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REVIEW 2 major objections 7 minor 178 references

Ignoring linear relativistic effects can shift local non-Gaussianity constraints by 1–3σ in Stage-IV galaxy surveys, and multi-tracer clustering can make some of those effects measurable.

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2026-07-10 23:10 UTC pith:A7Y3DMVQ

load-bearing objection First practical full-GR Bayesian SFB pipeline for Stage-IV PNG forecasts; the 1–3σ f_NL bias and multi-tracer Doppler gains are real under the stated assumptions. the 2 major comments →

arxiv 2607.06697 v1 pith:A7Y3DMVQ submitted 2026-07-07 astro-ph.CO

Impact and measurability of linear relativistic effects in galaxy surveys

Robin Y. Wen , Henry S. Grasshorn Gebhardt , Olivier Dor\'e This is my paper
classification astro-ph.CO
keywords primordial non-Gaussianityf_NLrelativistic effectsspherical Fourier-Besselgalaxy clusteringmulti-tracerDESIEuclid
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.

Stage-IV galaxy surveys will map structure on scales comparable to the Hubble horizon, where both primordial non-Gaussianity and general-relativistic corrections to galaxy clustering become important. This paper forecasts how well DESI, Euclid, and SPHEREx can measure local primordial non-Gaussianity and linear relativistic effects using the spherical Fourier-Bessel power spectrum, accelerated by a Chebyshev decomposition that makes full Bayesian inference practical. The central result is that treating the data as purely Newtonian can bias the local non-Gaussianity parameter at the one-to-three-sigma level for Euclid and SPHEREx, with the size of the bias strongly dependent on the tracer’s magnification and evolution biases. Lensing is detectable at high significance for several samples, multi-tracer combinations substantially improve the Doppler term, and relativistic clustering partially lifts the exact product degeneracy between the local non-Gaussianity amplitude and the response bias that plagues Newtonian analyses—though that response bias remains only weakly constrained for the survey setups considered. The work therefore maps both the contamination risk and the scientific opportunity in ultra-large-scale galaxy clustering.

Core claim

Neglecting linear-order general-relativistic contributions when analyzing the three-dimensional galaxy power spectrum can bias local f_NL constraints at the 1–3σ level for Euclid and SPHEREx. The degeneracy between relativistic and primordial-non-Gaussianity terms is strongly tracer-dependent; lensing is measurable at high significance for several tracers; multi-tracer analyses substantially improve Doppler measurability; and, assuming general relativity, relativistic clustering partially breaks the exact b_ϕ f_NL product degeneracy of Newtonian linear analyses, while the resulting b_ϕ constraints remain weak for the configurations studied.

What carries the argument

The spherical Fourier-Bessel (SFB) power spectrum of multi-tracer galaxy clustering on the light cone, evaluated with a Chebyshev decomposition of the radial kernels so that the full set of linear relativistic terms can be recomputed in roughly one second and used inside Bayesian inference.

Load-bearing premise

The forecasts assume that the local non-Gaussianity bias is tied to the linear bias by the universality relation and that this same bias equals the evolution bias, plus a default magnification bias of one for all SPHEREx samples that have not been measured directly.

What would settle it

Apply the same full-GR SFB pipeline to early DESI or Euclid spectroscopic catalogs (or to mocks with independently measured magnification and evolution biases) and check whether the recovered f_NL shifts by the predicted 1–3σ when GR terms are dropped, and whether multi-tracer Doppler constraints reach the forecasted few-sigma level.

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

If this is right

  • PNG analyses aiming for σ(f_NL) ~ 5 with Euclid or SPHEREx must include linear GR terms tracer by tracer or risk percent-to-factor-of-two level biases.
  • Lensing amplitude can be used as an independent cross-check of magnification bias measured from flux-perturbation pipelines.
  • Multi-tracer combinations of DESI and SPHEREx samples turn the Doppler term from undetectable into a several-sigma signal.
  • Joint PNG–GR inference provides a consistent way to fold residual b_ϕ uncertainty into marginalized f_NL without forcing an external prior.
  • Optimized subsample splits that maximize differences in linear, magnification, and evolution bias can further improve both PNG and GR measurability.

Where Pith is reading between the lines

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

  • Once real magnification-bias measurements exist for SPHEREx, the forecasted f_NL bias map will need to be recomputed; samples near s ≈ 0.4 may flip from ‘GR-critical’ to ‘GR-safe’.
  • The same Chebyshev-SFB engine is a natural backbone for joint analyses with CMB lensing or intensity mapping, where integrated GR terms gain extra leverage.
  • If future multi-tracer samples can push σ(b_ϕ,0) below ~1, power-spectrum-only f_NL constraints without external b_ϕ priors become realistic.
  • The tracer dependence of the GR–PNG degeneracy implies that sample selection itself is a design variable for Stage-V surveys, not only volume and number density.

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

2 major / 7 minor

Summary. This paper forecasts constraints on local primordial non-Gaussianity (f_NL) and linear-order relativistic effects in the spherical Fourier-Bessel (SFB) power spectrum for DESI, Euclid, and SPHEREx. A Chebyshev decomposition accelerates multi-tracer SFB evaluations with the full set of linear GR terms, enabling both Fisher forecasts and simulated Bayesian inference (MCMC and nested sampling). The central results are: (i) fitting full-GR data vectors with Newtonian models can bias f_NL at the 1–3σ level for Euclid Hα and SPHEREx; (ii) GR–PNG degeneracies are strongly tracer-dependent, with the largest degradation from the gravitational-potential term; (iii) lensing is detectable at high SNR for several tracers, while multi-tracer analyses substantially improve Doppler constraints; and (iv) under GR and the b_ϕ–be equivalence, relativistic clustering partially breaks the Newtonian b_ϕ f_NL product degeneracy, though residual b_ϕ constraints remain weak and projection-dominated.

Significance. The work is a timely and technically substantial contribution to ultra-large-scale structure forecasting for Stage-IV surveys. Its main methodological advance is a validated Chebyshev scheme that reduces full-GR SFB evaluations to O(1 s), enabling the first Bayesian inference with the complete linear relativistic kernel in 3D clustering. The mismatch tests (full-GR data vs Newtonian model), mode-cut scans, multi-tracer amplitude forecasts, and joint PNG–GR sampling of b_ϕ are carefully designed and clearly reported. If the results hold under more realistic windows and selection functions, they provide concrete guidance on when GR must be included for unbiased f_NL analyses and on the practical reach of multi-tracer relativistic measurements.

major comments (2)
  1. [Abstract; §III C 3; §IV B; Fig. 11; Table V] The headline claim that neglecting GR biases f_NL at the 1–3σ level for SPHEREx (Abstract; §IV B; Figs. 9–10) is computed under the fiducial choice s=1 for all five SPHEREx samples (§III C 3), which is not measured from data or simulation. Fig. 11 and Table V show that both the f_NL shift and the GR-amplitude constraints depend strongly on s (vanishing near s≈0.4). The abstract and conclusions should state this dependence explicitly and qualify the SPHEREx bias numbers as conditional on the assumed magnification bias, while leaving the Euclid result (which uses literature s) unqualified.
  2. [§IV B; §IV C 1; Figs. 11–12] In §IV B the authors attribute the GR-induced f_NL shifts primarily to lensing, supported by the s-variation test in Fig. 11 and by the small shift for DESI QSO (s≈0.276). A cleaner, load-bearing check would be a term-by-term mismatch: generate data vectors with only lensing, only Doppler, or only GP turned on, and refit with the Newtonian model. Without that decomposition, the claim that “lensing magnification [is] the dominant source of the GR-induced shifts” remains plausible but not fully isolated from residual GP–PNG confusion for tracers where ϵ_GP and f_NL are partially degenerate (§IV C 1, Fig. 12).
minor comments (7)
  1. [§III A] §III A and Eq. (22): the use of noiseless theory data vectors is standard for misspecification bias, but a short sentence clarifying that the reported “Nσ” shifts are relative to the posterior width under the same idealized covariance (not a single noisy realization) would help non-specialist readers.
  2. [§I; §III] §I and §III: the paper ignores survey masks and integral constraints in the theory model, retaining only an f_sky rescaling in the covariance and an ℓ_min cut. A brief quantitative estimate of residual IC leakage for SPHEREx (f_sky=0.75, ℓ_min=2) would strengthen confidence that the large-scale PNG/GR results are not artificially optimistic.
  3. [Fig. 2; §III; Fig. 17] Fig. 2 caption and §III: Fisher–MCMC agreement is shown only for DESI QSO under Newtonian modeling. A one-sentence note on whether similar agreement holds for the more non-Gaussian b_ϕ–f_NL posteriors (Fig. 17) would be useful, even if nested sampling is used there for that reason.
  4. [Table III; §IV A 1; §III C 3] Table III vs inference runs: baseline Fisher uses k_max=0.08 h/Mpc and full redshift ranges, while inference uses k_max=0.06 h/Mpc and z∈[0,2] for SPHEREx. Cross-referencing these choices more prominently when comparing σ(f_NL) numbers would avoid confusion.
  5. [Appendix B; Figs. 25–26] Appendix B: the Chebyshev accuracy for GR terms is stated as percent-level (Fig. 26). Given that GR is subdominant, this is adequate, but a short statement of the maximum fractional error on C_ℓnn for the full (density+RSD+GR) spectrum at the scales used in inference would complete the validation.
  6. [Throughout; Appendix B.4] Typographical: “evoluton bias” (p. 3), “diminsihes” (p. 17), “non-pertubative” (p. 29), and “Implementaion” (Appendix B.4 heading) should be corrected.
  7. [Fig. 1; §II C; §IV D] Fig. 1 is a helpful summary of the four bias cases; referring back to it when switching between Case 1 (baseline) and Case 3 (§IV D) would improve readability.

Circularity Check

0 steps flagged

No significant circularity: standard mismatch forecasts and model-conditional claims under externally motivated bias assumptions.

full rationale

This is a forecasting paper. Fiducial cosmology is Planck 2018; tracer n(z), b1, and s are taken from DESI data releases, Euclid/SPHEREx forecast products, or literature measurements (Secs. III C 1–3). The bϕ–be equivalence (Eq. 12) is imported from Sullivan & Seljak and related peak-background-split arguments, not derived from the same likelihood that is later sampled. Case 1 is adopted as a transparent baseline (Fig. 1, Sec. II C), and the paper quantifies sensitivity to s and to alternative bias parametrizations (Fig. 11, Tables V, VII; Sec. IV D). The central scientific results—1–3σ fNL bias when full-GR data vectors are fit with Newtonian models, tracer-dependent GR–PNG degeneracies, multi-tracer Doppler gains, and weak residual bϕ constraints—are obtained from controlled mismatch tests and amplitude forecasts under stated assumptions, not from fitting a parameter and re-labeling a related quantity as a prediction. Self-citations to the authors’ prior SFB methodology papers supply computational infrastructure (kernels, Iso-qr, discrete basis) that is validated against CLASS/angular spectra; they do not force the forecast conclusions by uniqueness theorems or ansatz smuggling. No step reduces a claimed prediction to its own input by construction.

Axiom & Free-Parameter Ledger

4 free parameters · 5 axioms · 0 invented entities

Forecasts rest on standard linear GR + PNG theory, the discrete SFB basis of prior work, the b_ϕ–be equivalence, universality (or p-parametrized) relations, Planck 2018 cosmology, and survey-specific number densities/biases taken from data or simulations. Phenomenological ϵ amplitudes and Chebyshev bias expansions are free parameters of the inference, not new physics entities.

free parameters (4)
  • Chebyshev coefficients of b1(z), s,0, b_ϕ,0 (or p)
    Amplitude and redshift-evolution parameters marginalized in every forecast; fiducial functions are external but overall scales are free.
  • ϵ_Dopp, ϵ_Lens, ϵ_GP
    Phenomenological amplitudes of individual GR terms, varied to assess detectability; fiducial = 1.
  • f_NL
    Primary parameter of interest; fiducial = 0.
  • SPHEREx magnification bias s
    Set by hand to s=1 for all five samples in the absence of a measurement.
axioms (5)
  • domain assumption Linear-order relativistic galaxy number counts (Eq. 2) in conformal Newtonian gauge, ignoring observer terms for ℓ≥2
    Standard result of Yoo/Challinor/Bonvin/Jeong et al.; adopted throughout.
  • domain assumption b_ϕ–be equivalence (Eq. 12) under peak-background split, used as Case 1 baseline
    Taken from Sullivan & Seljak 2025 and validated on simulations elsewhere; load-bearing for b_ϕ constraints.
  • domain assumption Universality relation b_ϕ = 2δ_c(b1−p) with p=1 (or 1.6 for QSO)
    Standard UMF assumption; relaxed only in the p-parametrization of Sec. IV D.
  • ad hoc to paper Gaussian likelihood for SFB power spectra + f_sky covariance approximation; noiseless simulated data vectors
    Explicit modeling choices in Sec. III A–B that simplify inference but omit window coupling and cosmic variance of the data vector.
  • domain assumption Planck 2018 ΛCDM + fixed late-time parameters; linear theory only up to k_max=0.06–0.08 h/Mpc
    Standard forecast setup; one-loop corrections left for future work.

pith-pipeline@v1.1.0-grok45 · 54319 in / 2833 out tokens · 36160 ms · 2026-07-10T23:10:58.893528+00:00 · methodology

0 comments
read the original abstract

The three-dimensional galaxy power spectrum is a powerful probe of primordial non-Gaussianity (PNG) and additional general relativistic (GR) effects on large scales, which can be constrained by current and upcoming large-scale structure surveys. In this work, we forecast the measurability of local PNG and linear-order relativistic effects in the spherical Fourier-Bessel (SFB) power spectrum for DESI, Euclid, and SPHEREx surveys. A Chebyshev-decomposition scheme is employed to accelerate the multi-tracer SFB power-spectrum calculations. Fisher forecasts establish baseline constraints and test the sensitivity of $f_{\rm NL}$ constraints to SFB mode cuts and to the marginalization over primordial cosmological parameters, while simulated Bayesian inference is used to quantify the impact and measurability of relativistic effects. We find that neglecting GR effects can bias $f_{\rm NL}$ constraints at the $1$-$3\sigma$ level for Euclid and SPHEREx. The degeneracy between GR and PNG terms is strongly tracer dependent, with the degradation of $\sigma(f_{\rm NL})$ ranging from a few percent to nearly a factor of two when the GR amplitudes are varied. Lensing can be detected at high significance for several tracers, while multi-tracer analyses substantially improve the measurability of the Doppler term. Assuming GR, we show that relativistic clustering partially breaks the exact $b_\phi f_{\rm NL}$ product degeneracy present in Newtonian linear power-spectrum analyses, although the resulting $b_\phi$ constraints remain weak for the survey configurations considered. The joint PNG-GR inference consistently propagates uncertainty in $b_\phi$ into the marginalized $f_{\rm NL}$ constraint. This firmly establishes the path toward extracting cosmological information from ultra-large-scale galaxy clustering.

Figures

Figures reproduced from arXiv: 2607.06697 by Henry S. Grasshorn Gebhardt, Olivier Dor\'e, Robin Y. Wen.

Figure 1
Figure 1. Figure 1: FIG. 1. Summary of four possible parameterizations of the [PITH_FULL_IMAGE:figures/full_fig_p005_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Comparison of constraints from Fisher forecast with [PITH_FULL_IMAGE:figures/full_fig_p009_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Survey parameters for DESI LRG, ELG, QSO, and Euclid H [PITH_FULL_IMAGE:figures/full_fig_p011_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. Survey parameters for the SPHEREx galaxy samples used in our forecasts. Shown are the comoving number density [PITH_FULL_IMAGE:figures/full_fig_p011_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: , we adopt kmax = 0.06 h/Mpc for all tracers in inference runs. This choice preserves most of the local PNG information while reducing the cost of the exact SFB PS calculations, whose computational complexity scales approximately as k 3 max. The off-diagonal cut with ∆nmax plays a different role. Since it is applied at the power-spectrum level rather than the mode level, it does not accelerate the theo- [… view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6. Sensitivity of [PITH_FULL_IMAGE:figures/full_fig_p014_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7. Fisher forecast for the DESI QSO sample under New [PITH_FULL_IMAGE:figures/full_fig_p015_7.png] view at source ↗
Figure 9
Figure 9. Figure 9: FIG. 9. Impact of ignoring linear relativistic effects in local PNG inference for DESI, Euclid, and SPHEREx single tracers. We [PITH_FULL_IMAGE:figures/full_fig_p016_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: FIG. 10. Impact of ignoring relativistic effects in local PNG inference for the combined SPHEREx five samples (SPHEREx [PITH_FULL_IMAGE:figures/full_fig_p017_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: FIG. 11. Impact of ignoring GR effects on local PNG infer [PITH_FULL_IMAGE:figures/full_fig_p018_11.png] view at source ↗
Figure 13
Figure 13. Figure 13: FIG. 13. Joint posteriors of [PITH_FULL_IMAGE:figures/full_fig_p019_13.png] view at source ↗
Figure 14
Figure 14. Figure 14: FIG. 14. One-dimensional marginalized constraints on [PITH_FULL_IMAGE:figures/full_fig_p019_14.png] view at source ↗
Figure 15
Figure 15. Figure 15: FIG. 15. Measurability of the Doppler and gravitational [PITH_FULL_IMAGE:figures/full_fig_p020_15.png] view at source ↗
Figure 16
Figure 16. Figure 16: FIG. 16. Constraints on [PITH_FULL_IMAGE:figures/full_fig_p021_16.png] view at source ↗
Figure 17
Figure 17. Figure 17: FIG. 17. Constraints of [PITH_FULL_IMAGE:figures/full_fig_p022_17.png] view at source ↗
Figure 18
Figure 18. Figure 18: FIG. 18. Joint constraints on [PITH_FULL_IMAGE:figures/full_fig_p023_18.png] view at source ↗
Figure 19
Figure 19. Figure 19: FIG. 19. Constraints on [PITH_FULL_IMAGE:figures/full_fig_p024_19.png] view at source ↗
Figure 20
Figure 20. Figure 20: FIG. 20. Illustration of the radial mixing matrix induced by [PITH_FULL_IMAGE:figures/full_fig_p025_20.png] view at source ↗
Figure 21
Figure 21. Figure 21: FIG. 21. Validation of the convolution approach for incor [PITH_FULL_IMAGE:figures/full_fig_p027_21.png] view at source ↗
Figure 22
Figure 22. Figure 22: FIG. 22. Comparison of perturbative and non-perturbative treatments of FoG/redshift-error effects in the SFB power spectrum [PITH_FULL_IMAGE:figures/full_fig_p028_22.png] view at source ↗
Figure 23
Figure 23. Figure 23: FIG. 23. Convergence of the non-perturbative redshift-error [PITH_FULL_IMAGE:figures/full_fig_p029_23.png] view at source ↗
Figure 24
Figure 24. Figure 24: FIG. 24. Example of Chebyshev interpolation of a radial func [PITH_FULL_IMAGE:figures/full_fig_p031_24.png] view at source ↗
Figure 25
Figure 25. Figure 25: FIG. 25. Accuracy of the Chebyshev method for the linear [PITH_FULL_IMAGE:figures/full_fig_p033_25.png] view at source ↗
Figure 26
Figure 26. Figure 26: FIG. 26. Accuracy of the Chebyshev method for the linear [PITH_FULL_IMAGE:figures/full_fig_p033_26.png] view at source ↗

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