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REVIEW 5 major objections 4 minor 75 references

The CSST survey is forecast to measure the gravitational statistic E_G at 3–9% precision across redshifts 0 to 1.2.

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2026-08-03 08:09 UTC pith:QHZ7CTPB

load-bearing objection Useful CSST E_G forecast whose precision hinges on unpublished β errors from the corresponding author; read the numbers conditionally. the 5 major comments →

arxiv 2601.17874 v2 pith:QHZ7CTPB submitted 2026-01-25 astro-ph.CO

Forecasting the E_G measurements from the photometric and spectroscopic surveys of Chinese Space Station Survey Telescope (CSST)

Yu Song , Yi Zheng This is my paper
classification astro-ph.CO
keywords E_G statisticmodified gravityCSSTweak lensinggalaxy clusteringredshift-space distortionstomographic forecastsµ–Σ parametrization
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 forecasts that the Chinese Space Station Survey Telescope (CSST) will measure the E_G statistic—a ratio of galaxy-lensing to galaxy-clustering signals that isolates the gravitational growth history—at a relative precision of 3% to 9% for redshifts 0 to 1.2. That would improve on current E_G measurements by several times to an order of magnitude. Within a phenomenological modified-gravity parametrization (µ–Σ), the Weyl-potential coupling Σ0 would be constrained to about 5%; if future spectroscopic surveys pin the redshift-space distortion parameter β to 1%, E_G errors drop to the percent level and Σ0 approaches 1%. The key insight is that the dominant uncertainty in E_G is not cosmic variance or shape noise but the precision on β, so the constraining power of CSST hinges on spectroscopy.

Core claim

The authors claim that, using realistic mock photometric and spectroscopic samples of CSST over 17,500 square degrees, a harmonic-space estimator of E_G—constructed from the galaxy-convergence cross-spectrum Cgκ and the galaxy auto-spectrum Cgg with full accounting of their covariance—will reach few-percent statistical precision. The forecast integrated E_G constraints are 3–9% in four redshift bins between 0 and 1.2, limited chiefly by the assumed uncertainty in the RSD parameter β. Translating these measurements into the µ–Σ modified-gravity framework, they find Σ0 constrained to ~5% (and µ0 to 30–50%), with a strong degeneracy between the two parameters. In the optimistic scenario where β

What carries the argument

The central object is the E_G statistic in harmonic space, defined as E_G(ℓ) = (Γ/β)·(Cgκ/Cgg), where the ratio R=Cgκ/Cgg cancels galaxy bias and cosmic variance partially, and Γ is a geometric prefactor. The analysis is carried by a covariance framework that propagates Gaussian cosmic-variance, shot-noise, shape-noise, and non-Gaussian trispectrum terms for both spectra, and by the error-propagation relation σ²EG/EG² = σ²R/R² + σ²β/β², which isolates the RSD parameter β as the dominant source of uncertainty. The µ–Σ parametrization links the predicted E_G to modified-gravity deviations via E_G = Ωm,0(1+Σ)/(2f).

Load-bearing premise

The forecast error budget hinges on the assumed precision of the redshift-space distortion parameter β, whose values are taken from an unpublished companion paper, and on the assumption that β's error is uncorrelated with the lensing-to-clustering ratio error.

What would settle it

A measurement of E_G from CSST's first data at z≈0.5 that yields an uncertainty larger than the predicted ~4–5%—after realistic treatment of photometric errors and intrinsic alignments—would indicate that the assumed β precision or the covariance model is too optimistic.

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

If this is right

  • CSST will measure E_G at 3–9% precision in 0<z<1.2, a factor of several to an order of magnitude better than current measurements.
  • The modified-gravity coupling Σ0 can be constrained to about 5% (baseline) or ~1% if β is measured to 1%, enabling a direct test of the effective gravitational constant of the Weyl potential.
  • The error budget of E_G is dominated by the RSD parameter β, so upgrading spectroscopic β measurements directly and proportionally improves E_G constraints.
  • The E_G statistic is independent of galaxy bias and σ8 and partially cancels cosmic variance, providing a stable, model-independent gravity diagnostic on linear scales.
  • The synergy between photometric weak lensing and spectroscopic surveys is quantified: the lensing signal supplies the geometry, and spectroscopy supplies the growth-rate anchor.

Where Pith is reading between the lines

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

  • If the assumed β errors (taken from an unpublished companion paper) are optimistic, the headline 3–9% E_G precision and 5% Σ0 constraint would be degraded; the actual discrimination power may be closer to current measurements.
  • The framework's neglect of correlation between R and β errors (treated as independent in the covariance combination) could under- or over-estimate the final error budget; joint estimation of R and β from the same survey would settle this.
  • The same harmonic-space covariance machinery could be applied to other next-generation photometric+spectroscopic surveys, potentially yielding comparable E_G forecasts without re-deriving the estimator.
  • The forecast assumes linear bias and no intrinsic alignments; including these systematics will likely widen the error bars, so the reported percentages should be read as statistical lower bounds.

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

5 major / 4 minor

Summary. This paper presents forecasts for the E_G statistic using realistic mock redshift distributions for the CSST photometric and slitless spectroscopic surveys. The authors build a harmonic-space covariance framework that includes Gaussian and non-Gaussian terms, combine E_G(ℓ) measurements across multipoles, and translate the resulting redshift-dependent E_G constraints into the (µ0, Σ0) modified-gravity parameter plane. The headline results are 3%–9% E_G precision over 0 < z < 1.2, a Σ0 constraint of ~5%, and a speculative scenario with σ(β)/β = 1% yielding ~1% E_G and Σ0 precision. The paper identifies β, the RSD parameter, as the dominant uncertainty and argues that CSST will provide a factor-of-several to order-of-magnitude improvement over current E_G measurements.

Significance. If the forecast is robust, this is a useful planning result for a Stage-IV survey: it demonstrates the statistical power of CSST for a key gravity diagnostic, uses realistic galaxy redshift distributions, and explicitly accounts for the covariance between galaxy-galaxy lensing and clustering. The emphasis on the β-limited nature of E_G and on the synergy between photometric lensing and spectroscopic RSD measurements is timely. However, the quantitative central claims are conditional on externally supplied σ(β)/β values and on several simplifying assumptions, so the significance of the paper in its current form is limited by the strength of those inputs rather than by the methodology itself.

major comments (5)
  1. [Table 1 and §3] The four baseline values of σ(β)/β (8.73%, 4.02%, 3.14%, 3.28%) are the dominant uncertainty in the forecast, as explicitly shown by the right panel of Fig. 3. Yet these values are taken from Ref. [53], an unpublished manuscript 'in preparation' by the corresponding author, with no derivation, survey assumptions, or validation provided. Because the integrated E_G error cannot fall below the β error floor, and because the Σ0 constraint inherits this floor, the headline 3–9% and ~5% claims are controlled by an unverifiable external input. Please derive these β errors within the paper (e.g., a Fisher forecast from the same CSST mocks) or replace them with published forecasts, and show how the headline results degrade under conservative alternatives such as σ(β)/β ≈ 10–20%.
  2. [§2.2, Eq. (2.10)] Eq. (2.10) adds σ²(β)/β² to the covariance of R in quadrature, implicitly assuming that the errors in R and β are statistically independent. In practice β = f/b_g is estimated from RSD analyses of the same spectroscopic sample that provides Cgg, and Cgg also appears in the denominator of R. Scale-dependent bias, nonlinear RSD modeling, Alcock–Paczynski effects, and photo-z error propagation can all enter both terms and induce correlations. The authors should quantify this correlation or explicitly treat β as a marginalized nuisance parameter; otherwise the quoted percent-level E_G errors are likely optimistic.
  3. [§4.2, Eq. (2.22)] The Gaussian likelihood for (µ0, Σ0) assumes that E_G measurements in different lens redshift bins are uncorrelated. But the lens and source redshift distributions overlap, the survey window is shared, and the non-Gaussian covariance framework developed in §2.2 is not applied across redshift bins. Because µ0 and Σ0 are continuous functions of redshift through ΩΛ(z)/ΩΛ(0), correlated errors between z bins can bias or overstate the χ² contours in Fig. 4. Please propagate the full cross-redshift covariance, or justify this approximation with a numerical demonstration that the off-diagonal blocks are negligible.
  4. [Abstract and §4.2] The abstract states that deviations from the Hu–Sawicki f(R) model and the normal-branch nDGP model 'remain detectable within the expected sensitivity of CSST', but the paper does not compute E_G predictions for these models or report a detection significance. Fig. 4 only shows constraints in the (µ0, Σ0) plane. Either add explicit forecasts for representative f(R) and nDGP parameter choices with a Δχ² or distinguishability criterion, or revise the abstract to state that the (µ0, Σ0) constraints would be interpretable within such models.
  5. [Eqs. (2.2) and (2.20)] There is an internal factor-of-two inconsistency in the theoretical relation used for modified gravity. Eq. (2.2) gives E_G = Ωm/f in GR, while Eq. (2.20) with Σ = 0 gives E_G = Ωm/(2f). This is not a cosmetic issue: the mapping from E_G(z) to (µ0, Σ0) in §4.2 depends on the normalization of Eq. (2.20), and a factor of two would shift the inferred Σ0. Please reconcile the sign/factor conventions among Eqs. (2.1), (2.2), and (2.18)–(2.20).
minor comments (4)
  1. [Eq. (2.3)–(2.5)] The lensing kernel Wκ is written as if for a single source plane, but the forecasts use a source redshift distribution. The expression should be integrated over the source distribution, Wκ(z) = ∫ dz_s n_s(z_s) Wκ(z, z_s), to match the mock galaxy samples.
  2. [Eq. (2.10)] The notation 'Cov[E_G(ℓ)E_G(ℓ′)]' is missing a comma. It would also help to state explicitly whether the β term is added to all (ℓ, ℓ′) elements, reflecting a fully correlated β error, or only to the diagonal.
  3. [Fig. 3, right panel] The caption refers to 'the combined contributions from all other sources' but does not define which terms are included. Please list them (shot noise, shape noise, cosmic variance, non-Gaussian contribution, etc.).
  4. [References] Ref. [53] is an in-preparation article by one of the authors and is used for the most load-bearing input. Even after addressing the major comment above, the manuscript should clearly flag this as private communication or better, replace it with a published or independently derived forecast.

Circularity Check

1 steps flagged

Headline E_G/Σ0 precision is controlled by σ(β)/β values imported from an unpublished in-preparation article co-authored by Y. Zheng; the rest of the forecast pipeline is self-contained.

specific steps
  1. self citation load bearing [Table 1 caption; Section 2.2 Eq. (2.10); Section 4.1 and Fig. 3]
    "The error prediction of the β parameter in the lens redshift bin comes from [53]. ... As anticipated, the total uncertainty on EG is dominated by the limited precision in determining β through the RSD effect."

    The headline few-percent E_G and ~5% Σ0 constraints are propagated through Eq. (2.10), which adds sigma(β)^2/β^2 in quadrature. The paper itself identifies β as the dominant error, and Fig. 3 shows β sets the floor. Yet the σ(β)/β values (8.73%, 4.02%, 3.14%, 3.28%) are taken from Ref. [53], an unpublished 'in preparation' article by co-author Y. Zheng, and no derivation or validation is given in this paper. Thus the central quantitative claim is inherited from the authors' own unverified work, not established by the presented analysis. This is load-bearing self-citation, though the E_G covariance machinery is otherwise independent.

full rationale

The derivation of E_G from R = Cgκ/Cgg and β (Eqs. 2.6–2.10) is standard and internally consistent; the covariance computation for R is self-contained and uses published CSST mock samples. The modified-gravity likelihood (Eqs. 2.20–2.22) is also a standard forward-modeling step, not a redefinition. No step reduces to its inputs by construction in the sense of a fitted parameter being renamed as a prediction. The one serious provenance issue is that the forecast's dominant uncertainty—σ(β)/β—is imported from Ref. [53], an unpublished in-preparation paper by co-author Y. Zheng, with no derivation shown. Because the paper itself stresses that β dominates and that the 3–9% E_G and ~5% Σ0 numbers depend on that input, this is more than a harmless self-citation. The conditional 1%-β scenario is explicitly labeled as an idealized assumption, so it is not a circular prediction, but it does inherit the same input sensitivity. Overall, the central claim is not definitionally circular, but it relies on a load-bearing, unverified self-citation for its headline precision, warranting a moderate score.

Axiom & Free-Parameter Ledger

6 free parameters · 8 axioms · 0 invented entities

The forecast relies mostly on standard cosmology and random-field covariance mathematics, but the headline numbers lean on several adopted inputs: β errors from an unpublished reference, a phenomenological µ–Σ late-time scaling, and the assumption that redshift bins are uncorrelated. No new particles, forces, or conserved quantities are introduced.

free parameters (6)
  • σ(β)/β per redshift bin = 8.73%, 4.02%, 3.14%, 3.28%; 1% in idealized scenario
    Adopted from unpublished Ref. [53] by co-author Y. Zheng. These errors dominate the forecast E_G uncertainty and are not derived or justified in the paper.
  • Intrinsic shape noise σγ = 0.2
    Adopted from Ref. [54]; enters the shape-noise term σγ²/n_s in the lensing covariance and affects small-scale errors.
  • Photometric redshift scatter σ_zp = 0.025(1+z)
    Fiducial photo-z mock chosen from two options; affects the lens/source redshift distributions and lensing kernel.
  • Spectroscopic redshift error and success fraction = σ_zs=0.002(1+z), f0_eff=0.5
    Adopted for the spec-z mock from Refs. [68,69]; sets the spectroscopic sample density and redshift reliability.
  • Redshift binning and multipole range = Five bins 0<z<1.5; ℓ=10–1000 in 20 log bins
    Analysis choices that define how much signal is included; no sensitivity study or optimization is presented.
  • µ0 and Σ0 fiducial values = µ0=0, Σ0=0 (GR)
    Target parameters in the µ–Σ likelihood; the constraints depend on the ad hoc late-time scaling µ=µ0ΩΛ(z)/ΩΛ(0), Σ=Σ0ΩΛ(z)/ΩΛ(0).
axioms (8)
  • standard math Limber approximation for angular power spectra (Eqs. 2.3-2.4)
    Used to convert 3D power spectra to angular spectra; standard but not exact at low ℓ.
  • domain assumption Scale-independent linear galaxy bias: Pδg=b g Pδδ, Pgg=b_g² Pδδ
    Invoked in §2.1; needed for bias cancellation in E_G. Fails on nonlinear scales.
  • domain assumption Linear velocity divergence relation θ(k)=f(z)δ(k)
    Used in the theoretical E_G definition Eq. (2.1); breaks down at small scales and in nonlinear RSD.
  • domain assumption β errors are independent of R and taken from Ref. [53]
    Eq. (2.10) assumes independent errors; Table 1 adopts β errors from an unpublished reference.
  • standard math Gaussian covariance plus connected trispectrum (Eqs. 2.12-2.16)
    Standard random-field covariance; the non-Gaussian term is evaluated with pyccl but no validation or code is shown.
  • ad hoc to paper Late-time µ(z), Σ(z) proportional to ΩΛ(z)/ΩΛ(0)
    Phenomenological choice in Eq. (2.21) that 'preserves early-universe constraints'; not derived from a specific theory and shapes the µ0–Σ0 constraints.
  • ad hoc to paper E_G measurements at different redshifts are uncorrelated
    Assumption in Eq. (2.22) for the χ² likelihood; lensing kernels overlap between bins, so cross-z covariance is likely non-negligible.
  • domain assumption Fiducial ΛCDM background and GR growth index γ=0.55
    Used for the theoretical E_G baseline Ωm0/f(z) and for integrating modified-growth equations in pyccl.

pith-pipeline@v1.3.0-alltime-deepseek · 13929 in / 14798 out tokens · 156325 ms · 2026-08-03T08:09:22.253469+00:00 · methodology

0 comments
read the original abstract

We present forecasts for the $E_G$ statistic using redshift distributions of realistic mock galaxy samples from the upcoming Chinese Space Station Survey Telescope (CSST). The dominant uncertainty in $E_G$ stems from the redshift space distortion parameter $\beta$, whose precision limits the overall constraining power. Our analysis shows that CSST will nevertheless achieve $E_G$ constraints at the few-percent level ($3\%-9\%$) over $0 < z < 1.2$, an improvement by a factor of several to an order of magnitude over current observations. Within the $\mu-\Sigma$ modified gravity framework, the parameter $\Sigma_0$, associated with the effective gravitational constant of the Weyl potential, can be constrained to $\sim 5\%$ precision. In a plausible scenario where upcoming spectroscopic surveys determine $\beta$ to $1\%$ accuracy, $E_G$ constraints tighten to the percent level, and $\Sigma_0$ becomes measurable at $\sim 1\%$. For representative modified gravity scenarios, we find that the potential deviations from the Hu--Sawicki $f(R)$ model and the normal-branch Dvali--Gabadadze--Porrati (nDGP) model remain detectable within the expected sensitivity of CSST. These results demonstrate that CSST will serve as a powerful facility for testing gravity and underscore the essential synergy between photometric weak lensing and spectroscopic surveys in probing cosmic acceleration.

discussion (0)

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