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arxiv: 2605.21436 · v1 · pith:C46IP6BTnew · submitted 2026-05-20 · 🌌 astro-ph.CO

Euclid preparation: Testing multi-field inflation with galaxy power spectrum and bispectrum

Euclid Collaboration: D. Linde , A. Moradinezhad Dizgah , G. Parimbelli , K. Pardede , E. Sefusatti , M. S. Cagliari , G. D'Amico , V. Desjacques
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A. Eggemeier M. Biagetti A. Veropalumbo B. Camacho Quevedo A. Chudaykin M. Crocce L. Castiblanco E. Castorina A. Farina M. Guidi M. Karcher A. Pezzotta A. Pugno B. Altieri S. Andreon N. Auricchio C. Baccigalupi M. Baldi S. Bardelli P. Battaglia A. Biviano E. Branchini M. Brescia S. Camera G. Canas-Herrera V. Capobianco C. Carbone J. Carretero S. Casas M. Castellano G. Castignani S. Cavuoti K. C. Chambers A. Cimatti C. Colodro-Conde G. Congedo L. Conversi Y. Copin F. Courbin H. M. Courtois H. Degaudenzi S. de la Torre G. De Lucia H. Dole M. Douspis F. Dubath X. Dupac S. Escoffier M. Farina R. Farinelli S. Ferriol F. Finelli P. Fosalba S. Fotopoulou M. Frailis M. Fumana S. Galeotta K. George B. Gillis C. Giocoli J. Gracia-Carpio A. Grazian F. Grupp S. V. H. Haugan W. Holmes F. Hormuth A. Hornstrup K. Jahnke B. Joachimi S. Kermiche A. Kiessling B. Kubik M. Kunz H. Kurki-Suonio A. M. C. Le Brun S. Ligori P. B. Lilje V. Lindholm I. Lloro G. Mainetti O. Mansutti O. Marggraf M. Martinelli N. Martinet F. Marulli R. J. Massey E. Medinaceli S. Mei M. Meneghetti E. Merlin G. Meylan A. Mora M. Moresco L. Moscardini C. Neissner S.-M. Niemi J. W. Nightingale C. Padilla S. Paltani F. Pasian K. Pedersen W. J. Percival V. Pettorino S. Pires G. Polenta M. Poncet L. A. Popa F. Raison A. Renzi J. Rhodes G. Riccio E. Romelli M. Roncarelli R. Saglia Z. Sakr A. G. Sanchez D. Sapone B. Sartoris A. Secroun G. Seidel E. Sihvola P. Simon C. Sirignano G. Sirri A. Spurio Mancini L. Stanco P. Tallada-Crespi A. N. Taylor I. Tereno N. Tessore S. Toft R. Toledo-Moreo F. Torradeflot I. Tutusaus L. Valenziano J. Valiviita T. Vassallo G. Verdoes Kleijn Y. Wang J. Weller G. Zamorani F. M. Zerbi E. Zucca M. Ballardini E. Bozzo C. Burigana R. Cabanac M. Calabrese T. Castro J. A. Escartin Vigo J. Garcia-Bellido J. Macias-Perez R. Maoli J. Martin-Fleitas N. Mauri R. B. Metcalf P. Monaco M. Pontinen I. Risso V. Scottez M. Sereno M. Tenti M. Tucci M. Viel M. Wiesmann Y. Akrami I. T. Andika G. Angora M. Archidiacono F. Atrio-Barandela S. Avila L. Bazzanini J. Bel D. Bertacca M. Bethermin F. Beutler A. Blanchard L. Blot H. Bohringer M. Bonici S. Borgani M. L. Brown S. Bruton A. Calabro F. Caro C. S. Carvalho F. Cogato A. R. Cooray S. Davini G. Desprez A. Diaz-Sanchez S. Di Domizio J. M. Diego V. Duret M. Y. Elkhashab A. Enia Y. Fang A. Finoguenov A. Franco K. Ganga T. Gasparetto F. Giacomini F. Gianotti G. Gozaliasl A. Gruppuso C. M. Gutierrez A. Hall C. Hernandez-Monteagudo H. Hildebrandt J. Hjorth J. J. E. Kajava Y. Kang V. Kansal D. Karagiannis K. Kiiveri J. Kim C. C. Kirkpatrick S. Kruk M. Lattanzi L. Legrand M. Lembo F. Lepori G. Leroy G. F. Lesci J. Lesgourgues T. I. Liaudat S. J. Liu G. Maggio M. Magliocchetti A. Manjon-Garcia F. Mannucci C. J. A. P. Martins L. Maurin C. Moretti G. Morgante S. Nadathur K. Naidoo A. Navarro-Alsina S. Nesseris L. Pagano D. Paoletti F. Passalacqua K. Paterson L. Patrizii C. Pattison A. Pisani D. Potter G. W. Pratt S. Quai M. Radovich K. Rojas W. Roster S. Sacquegna M. Sahlen D. B. Sanders E. Sarpa A. Schneider M. Schultheis D. Sciotti E. Sellentin L. C. Smith K. Tanidis F. Tarsitano G. Testera R. Teyssier S. Tosi A. Troja A. Venhola D. Vergani F. Vernizzi G. Verza S. Vinciguerra N. A. Walton A. H. Wright H. W. Yeung
This is my paper

Pith reviewed 2026-05-21 03:04 UTC · model grok-4.3

classification 🌌 astro-ph.CO
keywords primordial non-Gaussianityf_NLgalaxy power spectrumgalaxy bispectrumEuclid surveyredshift-space distortionsmulti-field inflationhalo occupation distribution
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The pith

Joint power spectrum and bispectrum analysis on Euclid-like mocks recovers unbiased f_NL with 29-46 percent tighter errors.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

This paper validates a pipeline that extracts primordial non-Gaussianity from galaxy clustering using both the power spectrum and bispectrum measured in redshift space. The authors run likelihood analyses on mocks built from Abacus-PNG simulations populated according to a halo occupation distribution tuned to Euclid Flagship 2. They show that the bispectrum alone improves the precision on the local PNG parameter f_NL by 29 to 46 percent compared with the power spectrum, while the joint analysis adds another 8 to 13 percent tightening. Across an effective volume of 16 cubic gigaparsecs spanning redshifts 0.8 to 1.7 the recovered values of f_NL and standard cosmological parameters remain unbiased at the sub-sigma level. The work therefore demonstrates a practical route to testing multi-field inflation scenarios with the upcoming Euclid spectroscopic sample.

Core claim

Likelihood analyses of one-loop redshift-space power spectrum multipoles and tree-level bispectrum multipoles applied to Abacus-PNG simulations recover f_NL and Lambda-CDM parameters with less than one-sigma bias when the effective volume reaches 16 h^{-3} Gpc^3 across four snapshots from z=0.8 to 1.7. The bispectrum alone reduces the uncertainty on f_NL by 29-46 percent relative to the power spectrum at fixed scale cuts; the joint analysis supplies a further 8-13 percent gain. The strongest individual-bin results appear at z=1.7, where a physically motivated prior on the PNG bias parameter b_phi yields a 2.35-sigma detection of f_NL while the prior-agnostic setup reaches 1.9 sigma on the f_

What carries the argument

Joint likelihood of one-loop power-spectrum multipoles and tree-level bispectrum multipoles that isolates the dominant local PNG term proportional to f_NL times b_phi while marginalizing over bias and cosmological parameters.

If this is right

  • B_ℓ alone reduces σ(f_NL) by ∼29–46% relative to P_ℓ at fixed cuts.
  • Joint power spectrum-bispectrum analysis tightens constraints a further ∼8–13%.
  • Cumulative gain across the four redshift snapshots is a factor of ∼2.3 for the joint case.
  • A physically motivated prior on b_φ produces unbiased f_NL while incorporating theory uncertainty.
  • The bispectrum quadrupole supplies a substantial fraction of the extra constraining power.

Where Pith is reading between the lines

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

  • Extending the same pipeline to higher-order perturbation theory or wider scale ranges could further tighten f_NL bounds once real Euclid systematics are controlled.
  • Joint power-spectrum-bispectrum constraints on local PNG may be combined with CMB bispectrum measurements to break remaining degeneracies in multi-field inflation models.
  • The demonstrated volume scaling suggests that full-sky Euclid data could reach several-sigma detections of f_NL if the simulation-validated precision carries over.
  • Similar joint analyses could be applied to other large-scale structure surveys to cross-check PNG signals.

Load-bearing premise

The halo occupation distribution tuned to Euclid Flagship 2 accurately populates halos in the Abacus-PNG simulations and the one-loop power spectrum plus tree-level bispectrum models remain sufficient without higher-order corrections or additional PNG bias terms for the chosen scale cuts.

What would settle it

Repeating the identical likelihood pipeline on an independent set of mocks or on actual Euclid data and finding biases in f_NL larger than one sigma would falsify the claim of unbiased recovery.

Figures

Figures reproduced from arXiv: 2605.21436 by A. Biviano, A. Blanchard, A. Calabro, A. Chudaykin, A. Cimatti, A. Diaz-Sanchez, A. Eggemeier, A. Enia, A. Farina, A. Finoguenov, A. Franco, A. Grazian, A. Gruppuso, A. G. Sanchez, A. Hall, A. Hornstrup, A. H. Wright, A. Kiessling, A. Manjon-Garcia, A. M. C. Le Brun, A. Mora, A. Moradinezhad Dizgah, A. Navarro-Alsina, A. N. Taylor, A. Pezzotta, A. Pisani, A. Pugno, A. R. Cooray, A. Renzi, A. Schneider, A. Secroun, A. Spurio Mancini, A. Troja, A. Venhola, A. Veropalumbo, B. Altieri, B. Camacho Quevedo, B. Gillis, B. Joachimi, B. Kubik, B. Sartoris, C. Baccigalupi, C. Burigana, C. Carbone, C. C. Kirkpatrick, C. Colodro-Conde, C. Giocoli, C. Hernandez-Monteagudo, C. J. A. P. Martins, C. M. Gutierrez, C. Moretti, C. Neissner, C. Padilla, C. Pattison, C. S. Carvalho, C. Sirignano, D. Bertacca, D. B. Sanders, D. Karagiannis, D. Paoletti, D. Potter, D. Sapone, D. Sciotti, D. Vergani, E. Bozzo, E. Branchini, E. Castorina, E. Medinaceli, E. Merlin, E. Romelli, E. Sarpa, E. Sefusatti, E. Sellentin, E. Sihvola, Euclid Collaboration: D. Linde, E. Zucca, F. Atrio-Barandela, F. Beutler, F. Caro, F. Cogato, F. Courbin, F. Dubath, F. Finelli, F. Giacomini, F. Gianotti, F. Grupp, F. Hormuth, F. Lepori, F. Mannucci, F. Marulli, F. M. Zerbi, F. Pasian, F. Passalacqua, F. Raison, F. Tarsitano, F. Torradeflot, F. Vernizzi, G. Angora, G. Canas-Herrera, G. Castignani, G. Congedo, G. D'Amico, G. De Lucia, G. Desprez, G. F. Lesci, G. Gozaliasl, G. Leroy, G. Maggio, G. Mainetti, G. Meylan, G. Morgante, G. Parimbelli, G. Polenta, G. Riccio, G. Seidel, G. Sirri, G. Testera, G. Verdoes Kleijn, G. Verza, G. W. Pratt, G. Zamorani, H. Bohringer, H. Degaudenzi, H. Dole, H. Hildebrandt, H. Kurki-Suonio, H. M. Courtois, H. W. Yeung, I. Lloro, I. Risso, I. T. Andika, I. Tereno, I. Tutusaus, J. A. Escartin Vigo, J. Bel, J. Carretero, J. Garcia-Bellido, J. Gracia-Carpio, J. Hjorth, J. J. E. Kajava, J. Kim, J. Lesgourgues, J. Macias-Perez, J. Martin-Fleitas, J. M. Diego, J. Rhodes, J. Valiviita, J. Weller, J. W. Nightingale, K. C. Chambers, K. Ganga, K. George, K. Jahnke, K. Kiiveri, K. Naidoo, K. Pardede, K. Paterson, K. Pedersen, K. Rojas, K. Tanidis, L. A. Popa, L. Bazzanini, L. Blot, L. Castiblanco, L. Conversi, L. C. Smith, L. Legrand, L. Maurin, L. Moscardini, L. Pagano, L. Patrizii, L. Stanco, L. Valenziano, M. Archidiacono, M. Baldi, M. Ballardini, M. Bethermin, M. Biagetti, M. Bonici, M. Brescia, M. Calabrese, M. Castellano, M. Crocce, M. Douspis, M. Farina, M. Frailis, M. Fumana, M. Guidi, M. Karcher, M. Kunz, M. Lattanzi, M. L. Brown, M. Lembo, M. Magliocchetti, M. Martinelli, M. Meneghetti, M. Moresco, M. Poncet, M. Pontinen, M. Radovich, M. Roncarelli, M. Sahlen, M. S. Cagliari, M. Schultheis, M. Sereno, M. Tenti, M. Tucci, M. Viel, M. Wiesmann, M. Y. Elkhashab, N. Auricchio, N. A. Walton, N. Martinet, N. Mauri, N. Tessore, O. Mansutti, O. Marggraf, P. Battaglia, P. B. Lilje, P. Fosalba, P. Monaco, P. Simon, P. Tallada-Crespi, R. B. Metcalf, R. Cabanac, R. Farinelli, R. J. Massey, R. Maoli, R. Saglia, R. Teyssier, R. Toledo-Moreo, S. Andreon, S. Avila, S. Bardelli, S. Borgani, S. Bruton, S. Camera, S. Casas, S. Cavuoti, S. Davini, S. de la Torre, S. Di Domizio, S. Escoffier, S. Ferriol, S. Fotopoulou, S. Galeotta, S. J. Liu, S. Kermiche, S. Kruk, S. Ligori, S. Mei, S.-M. Niemi, S. Nadathur, S. Nesseris, S. Paltani, S. Pires, S. Quai, S. Sacquegna, S. Toft, S. Tosi, S. V. H. Haugan, S. Vinciguerra, T. Castro, T. Gasparetto, T. I. Liaudat, T. Vassallo, V. Capobianco, V. Desjacques, V. Duret, V. Kansal, V. Lindholm, V. Pettorino, V. Scottez, W. Holmes, W. J. Percival, W. Roster, X. Dupac, Y. Akrami, Y. Copin, Y. Fang, Y. Kang, Y. Wang, Z. Sakr.

Figure 2
Figure 2. Figure 2: Abundance matching applied to the AbacusSummit halo mass function at z = 0.8. The top panel shows the FS2 halo mass function (solid dark blue) and the AbacusSummit ΛCDM mass function (dashed orange). The bottom panel presents their ratio relative to FS2, illustrat￾ing differences of up to ∼ 20%. Applying AM (dot-dashed green) brings the AbacusSummit mass function into excellent agreement with FS2. selected… view at source ↗
Figure 3
Figure 3. Figure 3: Posterior of the prior-agnostic analysis. Marginalised posterior distributions from the power spectrum (blue), bispectrum (green), and their combination (red) at the stated redshift and scale cuts. Shaded re￾gions denote 68% and 95% credible intervals. Nuisance parameters are marginalised. Dashed lines mark the simulation fiducial values. and the bispectrum alone. Finally, by progressively adding mul￾tipol… view at source ↗
Figure 4
Figure 4. Figure 4: Impact of prior choice on power spectrum analysis. The plot shows the parameter posteriors from the power spectrum under different treatments of the PNG-bias intercept pbϕ : we either fix it to the UHMF or GFM value, or fit it with a Gaussian prior (mean and width shown in the legend). Blue contours use a Gaussian prior centred on the UHMF value; orange contours are centred on the GFM value; green contours… view at source ↗
Figure 5
Figure 5. Figure 5: Same as [PITH_FULL_IMAGE:figures/full_fig_p012_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Same as [PITH_FULL_IMAGE:figures/full_fig_p013_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Measured versus assumed prior of bϕ. We compare the di￾rectly measured values of bϕ using SU simulations at four redshift bins (crosses) with UHMF (dashed blue line) and GFM (dashed orange line) predictions. Values of bϕ corresponding to our prior centre (converted using inferred b1 from joint power spectrum-bispectrum chains) are shown in green line, with the shaded regions showing the 1 and 2σ intervals.… view at source ↗
Figure 8
Figure 8. Figure 8: Null test on simulations with Gaussian initial conditions (fNL = 0). Parameter posterior distributions from power spectrum (blue), bispec￾trum (green), and their combination (red). Left: constraints form the model with PNG. Right: constraints from the model without PNG. tours), and joint power spectrum and bispectrum (red contours). In all cases, the marginalised constraint on fNL is centred on zero and co… view at source ↗
Figure 9
Figure 9. Figure 9: Best-fit galaxy biases and the corresponding 1σ error bars from joint power spectrum-bispectrum fit to simulations with Gaussian ini￾tial conditions. To make the figure clearer, we have slightly shifted the data points horizontally within each redshift to avoid overlap. However, these measurements still correspond to the same redshift bin, respec￾tively. The areas shaded in green and magenta show the co-ev… view at source ↗
Figure 10
Figure 10. Figure 10: Marginalised 1-dimensional posterior distributions in the four redshift bins and for five choices of scale cuts (for monopole and quadrupole). The violin errors represent the real posterior distribution for each parameter, with the blue and magenta error bars representing the 1σ and 2σ intervals of these distributions, respectively. The dashed lines are the fiducial values used in the simulations. The hex… view at source ↗
Figure 11
Figure 11. Figure 11: Marginalised 1-dimensional posterior distributions in the four redshift bins and for five choices of scale cuts (for monopole and quadrupole). The hexadecapole is discarded due to noisy measurements. The rest of the plot styling matches [PITH_FULL_IMAGE:figures/full_fig_p015_11.png] view at source ↗
Figure 12
Figure 12. Figure 12: Validity of perturbative model and information content. The plots illustrate the accuracy in terms of FoB (Eq. 47) and the precision in terms of FoM (Eq. 48) of various scale cuts across all redshifts for the combination of all the varied cosmological parameters. The FoM is normalised for both observables based on the lowest redshift and scale cut (z = 0.8, k Pℓ max = 0.2 h Mpc−1 and k Bℓ max = 0.1 h Mpc−… view at source ↗
Figure 13
Figure 13. Figure 13: Impact of the exclusion of large-scale modes. Left: we present the marginalised 1σ constraints on cosmological parameters from the power spectrum and bispectrum multipoles at z = 0.8. Right: we show the FoB and FoM for the combined parameters from Pℓ (blue) and Bℓ (red). In this context, kmin denotes the lower boundary of the considered bin, which implies excluding each kf bin individually. Moreover, the … view at source ↗
Figure 14
Figure 14. Figure 14: Best-fit models from joint power spectrum and bispectrum analysis versus measured spectra at z = 0.8. Left: redshift-space power spectrum multipoles. Middle: bispectrum multipoles in equilateral configurations. Right: bispectrum multipoles in squeezed configurations. The error bars are determined using the theoretical Gaussian covariance. The bottom panels show the deviation of the model from the measurem… view at source ↗
Figure 15
Figure 15. Figure 15: Joint analysis of power spectrum and bispectrum. Marginalised parameter posterior distributions from power spectrum (blue), bispectrum (green), and their combination (red). The dashed lines are fiducial values of simulations. The redshifts and scale cuts are noted on the plot. Article number, page 18 of 30 [PITH_FULL_IMAGE:figures/full_fig_p018_15.png] view at source ↗
Figure 16
Figure 16. Figure 16: Comparison of constraints from power spectrum and bispec￾trum alone and combined. Shown are 1σ error on fNL for fiducial value of fNL = 30 from power spectrum (blue) and bispectrum (green) multi￾poles, and their combination (red) at four redshift bins considered. 6. Conclusions Deciphering the origin of cosmic structure is a central open ques￾tion in modern cosmology. A detection of local-type PNG – or, c… view at source ↗
Figure 17
Figure 17. Figure 17: Information content of various multipoles on fNL. The inverse of the relative error on fNL with respect to the fiducial value of fNL = 30 for power spectrum multipoles (blue), bispectrum multipoles (green), and their combination (red). In each coloured bar, the crossed black bars show the constraints considering only the power spectrum and bispectrum monopoles and their combination. scales (via its higher… view at source ↗
read the original abstract

Primordial non-Gaussianity (PNG) is a powerful probe of the origin of cosmic structure. Stage-IV surveys like \Euclid will measure galaxy $2$- and $3$-point clustering at high signal-to-noise, whose exploitation requires robust joint analysis. We prepare for Euclid's spectroscopic sample by validating a redshift-space power-spectrum and bispectrum pipeline (one-loop $P_\ell$, tree-level $B_\ell$) on Euclid-like mocks from Abacus-PNG $N$-body simulations with Gaussian and local-PNG initial conditions, using a halo occupation distribution (HOD) tuned to Euclid Flagship 2. We stress-test analysis choices -- PNG-bias parametrisation, priors, and scale cuts -- and perform null tests without PNG. In a `prior-agnostic setup', detection of the dominant PNG term $\propto f_{\rm NL} \, b_\phi$ in single redshift bins is difficult; nevertheless, the bispectrum provides constraints on other PNG combinations that partially lift degeneracies. We propose a physically motivated prior on $b_\phi$ that yields unbiased $f_{\rm NL}$ while accounting for theory uncertainty, and determine scale cuts that give unbiased $\Lambda$CDM and $f_{\rm NL}$. With $V_{\rm eff}=16\,h^{-3}\,{\rm Gpc}^3$ across four snapshots ($0.8\le z\le1.7$), our likelihood analyses recover $<1\sigma$ bias in $f_{\rm NL}$ and $\Lambda$CDM. At fixed cuts, $B_\ell$ alone reduces $\sigma({f_{\rm NL}})$ by $\sim29$--$46\%$ relative to $P_\ell$, and joint power spectrum-bispectrum analysis tightens a further $\sim8$--$13\%$; the cumulative gain from $z=0.8$ to $1.7$ is $\sim2.3$ for the joint case. The bispectrum quadrupole is key. Our strongest results are at $z=1.7$: $1.9\sigma$ for $f_{\rm NL} \, b_\phi$ (prior-agnostic) and $2.35\sigma$ for $f_{\rm NL}$ (prior-based). Joint analyses thus offer strong prospects for testing multi-field inflation, pending end-to-end validation in the full Euclid geometry with observational systematics.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 3 minor

Summary. The manuscript validates a joint redshift-space power spectrum and bispectrum pipeline for constraining local primordial non-Gaussianity (f_NL) using Euclid-like mocks from Abacus-PNG N-body simulations populated with an HOD tuned to Euclid Flagship 2. It employs one-loop P_ℓ and tree-level B_ℓ models, stress-tests PNG-bias parametrization, priors, and scale cuts, introduces a physically motivated prior on b_φ to account for theory uncertainty, performs null tests, and reports unbiased recovery of f_NL and ΛCDM parameters with V_eff = 16 h^{-3} Gpc^3 across four snapshots (0.8 ≤ z ≤ 1.7). The bispectrum alone reduces σ(f_NL) by 29–46% relative to the power spectrum, with joint analysis providing an additional 8–13% tightening and a cumulative gain of ~2.3; the bispectrum quadrupole is highlighted as key, yielding up to 2.35σ for f_NL at z=1.7 under the prior-based setup.

Significance. If the adopted perturbative models and scale cuts prove sufficient, the work quantifies concrete gains from including the bispectrum (particularly the quadrupole) for multi-field inflation tests with Euclid and supplies a practical framework for handling degeneracies and theory uncertainties via a motivated prior on b_φ. The simulation-based recovery of injected f_NL with <1σ bias, combined with explicit stress-tests on Abacus-PNG mocks and null tests without PNG, provides a reproducible benchmark that strengthens prospects for Stage-IV PNG constraints. The reported improvement factors and strongest signals at z=1.7 constitute useful quantitative guidance for survey planning.

major comments (2)
  1. [§5] §5 (scale cuts and model validation): The central claim of <1σ bias in f_NL recovery and the 29–46% improvement from B_ℓ rests on the sufficiency of tree-level bispectrum plus one-loop power spectrum up to the chosen k-cuts. At z=1.7, where the bispectrum quadrupole drives the strongest results, an explicit test or estimate of the size of neglected two-loop corrections and additional PNG-induced bias operators (beyond the dominant f_NL b_φ term) within those cuts is needed; without it, the joint multi-redshift constraints and cumulative gain of ~2.3 could be compromised.
  2. [§4.2, §6.1] §4.2 and §6.1 (PNG-bias parametrization and prior on b_φ): The physically motivated prior on b_φ is presented as accounting for theory uncertainty while yielding unbiased f_NL. The manuscript should specify the exact functional form of this prior (including any dependence on the HOD or simulation parameters) and demonstrate that it does not inadvertently incorporate information from the same Abacus-PNG mocks used for the likelihood analyses, to ensure the 1.9σ (prior-agnostic) and 2.35σ (prior-based) detections at z=1.7 remain robust.
minor comments (3)
  1. [Figure 4] Figure 4 (or equivalent results figure): Axis labels and error-bar styles for the different redshift bins and analysis combinations (P_ℓ only, B_ℓ only, joint) could be made more distinct to improve readability of the σ(f_NL) comparisons.
  2. [Abstract, §3] Abstract and §3: The effective volume V_eff=16 h^{-3} Gpc^3 is stated without an explicit breakdown of the contribution per snapshot or per survey geometry; adding this would clarify how the four snapshots combine.
  3. [§2.2] §2.2: The HOD parameters tuned to Euclid Flagship 2 are summarized but lack a table of best-fit values or a brief discussion of how PNG-induced changes in halo properties are (or are not) propagated.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their careful reading of the manuscript and constructive comments. We address each major comment below and have incorporated revisions to strengthen the presentation of our model validation and prior specification.

read point-by-point responses

  1. Referee: [§5] §5 (scale cuts and model validation): The central claim of <1σ bias in f_NL recovery and the 29–46% improvement from B_ℓ rests on the sufficiency of tree-level bispectrum plus one-loop power spectrum up to the chosen k-cuts. At z=1.7, where the bispectrum quadrupole drives the strongest results, an explicit test or estimate of the size of neglected two-loop corrections and additional PNG-induced bias operators (beyond the dominant f_NL b_φ term) within those cuts is needed; without it, the joint multi-redshift constraints and cumulative gain of ~2.3 could be compromised.

    Authors: We agree that an explicit estimate of higher-order terms would further bolster the validation. The scale cuts in the manuscript were chosen precisely because they yield unbiased recovery of both f_NL and ΛCDM parameters across the mocks, providing implicit evidence that neglected contributions remain subdominant. In the revised manuscript we have added a paragraph in §5 that estimates the magnitude of two-loop corrections using standard perturbation-theory scaling relations from the literature, confirming they lie below the statistical errors for our adopted k_max at z=1.7. We also briefly discuss additional PNG bias operators, noting that they are either suppressed by extra powers of f_NL or enter at higher order in the bias expansion; their expected impact is therefore smaller than the dominant f_NL b_φ term already included. These additions clarify the robustness of the reported gains without changing the conclusions. revision: yes

  2. Referee: [§4.2, §6.1] §4.2 and §6.1 (PNG-bias parametrization and prior on b_φ): The physically motivated prior on b_φ is presented as accounting for theory uncertainty while yielding unbiased f_NL. The manuscript should specify the exact functional form of this prior (including any dependence on the HOD or simulation parameters) and demonstrate that it does not inadvertently incorporate information from the same Abacus-PNG mocks used for the likelihood analyses, to ensure the 1.9σ (prior-agnostic) and 2.35σ (prior-based) detections at z=1.7 remain robust.

    Authors: We thank the referee for requesting this clarification. The prior is constructed from the theoretical peak-background-split expectation for the PNG bias parameter and is assigned a finite width to marginalize over residual theoretical uncertainties in the bias expansion. Its functional form and width are determined from general considerations in the literature and do not depend on the specific HOD parameters or outputs of the Abacus-PNG mocks employed in the likelihood analyses. In the revised version we have expanded §4.2 to state the functional form explicitly and added a sentence in §6.1 confirming that the prior parameters were fixed independently of the present mock likelihoods. This ensures the quoted significances remain unaffected by any circularity. revision: yes

Circularity Check

0 steps flagged

No significant circularity; validation is externally benchmarked

full rationale

The paper validates a one-loop power spectrum plus tree-level bispectrum pipeline on independent Abacus-PNG N-body simulations that inject known f_NL values (Gaussian and local-PNG initial conditions). The HOD is tuned to the separate Euclid Flagship 2 simulation. Likelihood analyses recover the injected signals with <1σ bias, and the reported 29–46% improvement from B_ℓ (plus further 8–13% from joint analysis) are direct numerical outcomes measured on these mocks. The proposed prior on b_φ is described as physically motivated to account for theory uncertainty rather than being fitted to the analysis data. No load-bearing step reduces by construction to a fitted parameter renamed as prediction, a self-definition, or a self-citation chain. The central claims rest on external simulation benchmarks and are therefore self-contained.

Axiom & Free-Parameter Ledger

2 free parameters · 2 axioms · 0 invented entities

The central claim rests on the accuracy of the chosen perturbation theory order, the representativeness of the HOD, and the validity of the proposed b_φ prior; these are standard domain assumptions rather than new postulates.

free parameters (2)
  • prior on b_φ
    Physically motivated prior introduced to produce unbiased f_NL while incorporating theory uncertainty
  • scale cuts
    Chosen to ensure unbiased recovery of both ΛCDM and f_NL parameters
axioms (2)
  • domain assumption HOD tuned to Euclid Flagship 2 accurately represents galaxy population in Abacus-PNG mocks
    Used to generate realistic galaxy catalogs from halo catalogs
  • domain assumption One-loop P_ℓ and tree-level B_ℓ capture the relevant clustering signal including PNG effects
    Pipeline choice stated for redshift-space distortions and bispectrum modeling

pith-pipeline@v0.9.0 · 7552 in / 1467 out tokens · 73640 ms · 2026-05-21T03:04:50.709446+00:00 · methodology

discussion (0)

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Reference graph

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