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The paper claims that redefining galaxy-clustering nuisance parameters to absorb the signal amplitude removes the spurious shifts in evolving-dark-energy constraints, yielding purely late-universe measurements consistent with DESI.

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2026-08-04 18:52 UTC pith:Z6UIHJ42

load-bearing objection A clean reparametrization fix for prior-volume effects in w0wa full-shape analyses, but the noiseless-only validation leaves the noise-resilience question open. the 3 major comments →

arxiv 2509.09562 v1 pith:Z6UIHJ42 submitted 2025-09-11 astro-ph.CO

The simple way to measure evolving dark energy without prior-volume effects

Maria Tsedrik , Pedro Carrilho , Chiara Moretti This is my paper
classification astro-ph.CO
keywords dark energyevolving dark energyw0waCDMprojection effectsprior-volume effectsEFT of large-scale structurefull-shape analysisAlcock-Paczynski amplitude
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

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

The paper claims that the puzzling shifts and artificially tight constraints in w0waCDM full-shape analyses of galaxy clustering are prior-volume (projection) effects: flat priors on nuisance parameters that are degenerate with the overall amplitude of the power-spectrum multipoles drag the marginalized posterior away from the maximum of the full posterior. The proposed fix is to re-parametrize those nuisance parameters so they absorb the amplitude factor AAP(z)σ8,z^2(z), the Alcock-Paczynski amplitude times the redshift-scaled variance, which makes the Laplace term that causes the shift nearly independent of the dark-energy parameters. On noiseless synthetic BOSS DR12 and DESI DR1-like data this brings the posterior maximum inside the marginalized credible interval, performing comparably to Jeffreys priors. Applied to BOSS DR12 full-shape plus BAO and DES Y3 3x2pt data, the method gives w0=-0.72±0.21 and wa=-0.91(+0.78,-0.64), the first purely late-time large-scale-structure constraints on evolving dark energy, consistent with the DESI-preferred region. The importance, if right, is that the apparent preference for evolving dark energy can be assessed without CMB or supernova information.

Core claim

The central claim is that prior-volume effects in EFTofLSS full-shape w0waCDM analyses are dominated by nuisance parameters that enter the model linearly and are degenerate with the amplitude of the multipoles. Redefining those nuisance parameters (counterterms, shot noise, bΓ3) to absorb the combination AAPσ8,z^2 removes the implicit 1/amplitude prior from flat-prior choices, flattening the Laplace term in w0, wa, h. On synthetic data this puts the posterior maximum inside the marginalized interval; on BOSS DR12 plus external BAO and DES Y3 it gives w0=-0.72±0.21, wa=-0.91(+0.78,-0.64), agreeing with DESI's evolving-dark-energy region using only low-redshift probes.

What carries the argument

The key machinery is the re-parametrized set of analytically marginalized EFTofLSS nuisance parameters: each linearly appearing parameter is rescaled by the amplitude factor AAP(z)σ8,z^2(z), with the Gaussian prior mean and width rescaled by the same factor, plus a hand-set widening factor up to 3. This absorbs the two amplitude directions, the primordial/σ8 amplitude and the Alcock-Paczynski distance-ratio amplitude, that make the Laplace term, the log-volume factor from analytic marginalization, a steep function of w0, wa, and h. The reparametrization acts as a first-order, experiment-independent approximation to Jeffreys priors, which cancel the Laplace term exactly using the Fisher infor

Load-bearing premise

The load-bearing premise is that the projection bias in w0-wa comes almost entirely from linearly appearing nuisance parameters that are degenerate with the amplitude combination AAPσ8^2; as the paper itself notes, the reparametrization does not make the Laplace term completely cosmology-independent, so if nonlinearly entering bias parameters, scale-dependent degeneracies such as Ωm, or the hand-set rescaling factors (2 and 3 in Table 2) dominate, residual shifts would persis

What would settle it

Run the identical synthetic-data pipeline but with nuisance prior widths varied wider than the factors 2-3 used here and with nonlinearly appearing bias parameters (b2, bG2) sampled rather than fixed; if the MAP-vs-marginalized gap in w0 and wa reappears or grows, the amplitude-only reparametrization is not sufficient. A second decisive check is to apply full Jeffreys priors to all nuisance parameters on the same BOSS DR12 data: if the resulting w0-wa posterior does not contain w0=-0.72±0.21, wa=-0.91(+0.78,-0.64), the residual projection effects are larger than claimed.

Watch this falsifier. Get emailed when new claim-graph text bears on it.

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If this is right

  • In BOSS DR12 full-shape analyses, the previous shifts of h toward high values and w0< -1, wa>0 are eliminated; MAP values fall inside the 68% credible intervals.
  • The reparametrization is robust in a synthetic DESI DR1-like Stage IV setup for both ΛCDM and a fiducial with w0=-0.42, wa=-1.75, so it should be applied to Stage IV full-shape analyses.
  • Combining BOSS DR12 FS+BAO with external BAO and DES Y3 yields w0=-0.72±0.21, wa=-0.91(+0.78,-0.64), the first purely late-time LSS constraints in w0waCDM, consistent with DESI+CMB+SN.
  • The method also removes spurious narrowing: credible intervals broaden once projection effects are removed, and derived S8/sigma8 agree with CMB values.

Where Pith is reading between the lines

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

  • If the mechanism is as claimed, earlier full-shape dark-energy constraints that did not absorb AAPσ8^2 should be reinterpreted: their w0<-1, wa>0 tails and narrow contours are partly a prior artifact, not a measurement.
  • A direct extension is to apply the same reparametrization to DESI DR1/DR2 full-shape data; the method predicts that the inferred (w0, wa) will shift toward the BOSS+extBAO+DESY3 values and the credible intervals will widen.
  • The same logic can be tested on other extensions that change the background, such as curvature or interacting dark energy, by replacing the absorbed amplitude with the best-measured scale-dependent amplitude and checking whether the MAP-vs-marginalized gap closes.
  • A cheaper diagnostic on any existing chain: compare the MAP of the full posterior with the marginalized mean before and after reparametrization; if the method is right, the gap should shrink specifically when the amplitude factor is absorbed.

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

3 major / 5 minor

Summary. This paper addresses prior-volume (projection) effects in EFTofLSS full-shape analyses of galaxy power spectrum multipoles. The authors propose redefining the analytically marginalised nuisance parameters so that they absorb the Alcock-Paczynski amplitude AAP(z) and a time-dependent σ8^2 amplitude, thereby reducing the cosmology dependence of the Laplace term in Eq. (3.7). They illustrate the mechanism with a toy derivation (Eq. 3.13), compare several reparametrisation choices on noiseless synthetic BOSS DR12 and DESI DR1-like data, and compare against Jeffreys priors on the linear nuisance parameters. They then apply the chosen AAPσ8,z^2 reparametrisation to BOSS DR12 full-shape data combined with BOSS/external BAO and DES Y3 3×2pt, obtaining w0 = −0.72 ± 0.21 and wa = −0.91^{+0.78}_{−0.64}, in agreement with DESI-desired evolving-dark-energy contours.

Significance. If the central claim holds, the paper offers a practical, covariance-independent mitigation of projection effects that is much simpler to implement than Jeffreys priors and is applicable to Stage IV spectroscopic surveys. The strengths are the clean toy demonstration of the induced 1/As prior (Eq. 3.13), the explicit comparison of MAP and marginalised posterior locations in Tables 3–4, the physical motivation for absorbing AAP and σ8,z^2, and the prior-robustness checks in Appendix B. The paper is also careful to state that the reparametrisation does not make the Laplace term fully cosmology-independent (§3). However, the central MAP-inside-CI property is validated only on noiseless synthetic data and a single real-data realization, which leaves an important gap for a method whose whole purpose is to remove shifts that can depend on the noise level.

major comments (3)
  1. [§4.1, Figs. 4/6, Table 3] The headline claim that the reparametrisation places the full posterior MAP inside the marginalised credible intervals is demonstrated on noiseless synthetic data and on one real BOSS realization. The paper itself acknowledges (§3) that the method 'does not make the Laplace term completely independent' and (§4.1) that residual projection effects 'can impact or even cancel out other intrinsic non-Gaussianities'. Since the balance between χ2_* and ln det F2 in Eq. (3.7) depends on the data covariance, that balance changes with noise. A noiseless validation therefore does not establish that the real-data MAP-in-CI coincidence is systematic, and the final Eq. (5.1) could still carry noise-dependent residual projection bias. I request noisy mock realizations with w0waCDM fiducials (e.g., Patchy-like mocks) and a quantitative estimate of the residual MAP shift as a function of noise level.
  2. [§3, Table 2, Appendix A] The chosen reparametrisation is applied only to the analytically marginalised (linearly appearing) nuisance parameters; the sampled parameters b1, b2, bG2 retain cosmology-dependent effective priors. Appendix A shows that a full reparametrisation gives similar synthetic-data results, but it does not report MAP-in-CI diagnostics or residual Laplace-term dependence for the full case. Since the paper's core promise is that 'the actual posterior maximum values are within the marginalised credible interval', the non-linear nuisance directions need explicit validation or a quantitative statement of why they are subdominant. At present the claim is strictly demonstrated only for the linear subspace.
  3. [Table 2 and Appendix B] The rescaling factors of the nuisance prior widths (×2 for σ~8,z and ×3 for A~s) are set by hand. Appendix B shows that the final results are robust to increasing these widths, which is reassuring, but the method is presented as 'independent of the particular experiment' and as a first-order approximation to Jeffreys priors. The residual cosmology-dependence of the Laplace term is never quantified. A simple diagnostic, e.g., the derivative of ln det F2 with respect to w0, wa, h evaluated before and after reparametrisation, would make the approximation concrete and would strengthen the claim that the method is not just a particular prior choice.
minor comments (5)
  1. [Eq. (3.7)] Please state the sign convention explicitly: if χ2_m denotes −2 ln P, then the Laplace term enters with a plus sign, but this is not stated. Also clarify that 'profile likelihood' here is the partially maximized likelihood after analytic marginalisation, not the usual profile over all nuisance parameters.
  2. [Table 2] The baseline prior for c2 is listed as N(30,30), whereas c0 and c4 are N(0,30). If c2 has a non-zero mean by construction, this should be explained; otherwise it is likely a typo.
  3. [§5.1] The phrase 'we take four α's from the same sky-cuts' should define α; presumably these are the BAO distance parameters α∥ and α⊥ or the isotropically averaged α. Please define them explicitly.
  4. [Conclusion] The text 'SDSS DR7 MGC' should be 'SDSS DR7 MGS' (the Main Galaxy Sample), consistent with §2 and reference [53].
  5. [Figure 3] The color scales for χ2_* and ln det F2 are not labelled in the published figure. Adding colorbars or explicitly quoting the ranges in the caption would improve readability.

Circularity Check

0 steps flagged

No significant circularity: the reparametrization is a derived transformation validated on synthetic data; final dark-energy constraints are measurements, not fitted inputs.

full rationale

The paper's central method is a reparametrization of EFTofLSS nuisance parameters that absorb amplitude factors (A_AP, sigma8^2,z). The mitigation of projection effects is derived from the analytical marginalisation formula Eq. (3.7): for parameters appearing linearly in the model, absorbing a common amplitude factor removes that amplitude dependence from the Laplace term ln det F2. This is a mathematical consequence stated explicitly in Section 3 ('eliminating projection effects in those amplitudes via re-parametrisation or via Jeffreys priors is identical'), not an unexplained prediction. The stronger claim that MAP values fall within marginalised credible intervals is validated on noiseless synthetic data with a known fiducial cosmology, including a non-LambdaCDM evolution (w0=-0.42, wa=-1.75), and compared against Jeffreys priors. The final w0-wa constraints (Eq. 5.1) are derived from real BOSS, external BAO, and DES Y3 data; they are measurements, not constants fitted to produce the method. Self-citations to the PBJ pipeline and previous analyses (refs [19,23,31,69,70]) refer to independently validated code and earlier studies; they are not load-bearing for the reparametrization argument. The paper honestly notes that the Laplace term is not made fully cosmology-independent and that residual projection effects can remain, but this is a stated limitation, not a circular step. No prediction in the paper reduces by construction to its own input.

Axiom & Free-Parameter Ledger

4 free parameters · 5 axioms · 0 invented entities

Everything the central claim rests on is model-based and prior-choice-based; no new physical entities are introduced.

free parameters (4)
  • Analytically marginalised EFTofLSS nuisance parameters (bΓ3, c0, c2, c4, c∇4δ, N, e0, e2) = Not reported; fitted to BOSS/synthetic data
    Reparametrized as multiplying by AAP σ8,z^2 (Table 2). Their priors and values control the amplitude of the model and hence the projection effect.
  • Sampled nuisance parameters (b1, b2, bG2) = Not reported
    Galaxy bias parameters with broad priors; in the full reparametrisation (Appendix A) they also absorb amplitude factors.
  • Prior rescaling factors for reparametrized nuisance parameters = 2 (for σ8,z) and 3 (for As)
    Table 2, section 4.1: variances are increased by factors 2 and 3 to account for allowed As values. These are hand-set and affect the degree of projection mitigation.
  • Synthetic-data fiducial cosmology = ωc=0.12, ωb=0.02268, h=0.68, ns=0.97, ln(10^10As)=3.044, w0=-1, wa=0
    Used to generate noiseless BOSS/DESI-like data vectors in Sections 2 and 4. They are inputs, not fitted, but set the validation target.
axioms (5)
  • domain assumption EFTofLSS one-loop model with counterterms and stochastic terms accurately describes the observed galaxy power spectrum multipoles up to kmax=0.2 (BOSS) and 0.25 (DESI-like) h/Mpc.
    All likelihoods depend on Eqs. (3.1)-(3.4); see Section 2 for scale cuts.
  • standard math Gaussian likelihood with analytical marginalisation gives marginalised posterior proportional to exp(-χ_m^2/2) with χ_m^2 = χ_*^2 + ln det F2 + const.
    Eq. (3.7) defines the Laplace term and the entire prior-volume analysis.
  • standard math Flat prior on c induces a 1/As prior on the amplitude α=cAs under the change of variables.
    Eq. (3.13) and surrounding derivation; the Jacobian factor 1/As is the source of projection effects.
  • domain assumption The dominant amplitude degeneracies in w0waCDM full-shape analyses are captured by AAP, As, σ8,z, and growth factor D(z).
    Section 3-4 motivation for choosing which amplitudes to absorb; residual degeneracies are acknowledged.
  • standard math Jeffreys priors cancel the Laplace term for linearly appearing nuisance parameters, providing a benchmark.
    Section 3: Fisher matrix F2 equals the data term, so Jeffreys priors ∝ sqrt(|F|) cancel the Laplace term.

reviewed 2026-08-04 · how reviews work

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Cite this review

Pith. "Pith review of The simple way to measure evolving dark energy without prior-volume effects." pith.science (2026). https://pith.science/paper/Z6UIHJ42

@misc{pith2026250909562,
  author       = {Pith},
  title        = {Pith review of: The simple way to measure evolving dark energy without prior-volume effects},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/Z6UIHJ42}},
  note         = {Machine review of arXiv:2509.09562}
}
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read the original abstract

We present a simple yet effective method to resolve prior-volume effects, also known as projection effects, in full-shape analyses of the power spectrum multipoles within the Effective Field Theory of Large-Scale Structure (EFTofLSS). By re-defining the EFTofLSS nuisance parameters to incorporate the contribution from the parameters impacting the amplitude of the EFTofLSS modelling components, we substantially mitigate projection effects. With the re-parametrisation the actual posterior maximum values are within the marginalised credible interval, eliminating significant shifts observed in the baseline analysis. We demonstrate the robustness of this method in full-shape $w_0w_a$CDM analyses on synthetic data in BOSS DR12 and DESI DR1 setups. For the evolving dark energy model, we then analyse the BOSS DR12 measurements, in combination with BAO information (from BOSS DR12, 6DF, SDSS DR7 MGS and eBOSS DR16 surveys) and 3$\times$2pt measurements from DES Y3 -- all data combinations are converging into the $w_0-w_a$ parameter region preferred by DESI+CMB+SNIa. From total combination of these large-scale structure probes without additional CMB information we find $w_0=-0.72 \pm 0.21, \, w_a=-0.91^{+0.78}_{-0.64}$. Despite the low significance of deviation from standard cosmology, this result underscores the potential of our re-parametrisation approach in delivering low-redshift cosmological constraints. We argue for the use of this approach in spectroscopic Stage IV surveys, where the potential deviation from standard cosmology can be detected with higher significance.

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This paper was first reviewed by deepseek-v4-flash on August 4, 2026.