the phenomenological functions {μ(z), Σ(z)} by a factor of 3.37. The posteriors of {w0, wa} and {c_B, c_M} exhibit significant interdependence due to the gradient stability condition imposed as a theoretical prior. With CMB+BAO+SNe data alone the EFTofDE model deviates from ΛCDM at 2.9σ, comparable to the 3.1σ deviation found for the w0waCDM model.

What carries the argument

The Effective Field Theory of Dark Energy (EFTofDE) parameters {c_B, c_M} that encode dark energy perturbations, constrained jointly with background parameters under the gradient stability condition prior.

If this is right

  • The figure of merit for the phenomenological functions {μ(z), Σ(z)} improves by a factor of 3.37 with the full dataset combination.
  • Significant interdependence appears between the posteriors of {w0, wa} and {c_B, c_M} because of the gradient stability prior.
  • The EFTofDE model deviates from ΛCDM at 2.9σ when constrained with CMB+BAO+SNe data alone.
  • The deviation significance for EFTofDE is nontrivially close to the 3.1σ deviation found for the w0waCDM model on the same baseline datasets.

Where Pith is reading between the lines

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

  • The demonstrated complementarity implies that adding further large-scale structure observables from upcoming surveys could continue to shrink the allowed region for perturbation parameters.
  • The mapping from {c_B, c_M} to {μ(z), Σ(z)} permits direct comparison of these constraints with independent tests of modified gravity from galaxy clustering or weak lensing.
  • Relaxing the gradient stability prior would likely reduce the observed interdependence and allow more independent constraints on background versus perturbation sectors.

Load-bearing premise

The gradient stability condition must be imposed as a theoretical prior in the EFTofDE framework, which creates interdependence between the posteriors of background and perturbation parameters.

What would settle it

An independent measurement of the present-day values or redshift evolution of μ(z) or Σ(z) lying outside the joint posterior ranges obtained from the full dataset combination would falsify the constrained EFTofDE parameter space.

Figures

Figures reproduced from arXiv: 2606.31977 by Johannes Noller, Kazuya Koyama, Lanyang Yi, Neel Shah.

Figure 1
Figure 1. Figure 1: FIG. 1. A graph showing all the likelihoods used in this work and their various possible combinations. We split our likelihoods into five [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. The impact on the constraints on DE perturbations in the EFTofDE on adding an extra probe to our minimal combination of probes [PITH_FULL_IMAGE:figures/full_fig_p008_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. The impact on the constraints on DE perturbations in the EFTofDE on adding two complementary probes to our minimal combination of [PITH_FULL_IMAGE:figures/full_fig_p010_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. Strong constraints on the EFTofDE perturbations and background expansion obtained by adding three complementary probes of [PITH_FULL_IMAGE:figures/full_fig_p011_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. Constraints on the present-day values [PITH_FULL_IMAGE:figures/full_fig_p014_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6. The cosmic evolutions of [PITH_FULL_IMAGE:figures/full_fig_p015_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7. Comparison of constraints on [PITH_FULL_IMAGE:figures/full_fig_p015_7.png] view at source ↗
Figure 10
Figure 10. Figure 10: FIG. 10. Comparison of the constraints on [PITH_FULL_IMAGE:figures/full_fig_p016_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: FIG. 11. Joint posterior of [PITH_FULL_IMAGE:figures/full_fig_p017_11.png] view at source ↗
Figure 12
Figure 12. Figure 12: FIG. 12. The posteriors on [PITH_FULL_IMAGE:figures/full_fig_p019_12.png] view at source ↗
Figure 13
Figure 13. Figure 13: FIG. 13. The ISW predictions for the island in the ISW- [PITH_FULL_IMAGE:figures/full_fig_p020_13.png] view at source ↗
Figure 14
Figure 14. Figure 14: FIG. 14. Comparison of posteriors on [PITH_FULL_IMAGE:figures/full_fig_p020_14.png] view at source ↗
read the original abstract

To observationally pin down the nature of dark energy, it is essential to consistently model cosmological perturbations in the presence of dark energy alongside the background expansion and constrain this joint theory space with a large array of complementary probes. Here, we achieve this by constraining a model in the Effective Field Theory of Dark Energy (EFTofDE) framework by supplementing probes of the expansion history with several probes of large-scale structure: redshift space distortions (RSD) from DESI DR1, $3\times2$pt measurements from DES Y3, and the Integrated Sachs-Wolfe effect from cross-correlating CMB temperature anisotropies with galaxy number counts or CMB lensing. We demonstrate the complementarity of different probes which leads to strong improvements on constraints on DE perturbations. For our most constraining dataset combination that supplements CMB+BAO+SNe probes with DESI DR1 RSD, DES Y3 $3\times2$pt and ISW cross-correlations between CMB temperature and galaxy counts, we find an improvement in the Figure of Merit (FoM) for the DE perturbation parameters $\{c_B, c_M\}$ by a factor of 2.69. We show the phenomenological implications of these constraints by mapping them to the present-day values of the phenomenological functions $\{\mu(z), \Sigma(z)\}$, where we see an FoM improvement by a factor of 3.37. We find a significant interdependence between the posteriors of $\{w_0, w_a\}$ and $\{c_B, c_M\}$, caused by the theoretical prior imposed by the gradient stability condition within the EFTofDE framework. Finally, we compute the significance of deviation from $\Lambda$CM for the EFTofDE model when constrained with CMB+BAO+SNe datasets, finding it to be at 2.9$\sigma$. This significance is nontrivially similar to the significance for the $w_0w_a$CDM model for the same dataset combination which we find to be 3.1$\sigma$.

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

2 major / 2 minor

Summary. The paper constrains an EFTofDE model by combining CMB+BAO+SNe with DESI DR1 RSD, DES Y3 3×2pt, and ISW cross-correlations, reporting a 2.69× FoM gain for {c_B, c_M} and 3.37× for {μ(z), Σ(z)} in the most constraining combination; it notes interdependence between {w0, wa} and {c_B, c_M} posteriors induced by the gradient stability prior and finds ~2.9σ deviation from ΛCDM (comparable to 3.1σ in w0waCDM) for CMB+BAO+SNe.

Significance. Demonstrating that added LSS probes tighten DE perturbation constraints beyond background expansion would be valuable for multi-probe cosmology, provided the reported FoM gains are shown to be driven by the data rather than the stability prior.

major comments (2)
  1. [Abstract] Abstract: the headline FoM improvement of 2.69 for {c_B, c_M} (and 3.37 for {μ, Σ}) is measured inside the space restricted by the gradient stability condition, which the abstract states induces the observed interdependence between {w0, wa} and {c_B, c_M}. Without an explicit comparison (e.g., chains run with the stability condition removed) it is unclear whether the complementarity claim holds independently of this theoretical prior.
  2. [Abstract] Abstract: the reported deviation significances (2.9σ for EFTofDE vs. 3.1σ for w0waCDM with CMB+BAO+SNe) are nearly identical; this similarity, combined with the shared use of the same background datasets, requires explicit discussion of whether the EFTofDE extension meaningfully alters the tension or whether covariance modeling and error propagation are driving the result.
minor comments (2)
  1. All dataset combinations and their FoM values should be collected in a single table for direct comparison.
  2. Notation for the phenomenological functions μ(z) and Σ(z) and their mapping from EFTofDE parameters should be defined at first use.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their careful reading of the manuscript and for highlighting important points regarding the gradient stability prior and the interpretation of the deviation significance. We address each major comment below and will make revisions to improve clarity on these issues.

read point-by-point responses

  1. Referee: [Abstract] Abstract: the headline FoM improvement of 2.69 for {c_B, c_M} (and 3.37 for {μ, Σ}) is measured inside the space restricted by the gradient stability condition, which the abstract states induces the observed interdependence between {w0, wa} and {c_B, c_M}. Without an explicit comparison (e.g., chains run with the stability condition removed) it is unclear whether the complementarity claim holds independently of this theoretical prior.

    Authors: We agree that all reported FoM values are computed within the parameter space allowed by the gradient stability condition, which is an intrinsic theoretical requirement of the EFTofDE framework to exclude ghost instabilities. The manuscript already notes that this prior induces the observed interdependence between {w0, wa} and {c_B, c_M}. The complementarity claim refers to the ability of the LSS probes to further tighten constraints on the perturbation parameters inside this physically viable region, as demonstrated by the progressive FoM gains when successively adding DESI RSD, DES Y3 3×2pt, and ISW data. Running additional chains without the stability prior is not straightforward, as it would require the Boltzmann solver to explore regions where the theory is mathematically ill-defined, leading to numerical instabilities. In the revised manuscript we will add explicit text in the abstract and results section clarifying that the FoM improvements quantify data-driven tightening within the model’s valid domain, and we will include a brief discussion of why a direct comparison outside this domain is not physically meaningful. revision: partial

  2. Referee: [Abstract] Abstract: the reported deviation significances (2.9σ for EFTofDE vs. 3.1σ for w0waCDM with CMB+BAO+SNe) are nearly identical; this similarity, combined with the shared use of the same background datasets, requires explicit discussion of whether the EFTofDE extension meaningfully alters the tension or whether covariance modeling and error propagation are driving the result.

    Authors: The near-identical significances (2.9σ versus 3.1σ) indicate that the tension with ΛCDM is driven primarily by the background parameters w0 and wa, which are constrained by the same CMB+BAO+SNe data in both models. The additional EFTofDE perturbation parameters do not substantially shift the overall deviation because the data combination does not strongly favor values of {c_B, c_M} that would move the posterior away from the ΛCDM limit. We will revise the manuscript to expand the discussion of this result, explicitly stating that the EFTofDE extension does not meaningfully alter the tension level relative to w0waCDM for this dataset and addressing the possible role of covariance modeling between probes. This addition will make clear that the reported significance is a direct consequence of the data constraints rather than an artifact of error propagation. revision: yes

Circularity Check

0 steps flagged

No significant circularity in constraint chain or FoM claims

full rationale

The paper performs Bayesian constraints on EFTofDE parameters using independent datasets (CMB+BAO+SNe supplemented by DESI RSD, DES 3x2pt, ISW). The reported FoM gains (2.69 for {c_B, c_M}, 3.37 for {μ, Σ}) are measured from the addition of these external probes. The noted interdependence between {w0, wa} and {c_B, c_M} is explicitly attributed to the gradient stability prior, which is a standard theoretical requirement in the EFTofDE framework rather than a self-referential fit or self-citation. No derivation reduces to its inputs by construction, no fitted parameter is relabeled as a prediction, and no load-bearing step relies on self-citation or ansatz smuggling. The analysis remains self-contained against external data benchmarks.

Axiom & Free-Parameter Ledger

4 free parameters · 1 axioms · 0 invented entities

The central claim rests on standard cosmological parameters plus four EFTofDE parameters fitted to data, plus the gradient stability condition as a domain assumption that links parameter posteriors.

free parameters (4)
  • w0
    Present-day dark energy equation-of-state parameter, fitted to the combined datasets.
  • wa
    Dark energy equation-of-state evolution parameter, fitted to the combined datasets.
  • cB
    EFTofDE braiding parameter controlling perturbations, fitted to the combined datasets.
  • cM
    EFTofDE Planck-mass run rate parameter controlling perturbations, fitted to the combined datasets.
axioms (1)
  • domain assumption Gradient stability condition within EFTofDE
    Imposed as theoretical prior; explicitly stated to cause interdependence between expansion and perturbation parameter posteriors.

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discussion (0)

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