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arxiv: 2606.29735 · v1 · pith:XGNRJKHEnew · submitted 2026-06-29 · 🌌 astro-ph.CO

Modeling survey-window and integral-constraint effects on PNG in the galaxy power spectrum with light-cone mocks

Shintaro Nakano , Masahiro Takada , Toshiki Kurita , Ryo Terasawa This is my paper

Pith reviewed 2026-06-30 05:39 UTC · model grok-4.3

classification 🌌 astro-ph.CO
keywords primordial non-Gaussianitygalaxy power spectrumsurvey window functionintegral constraintlight-cone mocksBOSS surveyredshift-space distortions
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The pith

Analytical treatments of survey-window and integral-constraint effects on the galaxy power spectrum lose accuracy on scales k ≲ k_eq when primordial non-Gaussianity is present.

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

The paper builds light-cone galaxy mock catalogs from linear theory simulations that include the survey window function, redshift evolution of density fields, and redshift-space distortions. These mocks apply the identical power-spectrum estimator used on real data, so that the effects of discrete Fourier transforms, line-of-sight dependence, and wide-angle RSD are captured exactly. The resulting measurements reveal that super-survey modes comparable to or larger than the survey window strongly affect the integral constraint. As a result, the analytical convolution formulas routinely applied in earlier work begin to deviate on wavenumbers below the matter-radiation equality scale and become invalid once PNG-induced scale-dependent bias is included. The framework therefore supplies a route to unbiased PNG constraints from the large-scale galaxy power spectrum measured by wide-area surveys.

Core claim

Light-cone mock catalogs constructed from linear theory simulations that mimic the BOSS survey demonstrate that long-wavelength super-survey modes significantly alter the integral constraint, causing the analytical treatment of survey-window convolution and integral constraint to lose accuracy for k ≲ k_eq and to become invalid in the presence of primordial non-Gaussianity.

What carries the argument

Light-cone galaxy mock catalogs generated from linear theory simulations, which embed the survey window, redshift evolution, and the identical multipole estimator applied to real observations.

Load-bearing premise

Linear theory simulations are sufficient to capture the impact of super-survey modes, redshift evolution, and PNG-induced scale-dependent bias on the estimated power-spectrum multipoles.

What would settle it

A side-by-side comparison, on scales k < k_eq, between the power-spectrum multipoles measured from the light-cone mocks that contain PNG and the multipoles predicted by the standard analytical convolution formula would show whether the analytical result deviates from the mock result.

read the original abstract

We develop an analysis framework based on {\em light-cone} galaxy mock catalogs constructed from linear theory simulations in order to accurately model the impact of primordial non-Gaussianity (PNG) on galaxy power spectrum on large scales. These linear light-cone catalogs properly incorporate a variety of observational and cosmological effects, including the survey window function, the redshift evolution of matter and galaxy density fields, and redshift-space distortions (RSD). When estimating the multipole moments of the power spectrum from each light-cone mock, we employ the same estimator as used in actual analyses, thereby properly accounting for the effects of the discrete Fourier transform, the line-of-sight dependence of the fields, and wide-angle RSD effects. Using light-cone mock catalogs that mimic the BOSS survey, we demonstrate that long-wavelength modes comparable to or larger than the survey window scale, namely super-survey modes, have a significant impact on the integral constraint (IC) in power spectrum measurements. In particular, we show that the analytical treatment of the survey-window convolution and IC, which has been commonly used in previous studies, begins to lose accuracy on scales of $k\lesssim k_{\rm eq}$ (the matter-radiation equality scale), and becomes invalid in the presence of PNG. The method developed in this work enables unbiased searches for PNG using the galaxy power spectrum on long-wavelength scales probed by ongoing and future wide-area galaxy surveys.

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 / 0 minor

Summary. The manuscript develops a framework based on linear-theory light-cone galaxy mock catalogs (mimicking BOSS) that incorporate the survey window, redshift evolution, RSD, and PNG scale-dependent bias. By applying the same power-spectrum multipole estimator used on data, it demonstrates that the standard analytical treatment of survey-window convolution plus integral constraint loses accuracy for k≲k_eq and becomes invalid once PNG is included, due to the impact of super-survey modes.

Significance. If the central result holds, it would indicate that prior PNG analyses relying on analytical IC/window corrections may carry unaccounted biases on the largest scales, with direct relevance to constraints from ongoing and future wide-area surveys.

major comments (2)
  1. [Abstract and Methods] The demonstration that the analytical IC/window treatment is invalid with PNG rests entirely on linear-theory mocks (Abstract; Methods). Linear theory omits mode-coupling from non-linear gravitational evolution; such couplings can be enhanced by PNG-induced scale-dependent bias and super-survey modes, potentially changing the size or scale dependence of the reported discrepancy between analytical predictions and mock measurements. A quantitative test or justification that linear theory suffices to establish invalidity (rather than merely inconsistency with the linear approximation) is required.
  2. [Results] No comparison is presented between the linear light-cone results and any non-linear simulation or higher-order perturbation theory calculation that includes the same survey geometry and PNG. Without this, it remains unclear whether the claimed breakdown is robust or an artifact of the linear approximation.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their careful reading of the manuscript and for highlighting important considerations regarding the scope of linear theory. Below we provide point-by-point responses to the major comments. We have revised the manuscript to incorporate additional justification for our approach while maintaining the focus of the present work.

read point-by-point responses

  1. Referee: [Abstract and Methods] The demonstration that the analytical IC/window treatment is invalid with PNG rests entirely on linear-theory mocks (Abstract; Methods). Linear theory omits mode-coupling from non-linear gravitational evolution; such couplings can be enhanced by PNG-induced scale-dependent bias and super-survey modes, potentially changing the size or scale dependence of the reported discrepancy between analytical predictions and mock measurements. A quantitative test or justification that linear theory suffices to establish invalidity (rather than merely inconsistency with the linear approximation) is required.

    Authors: The analytical survey-window convolution and integral-constraint corrections we test are themselves derived under linear theory. Our linear light-cone mocks therefore provide a fully consistent framework in which to expose the breakdown of that analytical treatment once PNG and super-survey modes are included. The discrepancies we report originate from the linear response of the PNG scale-dependent bias to modes larger than the survey; these are precisely the effects captured by linear theory. While non-linear mode coupling would introduce further corrections, it cannot restore the validity of an analytical prescription that already fails at linear order. We have added a dedicated paragraph in Section 2 and a brief discussion in Section 5 justifying the sufficiency of linear theory for demonstrating this inconsistency, together with references to prior linear analyses of PNG bias. revision: partial

  2. Referee: [Results] No comparison is presented between the linear light-cone results and any non-linear simulation or higher-order perturbation theory calculation that includes the same survey geometry and PNG. Without this, it remains unclear whether the claimed breakdown is robust or an artifact of the linear approximation.

    Authors: We acknowledge that a direct comparison with non-linear mocks or higher-order perturbation theory would be valuable for quantifying additional corrections. However, generating non-linear light-cone catalogs that simultaneously incorporate PNG, the full BOSS-like survey geometry, redshift evolution, and the identical power-spectrum estimator is a substantial computational undertaking that lies outside the scope of the present study. The current linear framework is sufficient to establish that the standard analytical treatment is already inconsistent with linear theory once PNG is present. We have added a forward-looking statement in the conclusions noting that extension to non-linear simulations is an important direction for future work. revision: partial

Circularity Check

0 steps flagged

No circularity; forward simulation with mocks is independent of analytical claims.

full rationale

The paper constructs light-cone mocks from linear theory simulations and applies the data estimator to demonstrate limitations of prior analytical window/IC treatments. This is a standard forward-modeling validation with no derivation chain, fitted-parameter prediction, or self-citation that reduces the central claim to its own inputs. The approach is self-contained and externally falsifiable via the mocks themselves.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim rests on the domain assumption that linear theory suffices for the relevant large-scale effects; no free parameters or invented entities are introduced in the abstract.

axioms (1)
  • domain assumption Linear perturbation theory is adequate for modeling the galaxy density field, redshift-space distortions, and PNG effects on the scales of interest.
    Mocks are constructed from linear theory simulations as stated in the abstract.

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discussion (0)

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Reference graph

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