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This paper argues that the galaxy bispectrum, not the power spectrum, supplies most of the constraining power on folded primordial non-Gaussianity, and that whether such a signal can be detected depends as much on the width and morphology o

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load-bearing objection First non-separable folded-PNG galaxy bispectrum forecast; numbers are conditional on zero equilateral/orthogonal PNG, so treat σ(f_NL) as optimistic. the 2 major comments →

arxiv 2607.15337 v1 pith:E5GTP5G2 submitted 2026-07-16 astro-ph.CO gr-qchep-phhep-th

Searching for Folded Primordial Non-Gaussianity with Galaxy Surveys

Si-Xiang Yang , Oliver H. E. Philcox This is my paper
classification astro-ph.CO gr-qchep-phhep-th
keywords primordial non-Gaussianityfolded shapegalaxy bispectrumscale-dependent biaseffective field theory of large-scale structureFisher forecastexcited initial statesdissipative 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.

The paper asks whether the distribution of galaxies can reveal a family of primordial three-point correlations that are enhanced when one wavenumber is nearly the sum of the other two, the folded limit. It studies three concrete inflationary mechanisms: excited initial states, an imaginary speed of sound, and dissipative inflation. Using an effective-field-theory model of galaxy clustering and Fisher forecasts for a galaxy survey, it concludes that the galaxy bispectrum dominates the information. The key result is that detectability is set not only by the amplitude of the folded enhancement but by its width: power-law-width templates are measurable until the folded core becomes narrower than the survey's Fourier bin width, while exponentially narrow dissipative templates are never directly resolved and must be seen through their broad logarithmic shoulder. This makes folded non-Gaussianity a distinctive but morphology-dependent target, with a numerical pipeline that applies to any non-separable primordial bispectrum.

Core claim

The paper's central claim is that folded PNG is best hunted in the galaxy bispectrum, because the folded enhancement is intrinsically a property of triangle shapes; the power spectrum sees it only indirectly through scale-dependent bias and loop corrections. For the cutoff-regulated templates, the forecast uncertainty on the amplitude scales as sigma(f_NL) proportional to the square root of lambda in the idealized unbinned limit, degrading to proportional to lambda once the folded core is narrower than the Fourier bin. For dissipative inflation, the constraint scales as sigma(f_NL) proportional to H/gamma and is only weakly affected by binning, at the price of a larger overlap with the equil

What carries the argument

The central object is the scale-dependent bias response F_*^(3)(k), a smoothed integral of the primordial bispectrum over short modes that converts any squeezed-limit primordial shape into a galaxy-bias correction. Here the smoothing is a top-hat filter at R* = 3.1 h^-1 Mpc, and the amplitude is set by a single bias coefficient. This response feeds into the redshift-space galaxy kernels, and the comparisons are made with Fisher forecasts over power-spectrum multipoles (ell=0,2,4) and the bispectrum monopole, with binned versus unbinned forecasts isolating the role of the folded-core width.

Load-bearing premise

The forecasts assume that folded non-Gaussianity's effect on galaxy formation is fully captured by a single bias coefficient whose fiducial value comes from a simple universality relation; if that coefficient needs extra freedom, or the smoothing scale is different, the balance between power spectrum and bispectrum information could shift.

What would settle it

Measure the binned galaxy bispectrum from a large survey at two bin widths, say 0.005 and 0.010 h/Mpc, for a fixed lambda. For a narrow-core template, the paper predicts a clear degradation of sigma(f_NL) with coarser bins that follows a lambda scaling; if finer bins do not improve constraints, the core-dilution mechanism is wrong.

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

If this is right

  • Most of the folded-PNG signal is in the galaxy bispectrum; the power spectrum contributes only indirectly via scale-dependent bias and loop corrections.
  • For non-Bunch-Davies and imaginary-speed-of-sound templates, constraints follow sigma(f_NL) proportional to sqrt(lambda) until the folded core narrows below the Fourier bin width, after which they degrade as lambda.
  • For dissipative inflation, the exponentially narrow core is unresolvable; what is measurable is the logarithmic shoulder, so constraints scale as H/gamma and depend weakly on binning.
  • Folded templates remain distinguishable from equilateral and orthogonal shapes after bias marginalization, so dedicated folded searches would capture information standard template fits miss.
  • The numerical framework generalizes to arbitrary non-separable primordial bispectra, including other collider-type shapes beyond the three models studied.

Where Pith is reading between the lines

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

  • An extension the paper leaves implicit: adaptive, non-uniform Fourier binning concentrated near the folded boundary could recover part of the sqrt(lambda) information that uniform bins lose at high lambda.
  • The prediction of a k^{-1} scale-dependent bias in the cutoff-regulated models could be tested directly in the galaxy power spectrum, providing a cross-check independent of bispectrum template fitting.
  • The dissipative model's substantial overlap with the equilateral template suggests that joint fits including the equilateral amplitude will be needed; the paper's Fisher-cosine diagnostic only probes degeneracy direction, not a full joint likelihood recovery.
  • If the bias coefficient b_zeta departs from the universality fiducial value, the power spectrum's already subdominant role could grow, so the bispectrum-dominance conclusion deserves rechecking with a wider bias prior.

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 / 5 minor

Summary. This paper studies the prospects for constraining folded primordial non-Gaussianity (PNG) with galaxy clustering, focusing on three inflationary models: non-Bunch-Davies initial states, imaginary speed of sound, and dissipative inflation. The models are grouped into two classes—cutoff-regulated templates with power-law folded-core widths (∝1/λ) and dissipation-regulated templates with exponentially narrow cores (∝e^{-H/γ}). The authors develop a numerical pipeline that computes the PNG contributions to the one-loop redshift-space galaxy power spectrum multipoles and tree-level bispectrum monopole within EFTofLSS, including scale-dependent bias through the F_*^{(3)} construction. Using Fisher forecasts for a DESI-like survey, they find that the bispectrum provides the dominant constraining power, that nuisance marginalization causes only mild degradation for large folded enhancement in the cutoff-regulated cases, and that finite binning degrades constraints once the folded core becomes narrower than the bin width. For dissipative inflation, constraints scale as σ(f_NL)∝H/γ and are weakly binning-dependent. The paper also computes late-time Fisher cosines to assess distinguishability from equilateral and orthogonal templates.

Significance. If the results hold, this is a valuable contribution: it provides the first consistent EFTofLSS treatment of folded PNG shapes in galaxy clustering, going beyond the standard equilateral/local/orthogonal templates and demonstrating that the width and morphology of the folded enhancement are crucial for detectability. The distinction between cutoff- and dissipation-regulated folded bispectra is physically meaningful and likely to influence future survey analyses. The numerical pipeline is general for non-separable bispectra, and the validation against class-pt for equilateral/orthogonal shapes gives some confidence in the implementation. The scaling arguments for σ(f_NL) in the unbinned and binned cases are transparent and falsifiable. The main weakness is that the headline forecasts condition on vanishing equilateral and orthogonal amplitudes, which is not clearly stated as a limitation and could affect the quantitative conclusions.

major comments (2)
  1. [Sec. IV, Eq. (64), Figs. 4–7] The forecast parameter vector contains only a single PNG amplitude, f_NL for the folded template; f_NL_equil and f_NL_ortho are fixed to zero. The quoted σ(f_NL) values in Figs. 4–6 are therefore conditional on the absence of standard PNG amplitudes. This matters because Fig. 7 shows non-negligible late-time Fisher overlap between the folded templates and equilateral/orthogonal templates, especially for the dissipative π_a^3 template (which anti-correlates with equilateral) and for cutoff-regulated templates at moderate λ. In a joint analysis, the marginalized error on the folded amplitude is σ_cond/√(1−cos²), so even |cos|=0.9 would worsen the constraint by a factor ~2.3. Moreover, because the scale-dependent bias has different k-dependence for folded (∝k^{−1}) versus equilateral (∝k^0) shapes, marginalizing over equilateral/orthogonal amplitudes could alter the relative information con
  2. [Sec. III A, Eqs. (39)–(40), Fig. 3] The scale-dependent bias for folded shapes is modeled with a single response coefficient b_ζ and the F_*^{(3)} construction of [93], using a fixed smoothing scale R_*=3.1 h^{-1} Mpc and fiducial b_ζ from universality relations. This construction is not directly validated for folded shapes, whose moderately squeezed limits are constant or scale as (k_l/k_s)^{γ/H} rather than the local-like behavior for which the peak-background-split derivation is standard. If folded PNG requires additional bias parameters, a different smoothing prescription, or non-universal b_ζ, the power-spectrum contribution and the nuisance-marginalization behavior could change. The paper partially addresses this by showing that setting b_ζ=b_ζδ=0 changes the joint constraint by less than ~1% at large λ for the cutoff-regulated models, which suggests the bispectrum-dominance conclusion is robust. However, since the p
minor comments (5)
  1. [Fig. 5 caption] The statement that the equilateral and orthogonal pieces are 'projected out from the template' is important but the implementation is not described. Please clarify how the projection is performed (e.g., by orthogonalizing with respect to the Fisher inner product) and whether Fig. 4 uses the same projection or the raw template.
  2. [Sec. IV, Eq. (65)–(66)] The underbrace notation in the scaling estimates is hard to read. Please spell out in words that the unbinned Fisher information scales as (folded amplitude)^2 × (width in k-space), and similarly for the binned case.
  3. [Sec. III E] The numerical pipeline is not released. For reproducibility, consider providing the code or, at minimum, a more detailed description of the integration scheme (tolerances, grid resolution near the folded ridge, and the treatment of the exponentially narrow dissipative core).
  4. [Sec. IV, footnote 12] The choice k_max=0.155 h/Mpc with a tree-level bispectrum is somewhat aggressive. The footnote acknowledges this, but a sentence in the main text would help readers interpret the forecasts.
  5. [References] Several references (e.g., [3], [10], [72], [103]) lack publication years in the bibliography. Please complete the reference entries.

Circularity Check

0 steps flagged

No significant circularity: forecasts are f_NL=0 Fisher derivatives with externally sourced folded templates; same-group citations are minor, not load-bearing.

full rationale

The derivation chain is not circular. The folded bispectrum templates are taken from external inflationary-model literature: the non-Bunch-Davies shape is quoted from [14] (Eq. 10), the imaginary-speed-of-sound shape from [33] (Eq. 21), and the dissipative shape is computed here and checked against [41]. None of these templates is fitted to the forecast target f_NL or to galaxy-survey statistics. The forecast is performed at fiducial f_NL=0 (Sec. IV), so the quoted sigma(f_NL) values are Fisher derivatives of the model response, not fitted parameters renamed as predictions. The scale-dependent-bias response is imported from [93] ('A powerful way to estimate the scale-dependent bias generated by a general squeezed primordial bispectrum was introduced in [93]') and the EFTofLSS kernels from [72] ('We will mainly follow the treatment of local PNG in [72]'); [72] is co-authored by one of the current authors, but it is an established framework already applied to BOSS data, and the PNG loop implementation is additionally checked against class-pt for equilateral/orthogonal templates, so it constitutes independent support rather than a self-referential premise. The central claim that the bispectrum dominates folded-PNG constraints follows from the folded enhancement being a triangle-geometry feature and is robust to removing the scale-dependent-bias terms: the power-spectrum constraint changes by a factor of 2, while the bispectrum and joint constraints change by less than 1% at large lambda. The main modeling caveat, flagged by a skeptical reader, is that the Fisher parameter vector in Eq. (64) omits f_NL^equil and f_NL^ortho, and Fig. 7 shows non-negligible overlap with those standard shapes; the quoted constraints are therefore conditional and may be optimistic in a joint multi-shape analysis. That is a statistical/robustness limitation, not circularity: no equation in the paper equates a fitted input with the claimed prediction, and the self-citations present are minor and not load-bearing.

Axiom & Free-Parameter Ledger

7 free parameters · 8 axioms · 0 invented entities

The central numerical forecasts rest on standard in-in/EFTofLSS machinery plus several domain assumptions: the single-response bias construction, universality relations, Gaussian covariances, perturbative control at k_max=0.155 h/Mpc, and the omission of PNG counterterms and IR resummation. The paper discloses most of these, but they still control the quantitative results.

free parameters (7)
  • Fiducial f_NL = 0
    Fisher forecast expansion point; all forecasts are local derivatives at zero signal, which is standard but central to the results.
  • Fiducial linear bias b1 = 2.5
    Chosen in Sec. IV to mimic DESI LRGs; sets amplitude and degeneracies for all spectra.
  • Fiducial b2, b_G2, b_Gamma3 = fitting relations of [104] and coevolution
    Simulation-calibrated values used as fiducial nuisance parameters; marginalization behavior depends on their priors.
  • Fiducial b_zeta, b_zeta-delta, b_zeta-epsilon = universality relations [91]; b_zeta-epsilon=0
    Scale-dependent-bias amplitudes are set by universality; the paper tests only b_zeta=b_zeta-delta=0, not other values.
  • Survey setup = V=2.5 h^-3 Gpc^3, nbar=4e-4 h^3 Mpc^-3, kmin=0.005, kmax=0.155, Delta k=0.005 h/Mpc, z=0, R*=3.1 h^-1 Mpc
    DESI-like choices; absolute sigma(f_NL) numbers depend on these.
  • non-Bunch-Davies Bogoliubov phase delta = pi/3
    Representative phase chosen in Sec. II.A; avoids special values pi/2 and 3pi/2 where subleading terms matter; affects oscillation morphology.
  • Model parameters lambda and H/gamma = scanned from ~10 to 10^3
    Physical parameters controlling folded-core width; the paper's scaling results are functions of them, not fits.
axioms (8)
  • standard math In-in formalism and the positive/negative-frequency mode-function decomposition correctly compute the primordial bispectra for the three models.
    Used throughout Sec. II, e.g., Eqs. (8)-(10), (20)-(21), (26).
  • domain assumption Scale-dependent bias is captured by the F*^(3)(k) variance-modulation response of [93] with smoothing scale R*=3.1 h^-1 Mpc; folded squeezed limits are no more singular than local PNG so the same bias expansion applies.
    Stated in Sec. III.A, Eqs. (38)-(40); this is the main modeling premise.
  • domain assumption Universality and coevolution relations fix fiducial b_zeta, b_zeta-delta, and b_Gamma3.
    Sec. IV parameter setup; the paper tests only the b_zeta=0 limit.
  • domain assumption Perturbative control holds for one-loop power spectrum and tree-level bispectrum up to k_max=0.155 h/Mpc, and PNG-induced counterterms are higher order and negligible.
    Sec. III.D scaling estimates and Sec. IV footnote 12; k_max is admitted to be somewhat optimistic.
  • domain assumption Gaussian covariance for P and B, with no cross-covariance, adequately represents survey errors for Fisher forecasts.
    Sec. IV: 'We assume Gaussian covariances for both statistics... and neglect the cross-covariance between the two.'
  • domain assumption IR resummation of fast non-Bunch-Davies oscillations can be omitted without changing the constraints.
    Sec. III.E: 'the constraining power for the non-Bunch-Davies case does not significantly rely on the fast oscillations.'
  • ad hoc to paper Normalization convention S(k/2,k/2,k)=1 for folded templates.
    Sec. II.A: normalized such that |S(k/2,k/2,k)|=1; all f_NL forecasts are in this convention, not the equilateral convention.
  • domain assumption Fisher information at f_NL=0 with broad Gaussian priors approximates survey sensitivity.
    Standard forecast assumption, used throughout Sec. IV.

pith-pipeline@v1.3.0-alltime-deepseek · 28958 in / 16999 out tokens · 159859 ms · 2026-08-01T23:38:30.372333+00:00 · methodology

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read the original abstract

Large-scale structure provides a powerful probe of inflationary physics through primordial non-Gaussianity (PNG): the galaxy power spectrum depends on local PNG through scale-dependent bias, while the galaxy bispectrum depends sensitively on both equilateral and orthogonal PNG. In this paper, we study whether galaxy surveys can also probe folded PNG, whose shape is enhanced near $k_1+k_2-k_3\rightarrow0$. We consider three inflationary models with folded PNG, including excited initial states, imaginary speeds of sound, and dissipative inflation. These models fall into two classes: cutoff-regulated cases in which the folded-enhanced region has a power-law width, and dissipation-regulated cases in which the enhanced region is exponentially narrow. We develop a numerical pipeline for computing the corresponding PNG contributions to the redshift-space galaxy power spectrum multipoles and bispectrum monopole within the EFTofLSS. Using Fisher forecasts, we show that most of the constraining power on folded PNG comes from the galaxy bispectrum. For the cutoff-regulated models, nuisance parameter marginalization causes only a mild loss of information at large folded enhancement, but finite Fourier-space binning degrades constraints once the folded region becomes narrower than the bin width. For the dissipation-regulated models, the exponentially narrow folded enhancement is hard to resolve and the observable signal instead comes from the broader support of the template, leading to weaker binning dependence but larger overlap with the equilateral template. Our results show that folded PNG is a distinctive and promising target for galaxy bispectrum analyses, and the detectability depends on the width and morphology of the folded enhancement. The numerical pipeline developed in this work is general and can be used to study a wide class of non-separable primordial bispectra.

Figures

Figures reproduced from arXiv: 2607.15337 by Oliver H. E. Philcox, Si-Xiang Yang.

Figure 1
Figure 1. Figure 1: FIG. 1. Shape function [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Folded and squeezed behavior of the shape function generated by the operator [PITH_FULL_IMAGE:figures/full_fig_p008_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Scale-dependent bias contributions ∆ [PITH_FULL_IMAGE:figures/full_fig_p010_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: ), with the information loss further reduced by the oscillatory feature in the non-Bunch-Davies model. As discussed in Sec. II, the width of the folded core shrinks as λ −1 . Since any realistic galaxy survey uses finite-width k-bins (set by the fundamental mode), it is important to ask when the narrowing folded core becomes unresolved due to binning. Schematically, without binning, the Fisher information … view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. Effect of binning on the PNG Fisher forecasts for the non-Bunch-Davies model (left) and imaginary speed-of-sound [PITH_FULL_IMAGE:figures/full_fig_p016_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6 [PITH_FULL_IMAGE:figures/full_fig_p017_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7. Distinguishability of the folded templates from the standard equilateral and orthogonal templates. Solid curves show [PITH_FULL_IMAGE:figures/full_fig_p018_7.png] view at source ↗

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