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REVIEW 3 major objections 6 minor 67 references

Stage-V galaxy surveys can resolve the mass-dependent shape of inflationary non-Gaussianity, not only its amplitude, once local PNG is detected at high significance.

Reviewed by Pith at T0; open to challenge. T0 means a machine referee read the full paper against a public rubric. the ladder, T0–T4 →

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2026-07-30 11:00 UTC pith:RXEQRUA3

load-bearing objection Solid methods-and-forecast paper: first real-data beyond-local ACF on DESI Imaging plus a usable Stage-V σ(Δ)–σ(f_NL^loc) planning bridge, carefully caveated and not oversold. the 3 major comments →

arxiv 2607.27175 v1 pith:RXEQRUA3 submitted 2026-07-29 astro-ph.CO

Searching for signatures of inflationary massive fields in DESI Imaging data and Stage-V galaxy surveys

Walter Riquelme , Santiago Avila , Lucas Pinol , Hui Kong , Anna Porredon This is my paper
classification astro-ph.CO PACS 98.80.Cq98.65.Dx98.80.Es
keywords primordial non-Gaussianityscale-dependent biasmassive fields during inflationDESI ImagingStage-V surveysLyman-break galaxiesangular correlation functionquasi-single-field inflation
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.

Light massive fields during inflation leave a scale-dependent mark on galaxy clustering that is not the usual local primordial non-Gaussianity shape. The signal scales as f_NL,Δ times k to the power Δ−2, where Δ is set by the field’s mass in Hubble units and runs from 0 (the local limit) up to 3/2. This paper maps that signature onto the angular clustering of DESI Imaging luminous red galaxies and shows how an apparent local-PNG hint, under a milder systematics treatment, projects into a preference near Δ≈0.9—presented only as a showcase, not a detection, because the preference vanishes under stronger decontamination. The main result is a forecast for three Stage-V Lyman-break-galaxy surveys: around the local limit with fiducial amplitude 4 they can reach σ(Δ)≈0.17–0.50, and the paper supplies an empirical relation that converts a survey’s ordinary local-PNG error bar into the expected error on Δ. That relation lets future planners estimate how deep a survey must go before it can tell a pure local signal from a massive-field imprint.

Core claim

For Stage-V LBG surveys near the local limit (Δ^fid=0, f_NL,Δ^fid=4), free-bias forecasts give σ(Δ)≃0.17 (WST), 0.34 (MUST) and 0.50 (Spec-S5). Above a reference local significance of roughly 4, the constraints from different surveys collapse onto the common power law σ(Δ)≃1.27 SNR_loc,ref^−0.90; the same scaling can be generalized to nonzero Δ^fid through fitted amplitude and slope functions of Δ. DESI Imaging under a less aggressive weight set yields a non-robust preference f_NL,Δ≈5×10^3, Δ≈0.91 that illustrates how such a mapping works on real data.

What carries the argument

The linear scale-dependent bias induced by the squeezed massive-field bispectrum: b(k,z)=b+f_NL,Δ(k R_*)^Δ 2δ_c(b−p)α(k,z), with Δ=3/2−√(9/4−m²/H²). This single expression carries both the DESI parameter mapping and the Stage-V forecast relation between σ(Δ) and local-PNG sensitivity.

Load-bearing premise

The whole analysis assumes the massive-field signal is completely captured by that linear k^{Δ−2} bias formula with fixed universality and a single short-mode smoothing radius; if higher-order bias or residual large-scale systematics change the shape, both the DESI mapping and the forecast relation misestimate the true reach.

What would settle it

Inject controlled Δ signatures into DESI-like imaging mocks, re-run the identical angular-correlation pipeline under the same weight maps, and check whether the recovered (f_NL,Δ, Δ) posterior centers on the injected values and whether the Stage-V power-law σ(Δ)–SNR relation still holds when the mocks include realistic residual systematics.

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

If this is right

  • A Stage-V detection of local PNG at SNR≳4 automatically supplies a quantitative handle on whether the signal is exactly local or carries a massive-field tilt Δ.
  • External priors that pin down galaxy bias can shrink σ(Δ) by roughly 60 percent, turning a marginal shape measurement into a decisive one.
  • The inverted relation σ_req(f_NL^loc)≃f_NL,Δ^fid [σ_target(Δ)/A(Δ)]^{1/m(Δ)} gives survey designers a concrete sensitivity target for any predicted (f_NL,Δ, Δ) pair.
  • Larger fiducial Δ weakens the scale dependence and forces surveys to reach still smaller σ(f_NL^loc) before Δ itself becomes measurable.

Where Pith is reading between the lines

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

  • If residual imaging systematics can mimic Δ≈0.9 as readily as they mimic local f_NL, then any future claim of massive fields from photometry will need multi-tracer or spectroscopic cross-checks before it can be trusted.
  • The same SNR-scaling logic should apply to other squeezed templates (e.g., equilateral-to-squeezed hybrids) once their effective Δ is defined, offering a cheap forecast shortcut without full Fisher matrices.
  • A null Stage-V result at the forecasted σ(Δ) would push the lightest extra fields during inflation above m∼H, tightening the window on quasi-single-field models.

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 / 6 minor

Summary. This paper searches for inflationary massive-field signatures via beyond-local primordial non-Gaussianity in the scale-dependent galaxy bias, parameterized by amplitude f_NL,Δ and scaling Δ (Eq. 5). Using the angular correlation function on DESI Legacy Imaging LRGs, the authors validate their pipeline against the local-PNG results of Rezaie et al. (2024), recover no local signal under the most aggressive (nine-map) decontamination, and find a non-robust preference f_NL^loc≈27 and (f_NL,Δ,Δ)≈(5×10^3,0.91) under three-map weights, which they present only as a methodological showcase given residual systematics. They then forecast Stage-V LBG surveys (WST, MUST, Spec-S5), reporting σ(Δ)≃0.17–0.50 around Δ^fid=0 for f_NL,Δ^fid=4, and derive an empirical bridge σ(Δ)≃A(Δ^fid) SNR_loc,ref^{-m(Δ^fid)} that can be inverted into a required local-PNG sensitivity for a target σ(Δ).

Significance. If the forecast results hold within the stated model class, the paper supplies a practical planning relation connecting Stage-V local-PNG reach to the ability to resolve departures from the local squeezed limit—something not previously quantified for WST/MUST/Spec-S5 LBG samples in this parameterization. Strengths include: (i) real-data validation of the ACF+integral-constraint pipeline against Rezaie24 across three systematics treatments; (ii) nested sampling of the highly degenerate (f_NL,Δ,Δ,b) space with explicit prior-volume discussion; (iii) clear non-claim of a massive-field detection in DESI Imaging; and (iv) a falsifiable, survey-comparable SNR scaling that collapses different Stage-V setups onto a common curve above a significance threshold. The work is incremental rather than transformative, but useful for Stage-V design discussions.

major comments (3)
  1. [Section V, Eqs. (22)–(27)] §V.A–B, Eqs. (22)–(27) and Figs. 4 and 6: The central planning tool σ(Δ)≃A(Δ^fid) SNR_loc,ref^{-m(Δ^fid)} is obtained by fitting the authors’ own forecasts after discarding the low-SNR funnel regime (SNR_loc,ref≲4 for Δ^fid=0; analogous cuts for nonzero Δ^fid). The fit therefore inherits the full forecast idealization—linear scale-dependent bias with fixed p=1 and single R_* (Eq. 5), linear Kaiser RSD, fixed cosmology, and diagonal PS covariance. The abstract and §VI present the inverted relation as a general survey-sensitivity estimator. Please state the domain of validity explicitly (model class and SNR cuts), and either (a) add a brief robustness test varying p and/or R_*, or (b) reframe Eq. (27)/Table IV as an in-model benchmark rather than a model-independent requirement. Without that, the claimed generality for survey planning is overstated.
  2. [Section II.A, Equation (5)] §II.A, Eq. (5): The entire DESI mapping and Stage-V σ(Δ)–SNR relation assume b(k,z)=b+f_NL,Δ(kR_*)^Δ 2δ_c(b−p)α(k,z) with universality p=1 and a single short-mode radius R_*≃2.66 h^{-1} Mpc tied to 10^{13} M_⊙ halos. LBGs in the Stage-V forecasts are lower-mass, higher-z tracers; a tracer-dependent p or R_* would change the k^{Δ−2} shape that breaks the f_NL,Δ–Δ degeneracy. The paper should quantify (even approximately) how σ(Δ) and the fitted A(Δ), m(Δ) shift under plausible p≠1 or R_* variations, or justify why the LRG-calibrated R_* remains appropriate for the LBG forecasts in Table I.
  3. [Section IV, Table II] §IV, Table II and the Δχ^2=3.95 (≈2.3σ via Chernoff) preference for beyond-local PNG under Nonlinear Three Maps at 0.5°<θ<25°: The text correctly states the preference is not robust and is likely residual systematics, yet still quotes closed 1D constraints Δ=0.91^{+0.25}_{-0.19} and a model-comparison significance. Given that the nine-map case yields only a prior-driven one-sided limit and the unweighted sample produces a spurious closed Δ≈0.22, please either (i) demote the Three-Maps beyond-local numbers to an appendix illustration without 1D medians in the main table, or (ii) add a quantitative statement that no decontamination scheme yields a stable Δ preference, so that the showcase cannot be misread as a data-driven mass constraint.
minor comments (6)
  1. [Abstract / full text] Throughout the compiled text there are widespread missing word spaces (e.g., abstract opening, §I). These appear to be PDF-extraction artifacts but should be checked in the journal source.
  2. [Section II.D] §II.D: DESI Imaging uses Ω_m=0.25, n_s=0.95, h=0.7 while Stage-V forecasts use Planck 2018 values. A one-sentence justification that this does not affect the pipeline validation or the relative Stage-V comparison would help.
  3. [Section II.C, Figure 1] Figure 1 bottom panel and Eq. (13): θ_lim∼140° for the integral constraint vs θ_max=20–25° in the data vector is important; consider marking θ_lim on the figure or stating the RR-weighted effective scale more explicitly.
  4. [Table I] Table I: Spec-S5 is listed with only u- and g-dropouts (no r-dropout), while WST/MUST include r-dropouts. The text explains LSST-based selection, but a footnote in the table would prevent misreading the survey comparison.
  5. [Section V.B, Figure 5] §V.B, Figure 5: For Δ^fid=1.0 the free-bias posterior hits the Δ prior edge; the caption could note that the reported lower limit is prior-bounded, consistent with the DESI nine-map behavior.
  6. [References] References: several 2025–2026 arXiv entries are cited as published journal pages (e.g., JCAP 2025/2026). Verify final bibliographic status at acceptance.

Circularity Check

1 steps flagged

No load-bearing circularity: DESI fits are external-data constraints; Stage-V scalings are honest empirical summaries of the authors' own forecasts, not disguised first-principles predictions.

specific steps
  1. fitted input called prediction [§V.A–B, Eqs. 22–27, Figs. 4 and 6]
    "For the free-bias case, the common trend is well described by the empirical relation σ(Δ)≃1.27 SNR_loc,ref^{-0.90}... After removing the low significance points affected by projection effects, the constraints are well described by the empirical relation σ(Δ)≃A(Δ^fid)SNR_loc,ref^{-m(Δ^fid)}. ... For a target uncertainty σ_target(Δ), the same relation can be inverted to estimate the local PNG sensitivity required... σ_req(f_NL^loc)≃f_NL,Δ^fid [σ_target(Δ)/A(Δ)]^{1/m(Δ)}."

    SNR_loc,ref and σ(Δ) are both outputs of the same Stage-V forecast pipeline; the power-law coefficients (and the SNR≳4 cut) are fit to those outputs, then inverted to quote a 'required' σ(f_NL^loc). The inverted requirement therefore restates the fitted forecast grid inside the assumed linear bias model rather than independently predicting survey reach. Mild and disclosed as empirical—not a definitional identity or a fake detection.

full rationale

The DESI Imaging section applies an external massive-field bias template (Eq. 5, from the literature) to public catalogs under stated systematics treatments; posteriors on (f_NL,Δ, Δ) are ordinary likelihood fits, and the paper explicitly disclaims cosmological interpretation when the signal is mitigation-dependent. Stage-V results are standard theory-vector forecasts: the data vector equals the model at Θ_fid by construction (stated in §II.D), which is the normal setup for sensitivity studies and does not force the reported σ(Δ) values or the near-inverse SNR scaling. The empirical relations σ(Δ)≃1.27 SNR_loc,ref^{-0.90} and the later A(Δ^fid), m(Δ^fid) fits (§V, Eqs. 23–27) are fitted summaries of that same forecast grid, then inverted as a planning tool. That is mild re-packaging of self-generated numbers, not a self-definitional loop or a statistically forced 'prediction' of an independent observable. Self-citations (Riquelme23 pipeline; Rezaie24 data) supply methods and comparison benchmarks and are cross-checked against an independent harmonic-space analysis. No uniqueness theorem or ansatz is smuggled in to forbid alternatives. Overall circularity is negligible.

Axiom & Free-Parameter Ledger

6 free parameters · 6 axioms · 0 invented entities

The paper inherits the quasi-single-field/massive-field squeezed template and the scale-dependent bias map from prior inflation and LSS literature, then fits or forecasts amplitudes inside that template. No new physical entity is postulated. Load-bearing modeling choices (p=1, fixed R_*, linear Kaiser, fixed ΛCDM, Gaussian covariance, idealized Stage-V LBG specs) and free fit parameters (f_NL,Δ, Δ, b; empirical SNR-fit coefficients) carry the claims.

free parameters (6)
  • f_NL,Δ (and f_NL^loc) = DESI Three Maps: 5.12^{+6.13}_{-3.62}×10^3; forecasts use fiducials 4 and 18 (and 16)
    Primary PNG amplitude fitted to DESI ACF or set as forecast fiducial; DESI Three-Maps showcase gives ~5×10^3.
  • Δ = DESI Three Maps showcase: 0.91^{+0.25}_{-0.19}
    Mass-scaling exponent fitted jointly with amplitude; constrained only when a local-like signal is present.
  • galaxy linear bias b = fiducial DESI ~1.9; Stage-V dropout fiducials 4.5–6.4
    Marginalized (or fixed in optimistic forecasts) nuisance; strongly degenerate with PNG amplitude.
  • R_* short-mode smoothing scale = 2.66 h^{-1} Mpc
    Hand-set reference Lagrangian radius entering (kR_*)^Δ; taken from Green et al. as 2.66 h^{-1} Mpc.
  • Empirical SNR scaling coefficients (1.27, −0.90; A(Δ), m(Δ)) = σ(Δ)≃1.27 SNR^{-0.90}; m≃0.72+0.50Δ; A≃0.32 e^{5.60Δ} (fixed-bias)
    Fitted to the authors’ own Stage-V posterior widths after SNR cuts; inverted into survey requirements.
  • Fixed background cosmology = DESI: Ωm=0.25, σ8=0.8, h=0.7; Stage-V: Planck-like Ωm=0.31, As=2.1e-9
    Ωm, σ8, n_s, etc. held fixed separately for DESI and Stage-V rather than marginalized.
axioms (6)
  • domain assumption Squeezed massive-field bispectrum B_ζ ∝ f_NL,Δ (k_S/k_L)^Δ P_ζ(k_S)P_ζ(k_L) for m<3H/2, with Δ=3/2−√(9/4−m²/H²)
    §II.A Eqs. 3–4; standard quasi-single-field template assumed universal in the squeezed limit.
  • domain assumption PNG imprints only through linear scale-dependent bias with universal mass-function response p=1 and δ_c=1.686
    Eq. 5; higher-order bias, assembly bias, and non-universal p are neglected.
  • domain assumption Observed clustering on used scales is described by linear Kaiser RSD times matter PS from CAMB, with Gaussian covariance
    §II.B–D; k_max=0.1 h Mpc^{-1} and θ_min=0.5° taken as linear-regime boundary.
  • domain assumption Flat priors and fixed-ΛCDM background; integral constraint fully captures survey-mean effects on large-angle ACF
    §II.C–D; cosmology not varied jointly with PNG.
  • ad hoc to paper Stage-V LBG number densities, areas, and bias(z) from white papers plus Wilson & White-style bias formula are adequate forecast inputs
    Table I and §III.B standardize dropouts and assign common fiducial biases across surveys.
  • standard math Nested-sampling posterior widths under the model equal expected experimental uncertainties
    Standard Gaussian-likelihood forecast logic in §II.D and §V.

pith-pipeline@v1.2.0-daily-grok45 · 29495 in / 4416 out tokens · 97803 ms · 2026-07-30T11:00:23.821292+00:00 · methodology

0 comments
read the original abstract

We investigate the cosmological imprints of massive fields during inflation through primordial non-Gaussianity (PNG). When these fields are sufficiently light, they produce a signal in galaxy clustering, $\propto f_{\rm NL,\Delta}k^{\Delta-2}$ with $\Delta\in(0,3/2]$, corresponding to a beyond-local PNG contribution to the scale-dependent bias. We use the angular correlation function to constrain $f_{\rm NL,\Delta}$ and $\Delta$ using imaging data used for the targeting of the Dark Energy Spectroscopic Instrument (DESI). For the most aggressive systematics treatment, there is no evidence for local PNG, hence no constraint on $\Delta$. However, when considering a less aggressive treatment, a hint is found with $f_{\rm NL}^{\rm loc}=27^{+10}_{-9}$, consistent with previous analyses. For beyond-local PNG, that signal gives a preference for $f_{\rm NL, \Delta}=5.12^{+6.13}_{-3.62}\times10^{3}$ and $\Delta=0.91^{+0.25}_{-0.19}$. This preference is not robust under decontamination choices, likely driven by residual systematics, and we present it as a showcase for future constraints. Additionally, we forecast the sensitivity of upcoming Stage-V surveys, the Wide-field Spectroscopic Telescope (WST), the MUltiplexed Survey Telescope (MUST), and the Spectroscopic Stage 5 Experiment (Spec-S5), to constrain $\Delta$ using Lyman-break galaxies. Around the local limit, $\Delta^{\rm fid}=0$, we find that they can reach uncertainties of $\sigma(\Delta)\simeq0.17-0.50$, depending on the survey, for a fiducial $f_{\rm NL,\Delta}^{\rm fid}=4$. The constraining power on $\Delta$ increases as we increase $f_{\rm NL,\Delta}^{\rm fid}$ and decreases for larger fiducial $\Delta$. Finally, we derive a relation between the detectability of $\Delta$ and the local PNG constraints, $\sigma(f_{\rm NL}^{\rm loc})$. This provides a tool to estimate the survey sensitivity required to resolve massive-field signatures.

Figures

Figures reproduced from arXiv: 2607.27175 by Anna Porredon, Hui Kong, Lucas Pinol, Santiago Avila, Walter Riquelme.

Figure 1
Figure 1. Figure 1: FIG. 1 [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Marginalized posterior distributions for the local PNG am [PITH_FULL_IMAGE:figures/full_fig_p007_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Marginalized contours for the linear bias [PITH_FULL_IMAGE:figures/full_fig_p009_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4 [PITH_FULL_IMAGE:figures/full_fig_p010_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. Forecasted free- and fixed-bias contours for WST, assuming [PITH_FULL_IMAGE:figures/full_fig_p011_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6 [PITH_FULL_IMAGE:figures/full_fig_p012_6.png] view at source ↗

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