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REVIEW 3 major objections 5 minor 3 cited by

The covariance between pre-reconstruction power spectrum and post-reconstruction correlation function is captured analytically in three equations that, the paper shows, can replace mock estimates in joint BAO and full-shape fits.

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2026-08-02 23:50 UTC pith:JZQMFQCP

load-bearing objection First analytic pre-post cross-covariance; honest and useful, though validation is mostly visual and the BAO-damping model has an admitted, untested caveat. the 3 major comments →

arxiv 2602.12343 v2 pith:JZQMFQCP submitted 2026-02-12 astro-ph.CO

An analytic approximation to the covariance between pre- and post-reconstruction galaxy two-point statistics

M. Maus , A. Baleato Lizancos , M. White , A. de Mattia , S. Chen This is my paper
classification astro-ph.CO
keywords galaxy clusteringbaryon acoustic oscillationsBAO reconstructioncovariance matrixpower spectrumtwo-point correlation functionanalytic covariancefull-shape analysis
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 covariance between pre-reconstruction galaxy power spectrum measurements and post-reconstruction correlation functions can be approximated analytically with a simple three-equation prescription. The model starts from the disconnected (Gaussian) contribution to the covariance and uses a damped cross-power spectrum, with damping set by the variance of the pairwise displacement caused by BAO reconstruction. Against mock galaxy catalogs with realistic survey geometry, fiber-assignment cuts, and window rotation, the analytic cross-covariance matches the simulation-based values well, and a hybrid covariance that uses the analytic block yields essentially identical cosmological parameter constraints as the full mock covariance. If correct, this removes a major computational bottleneck in joint BAO and full-shape analyses and paves the way toward fully analytic covariance matrices for next-generation surveys.

Core claim

The paper's central claim is that Cov[P_pre_ℓ1(k), ξ_post_ℓ2(r)] — the cross-covariance between Legendre multipoles of the pre-reconstruction power spectrum and the post-reconstruction correlation function — is well described by the disconnected covariance evaluated with an approximate cross-power P×(k) = exp(−k²σ²(µ)/2)[(b + f µ²)²P_lin(k) + S_N]. The damping scale σ²(µ) is the pairwise displacement variance in the small-separation limit, [1+(1+f)²µ²]Σ₀², with Σ₀² the integral of the linear power spectrum filtered by the reconstruction smoothing window. Despite neglecting survey window functions, connected trispectrum terms, and fiber-assignment effects in the analytic calculation, comparis

What carries the argument

The load-bearing identity is Eq. (2.5), which reduces the pre-post covariance to an angular integral of Legendre polynomials weighted by products of the cross-power multipoles P×,L(k), divided by the survey volume V. This is closed by two modeling equations: a perturbative expression for the pre-post cross-power, P× ≈ exp(−k²σ²(µ)/2)[(b + f µ²)²P_lin + S_N], and the small-separation pairwise displacement variance σ²(µ) ≈ [1 + (1+f)²µ²]Σ₀², where Σ₀² = (1/3)∫(dk/2π²)P_lin(k)W²(k) and W is the reconstruction smoothing window. The trio (2.5)-(2.7) constitutes the entire analytic prescription: it needs only the linear power spectrum, bias, growth rate, shot noise, smoothing scale, and survey vol

Load-bearing premise

The model assumes that the small-separation (q→0) pairwise-displacement variance sets the correct BAO damping in the cross-power P×, but the authors note this limit over-predicts the BAO amplitude and that a faithful treatment needs the displacement variance evaluated at the BAO scale (q = r_d), so the analytic cross-covariance may be systematically off on exactly the scales the post-reconstruction correlation function is designed to measure.

What would settle it

Compute the analytic covariance of Eq. (2.5)–(2.7) and compare it bin-by-bin to a high-statistics mock covariance over the BAO r-range (82–102 h⁻¹Mpc), using jackknife errors from many realizations. If the normalized residuals exceed ~1 per bin (or a chi² per degree of freedom well above 1), the 'essentially identical' claim fails at these scales. A sharper test: re-run the parameter fits replacing the q→0 damping with the BAO-scale-damped cross-power (the q=r_d form) and check whether the resulting constraints shift by more than the statistical error relative to the hybrid case; if they do, t

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

If this is right

  • Joint BAO and full-shape analyses can replace the mock-derived pre-post cross-covariance block with the analytic one and recover essentially the same parameter constraints.
  • The analytic block can be used to denoise simulation-based covariance estimates, since it is noiseless and free of Monte-Carlo scatter.
  • Because the cross-covariance is small, even a rough treatment is adequate; ignoring the block entirely is a worse but still close approximation, with a visible effect of artificially narrowing error bars in the H0–Ωm plane.
  • The prescription offers a way to update covariance matrices when the fiducial cosmology changes without regenerating thousands of mock catalogs.
  • Together with other analytic covariance efforts, it points toward fully analytic covariance matrices that could remove the need for large suites of low-fidelity mocks in future surveys.

Where Pith is reading between the lines

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

  • A corrected damping model that evaluates the pairwise displacement variance at the BAO scale rather than in the q→0 limit would likely improve agreement exactly in the r≈82–102 h⁻¹Mpc range where post-reconstruction ξ is most informative.
  • The demonstrated smallness suggests the same analytic route may extend to compressed BAO statistics such as α∥ and α⊥, or to cross-covariances between pre- and post-reconstruction correlation functions, though those would need their own validation.
  • The method could be extended naturally to other tracers (e.g., quasars or emission-line galaxies) by re-estimating bias and shot noise, a next test the paper does not perform.
  • The noiseless analytic block could also be used to define a prior on covariance shape in hierarchical analyses, where mock noise is otherwise propagated.

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 derives a closed-form analytic approximation for the cross-covariance between pre-reconstruction power spectrum multipoles and post-reconstruction correlation function multipoles, based on the disconnected (Gaussian) contribution to the covariance and a perturbative model for the pre-post cross-power P× (Eqs. 2.5–2.7). The approximation is validated against covariance matrices estimated from 1000 EZmocks in both cubic and DESI cut-sky geometries, including the θ-cut and the window-rotation variant. The authors report that a hybrid covariance with the analytic cross-block yields parameter constraints 'essentially identical' to those from the full simulation covariance, and that even setting the cross-block to zero changes constraints only mildly. They conclude that the pre-post correlation is small enough that approximate analytic treatments are sufficient for joint BAO+full-shape analyses, and they make the code publicly available.

Significance. If the quantitative claims are established, this is a useful practical result for DESI/Euclid-era analyses: it removes a simulation-dependent component of the joint covariance matrix, provides a noiseless and cosmology-dependent estimate, and allows cheap updates when the fiducial cosmology changes. The derivation is transparent, the inputs are not fitted to the target covariance, and the validation setup is appropriate (1000 EZmocks, cubic and realistic footprints, θ-cut and window rotation). The code release is a strength. However, the headline claims of 'excellent agreement' and 'essentially identical constraints' currently rest on visual inspection, and the model for P× is admitted in Appendix B to be inaccurate at precisely the BAO scales that motivate the post-reconstruction ξ. The paper therefore needs a quantitative demonstration that this admitted model error does not affect the covariance entries and parameter constraints it is designed to replace.

major comments (3)
  1. [§2, Appendix B (Eqs. 2.6, 2.7, B.3–B.4)] The model uses the q→0 pairwise-displacement limit σ²(μ) = [1+(1+f)²μ²]Σ₀² in Eq. (2.7). Appendix B explicitly states that this limit 'over-predicts the amplitude of the BAO in the cross' and that the BAO damping should instead be evaluated at q=r_d (Eq. B.4). Since Cov[P_l1, ξ_l2] ∝ Pײ (Eq. 2.5) and the post-reconstruction ξ_l2 enters the analysis precisely because of BAO information at r≈82–102 h^{-1} Mpc, a model error in P× at BAO scales propagates into the very block the paper proposes to replace. The paper does not quantify the size of this effect. Please compare the q→0 model with the r_d-damped model against the mock covariance at the BAO radii, or demonstrate explicitly that the affected entries are small compared with the simulation covariance and with the resulting parameter shifts.
  2. [§3, Figs. 1, 2, and 4] The central validation claims — 'excellent agreement' in §3.2 and 'essentially identical constraints' in §3 and §4 — are supported only by visual comparisons of dashed curves with jackknife error bars and of posterior contours. No chi-square, residual norm, maximum fractional difference, or parameter-shift statistic is reported. Please add a quantitative agreement metric for the cross-covariance blocks (e.g. χ² using the jackknife covariance of the mock covariance estimates) and report shifts in Ω_m and H_0 (and σ_8 if used) between the hybrid and full simulation covariance in units of the posterior width. Without this, the falsifiability of the main claim is limited and the stated precision of agreement is not established.
  3. [§3.2, Fig. 2] The comparison with cut-sky mocks is shown for only two r-bins, r=82 and 102 h^{-1} Mpc. The post-reconstruction ξ data vector in a BAO+full-shape analysis generally includes a wider range of r bins (and the covariance binning used in §3.2 is not specified). Showing all ℓ1-ℓ2 blocks at two radii cannot establish agreement over the full ξ_post vector. Please present residuals or χ² per r-bin over the full r range used in the inference, or state the complete r range and explain why the two displayed radii are sufficient.
minor comments (5)
  1. [Appendix A] Typo: 'ingnoring' should be 'ignoring'.
  2. [Eq. (B.3)] The prefactor A appears undefined; the notation AδD(q) should be clarified, probably as A δ_D(q) with A defined.
  3. [Fig. 2 and Fig. 3 captions] The sentence about shifting 'the orange data points' is confusing because both analytic and simulated series are shown. Specify which series is shifted.
  4. [§3.1] The cubic-geometry agreement is stated but not shown explicitly; a small figure or a short quantitative statement (e.g. maximum fractional difference per block) would help the reader assess the first validation.
  5. [§2, Eq. (2.5)] The derivation assumes even ℓ1 and ℓ2; the text should state explicitly that the data vector is restricted to even multipoles, as is standard for these statistics.

Circularity Check

0 steps flagged

No significant circularity: the analytic covariance is constructed from an external perturbative P× model and validated against independent mocks.

full rationale

The derivation chain is self-contained in the relevant sense. The target object, Cov[P_pre, ξ_post], is built from Eq. (2.5), the standard disconnected covariance of the pre- and post-reconstruction density fields, with the only nontrivial model input being the cross-power P× from Eqs. (2.6)–(2.7). That P× model is taken from perturbation theory (with refs. [22,26]) and its parameters are external to the target covariance: Plin from the fiducial Abacus cosmology via CLASS, f=0.838 from that cosmology, b=2.03/2.05 from prior clustering fits, S_N=0.6/(nbar) from ref. [31], and V from mock randoms. None of these values is fit to the simulation covariance that the paper claims to predict; the EZmocks are used only for validation after the model is fixed. The heavy self-citation for the P× form and the velocileptors checks involves independent derivations/code, not a restatement of the target covariance, so it does not constitute load-bearing circularity. Appendix B's admission that the q→0 limit over-predicts the BAO amplitude in P× is a model-accuracy caveat, not a circularity: it means some covariance entries may be quantitatively off, but the prediction is not equivalent to its input by construction. The validation is largely visual and the posterior comparisons are qualitative, but absence of a quantitative metric is a reporting weakness, not evidence that the analytic block was derived from the simulation covariance.

Axiom & Free-Parameter Ledger

4 free parameters · 4 axioms · 0 invented entities

The central claim rests on three domain assumptions: disconnected covariance dominance, a perturbative cross-power spectrum with q→0 damping, and neglect of the survey window in the cross block. All numerical inputs (b, S_N, V_eff, W) are imported from external fits or survey geometry; none is fitted to the target covariance. No new physical entities are introduced.

free parameters (4)
  • Eulerian linear galaxy bias b = 2.03 (cubic); 2.05 (cut-sky)
    Enters the amplitude of P× through (b+f μ^2)^2 in Eq. 2.6; taken from fits to DESI/Abacus mocks, not predicted by the model.
  • Shot-noise prefactor S_N = 0.6 × 1/n̄ = 0.6 × (1/5000 h^{-3} Mpc^3)
    Additive constant in the P× model (Eq. 2.6); prefactor taken from ref. [31] and n̄ from the mock sample; shifts the overall covariance amplitude.
  • Effective survey volume V_eff = 8 (h^{-1} Gpc)^3 (cubic); 2.87 (h^{-1} Gpc)^3 (cut-sky)
    Normalizes the disconnected covariance in Eq. 2.5; measured from mock boxes/randoms rather than fitted to the covariance.
  • Reconstruction smoothing window W(k) = not stated
    Enters the damping σ^2 integral in Eq. 2.7; the paper assumes a Gaussian smoothing but does not report the numerical smoothing scale used in the validation.
axioms (4)
  • domain assumption Disconnected (Gaussian) contribution dominates the pre-post covariance (Eq. 2.4).
    Connected trispectrum, super-sample covariance, and beat-coupling terms are neglected; the paper notes the connected part is likely too complicated to treat analytically (Section 1).
  • domain assumption P× model of Eq. 2.6, with q→0 pairwise-displacement damping, is adequate for the scales entering the covariance.
    Perturbative cross-power is taken from refs. [22,26]; Appendix B concedes this limit over-predicts the BAO amplitude of the cross, which would require Eq. B.4.
  • domain assumption Survey window, θ-cut, and fiber-assignment effects can be neglected in the analytic cross-covariance block.
    The model omits the survey window; the paper validates this by comparing to cut-sky mocks rather than deriving the window contribution.
  • standard math Slow variation of P_pre over the k-bin and even multipoles.
    Used to reduce the integral expression in Eq. 2.1 and to simplify Eq. 2.3 to Eq. 2.5.

pith-pipeline@v1.3.0-alltime-deepseek · 10345 in / 15093 out tokens · 133716 ms · 2026-08-02T23:50:38.666021+00:00 · methodology

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read the original abstract

We present a simple analytic approximation for the covariance between pre-reconstruction galaxy power spectrum measurements and post-reconstruction two-point correlation functions. This cross-covariance is essential for joint analyses that combine full-shape clustering information with baryon acoustic oscillation (BAO) measurements, as commonly performed in modern spectroscopic surveys. Our model builds on the disconnected contribution to the covariance and accounts for the damping of correlations due to the BAO reconstruction process. We validate our analytic prescription against numerical simulations from the Dark Energy Spectroscopic Instrument (DESI), testing both idealized cubic geometries and realistic survey configurations including complex footprints and fiber assignment effects. Despite neglecting survey window functions in the analytic calculation, we find excellent agreement with simulation-based covariances and demonstrate that cosmological parameter constraints are virtually unchanged when using our approximation. Our results show that the pre-post cross-covariance is sufficiently small that even approximate treatments are adequate for cosmological inference, opening a pathway toward fully analytic covariance matrices for next-generation galaxy surveys.

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