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arxiv: 2512.03824 · v2 · pith:RSDZENLEnew · submitted 2025-12-03 · 🌌 astro-ph.CO

The impact of our peculiar motion on primordial non-Gaussianity measurements using the LIGER4GAL framework

Bartolomeo Bottazzi Baldi , Mohamed Yousry Elkhashab , Daniele Bertacca , Cristiano Porciani This is my paper

Pith reviewed 2026-05-22 11:31 UTC · model grok-4.3

classification 🌌 astro-ph.CO
keywords primordial non-Gaussianityrelativistic redshift-space distortionsfinger-of-the-observergalaxy power spectrumLIGER4GALluminous red galaxiesDESI surveylarge-scale structure
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The pith

Omitting the observer's peculiar velocity effect in galaxy power spectra biases f_nl measurements by more than one sigma in 40 percent of cosmic realizations.

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

The paper introduces LIGER4GAL, an update to a simulation method that adds all linear-order relativistic redshift-space distortions directly to the positions and velocities of tracers in N-body simulations. The authors run this code on a large simulation to create a DESI-like catalog of luminous red galaxies and then compare power spectrum multipoles computed with and without the full set of relativistic effects. They focus on the finger-of-the-observer contribution, which comes from the observer's own peculiar velocity, and measure how its absence shifts the recovered value of the local primordial non-Gaussianity parameter f_nl. A reader would care because next-generation surveys target percent-level constraints on f_nl, and an unmodeled systematic that affects a large fraction of possible universes could produce spurious detections or hide real signals. The work therefore supplies both a practical tool and a quantitative warning about the scale at which these relativistic corrections become essential.

Core claim

By implementing all linear-order relativistic RSDs at the tracer level in high-resolution N-body simulations, LIGER4GAL produces mock galaxy samples whose power spectrum multipoles show that the finger-of-the-observer effect must be included in the modeling; otherwise the inferred f_nl is biased by more than 1 sigma_fnl in 40 percent of realizations and by more than 0.25 sigma_fnl in 80 percent of realizations when fitting scales down to k_min = 0.0015 h/Mpc.

What carries the argument

LIGER4GAL, the updated implementation that adds every linear-order relativistic redshift-space distortion at the individual tracer level inside N-body simulations while preserving non-linear clustering on smaller scales.

If this is right

  • Power-spectrum analyses of upcoming surveys must include the observer's peculiar velocity term to keep f_nl constraints unbiased at the target precision.
  • The reported bias fractions imply that the effect is common rather than a rare outlier, so it cannot be ignored in standard modeling pipelines.
  • The same framework can be applied to test whether other relativistic RSD contributions produce comparable shifts in f_nl or in other large-scale parameters.
  • Surveys that reach k_min values around 0.0015 h/Mpc will need this level of modeling; shallower k_min cuts reduce but do not eliminate the potential bias.

Where Pith is reading between the lines

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

  • Similar observer-motion corrections may be needed for other ultra-large-scale observables such as the integrated Sachs-Wolfe cross-correlation or the scale-dependent bias induced by PNG itself.
  • Real-data pipelines could adopt the LIGER4GAL approach to forward-model the full set of linear relativistic effects rather than applying analytic corrections after the fact.
  • The 40 percent figure suggests that a single survey realization has a substantial chance of being affected, which strengthens the case for including the term as a default rather than an optional check.

Load-bearing premise

Linear-order relativistic RSDs placed at the tracer level are enough to produce the reported bias percentages on f_nl, and higher-order or non-linear corrections would not change those fractions.

What would settle it

Generate many independent realizations of the same DESI-like sample with and without the finger-of-the-observer term, fit each for f_nl down to k_min = 0.0015 h/Mpc, and check whether the fraction of realizations showing a bias larger than 1 sigma_fnl is close to 40 percent.

Figures

Figures reproduced from arXiv: 2512.03824 by Bartolomeo Bottazzi Baldi, Cristiano Porciani, Daniele Bertacca, Mohamed Yousry Elkhashab.

Figure 1
Figure 1. Figure 1: FIG. 1 [PITH_FULL_IMAGE:figures/full_fig_p005_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2: Schematic summarising how the haloes (Section [PITH_FULL_IMAGE:figures/full_fig_p007_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3: Mollweide projection in ecliptic coordinates of the [PITH_FULL_IMAGE:figures/full_fig_p008_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4: Halo and LRG galaxies survey functions. With a grey [PITH_FULL_IMAGE:figures/full_fig_p008_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5 [PITH_FULL_IMAGE:figures/full_fig_p010_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6: We plot the FOTO signal for the power spectrum [PITH_FULL_IMAGE:figures/full_fig_p010_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: The lower panel shows the residuals between the data and the model in units of the standard deviation. In all cases, the data remain within 3σ over most of the k-range, except at the largest scales of the LRG-FS-O and LRG-DESI-Os mea￾surements, where the residuals are driven by the high FOTO signal. The amplitude of the FOTO signal is both oscillatory and rapidly decreasing with k. To assess the scale at w… view at source ↗
Figure 9
Figure 9. Figure 9: FIG. 9 [PITH_FULL_IMAGE:figures/full_fig_p014_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: FIG. 10: Fraction of masked-sky BCLRG-DESI mock real [PITH_FULL_IMAGE:figures/full_fig_p014_10.png] view at source ↗
Figure 12
Figure 12. Figure 12: As seen from the figure, the FOTO signal leads to a [PITH_FULL_IMAGE:figures/full_fig_p015_12.png] view at source ↗
Figure 11
Figure 11. Figure 11: FIG. 11: Corner plot showcasing shifts in cosmological con [PITH_FULL_IMAGE:figures/full_fig_p016_11.png] view at source ↗
Figure 12
Figure 12. Figure 12: FIG. 12: FoB values obtained from di [PITH_FULL_IMAGE:figures/full_fig_p016_12.png] view at source ↗
Figure 13
Figure 13. Figure 13: FIG. 13: In the upper panel, we compare the halo radial num [PITH_FULL_IMAGE:figures/full_fig_p019_13.png] view at source ↗
Figure 14
Figure 14. Figure 14: FIG. 14: In the upper panel, we compare the HMF of H-FS [PITH_FULL_IMAGE:figures/full_fig_p020_14.png] view at source ↗
read the original abstract

Current and forthcoming galaxy surveys will map the observable Universe with unprecedented depth, sky coverage, and precision. These maps are affected by relativistic redshift-space distortions (RSDs), which become increasingly relevant on ultra-large scales. Accurate modelling of these relativistic RSDs is essential to avoid systematic biases in key cosmological measurements, such as primordial non-Gaussianity (PNG). To address this, we introduce an updated implementation of the LIGER method, LIGER4GAL, which incorporates all linear-order relativistic RSDs directly at the tracer level of high-resolution N-body simulations. We demonstrate that LIGER4GAL improves upon previous iterations of the LIGER method by reproducing the expected non-linear clustering while maintaining accuracy for relativistic RSDs on large scales. We use the updated code to generate a DESI-like sample of luminous red galaxies from the Huge MultiDark Planck simulation. By measuring the power spectrum multipoles of this sample with and without the imprint of relativistic RSDs, we assess the impact of relativistic effects on measurements of the local PNG signal ($f_\mathrm{nl}$). We find that the omission of the''finger-of-the-observer'' (sourced by the peculiar velocity of the observer) effect in the power spectrum modelling can bias measurements of $f_{\rm nl}$ by more than $1$ ($0.25$) $ \sigma_{f_{\rm nl}}$ in 40% (80%) of the possible realizations of the universe if scales down to $k_\mathrm{min} = 0.0015\,h/\mathrm{Mpc}$ are included.

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 / 2 minor

Summary. The paper introduces LIGER4GAL, an updated implementation of the LIGER method that incorporates all linear-order relativistic redshift-space distortions directly at the tracer level in high-resolution N-body simulations. Using a DESI-like sample of luminous red galaxies drawn from the Huge MultiDark Planck simulation, the authors measure power spectrum multipoles with and without the imprint of these relativistic RSDs. They quantify the resulting bias on local primordial non-Gaussianity parameter f_nl, reporting that omission of the finger-of-the-observer effect (sourced by the observer's peculiar velocity) can bias f_nl measurements by more than 1 sigma_fnl in 40% of realizations (and more than 0.25 sigma_fnl in 80%) when scales down to k_min = 0.0015 h/Mpc are included.

Significance. If the linear-order treatment proves sufficient, the work provides a concrete, simulation-based estimate of a previously under-appreciated systematic for ultra-large-scale PNG analyses. The direct with/without comparison within the same simulation suite is a strength, as it avoids circularity in the bias measurement and offers falsifiable percentages that can be tested against analytic expectations or higher-resolution runs. This is relevant for DESI and future surveys where relativistic effects on the largest scales must be controlled to reach the target precision on f_nl.

major comments (2)
  1. [Validation of LIGER4GAL and results on f_nl bias] The central percentages (40% and 80% of realizations) rest on the assumption that linear-order relativistic RSDs implemented at the tracer level fully capture the finger-of-the-observer contribution without higher-order relativistic or non-linear corrections altering the bias distribution on k_min = 0.0015 h/Mpc scales. The validation section demonstrates reproduction of non-linear clustering and large-scale RSD accuracy, but does not quantify the size of second-order terms or their cross-talk with PNG; this directly affects whether the reported fractions remain robust.
  2. [Power spectrum multipole measurements and f_nl impact assessment] The assessment of bias relative to sigma_fnl is obtained from the with/without power-spectrum comparison, yet the manuscript provides no error bars on the reported percentages, no convergence tests with respect to simulation volume or resolution, and no explicit comparison against analytic expectations for the relativistic correction. These omissions make it difficult to judge the statistical significance of the 40% and 80% figures.
minor comments (2)
  1. [Abstract] The abstract states that LIGER4GAL 'improves upon previous iterations of the LIGER method by reproducing the expected non-linear clustering while maintaining accuracy for relativistic RSDs'; a short quantitative statement (e.g., fractional difference in the quadrupole or hexadecapole on large scales) would make this claim more precise.
  2. [Introduction and method description] Notation for the observer's peculiar velocity contribution to the finger-of-the-observer effect is introduced without a brief equation or reference to the standard relativistic RSD expansion; adding this would aid readers new to the topic.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their positive assessment of the work's significance and for the constructive major comments. We respond to each point below, indicating planned revisions to the manuscript.

read point-by-point responses

  1. Referee: [Validation of LIGER4GAL and results on f_nl bias] The central percentages (40% and 80% of realizations) rest on the assumption that linear-order relativistic RSDs implemented at the tracer level fully capture the finger-of-the-observer contribution without higher-order relativistic or non-linear corrections altering the bias distribution on k_min = 0.0015 h/Mpc scales. The validation section demonstrates reproduction of non-linear clustering and large-scale RSD accuracy, but does not quantify the size of second-order terms or their cross-talk with PNG; this directly affects whether the reported fractions remain robust.

    Authors: We agree that higher-order terms could in principle modify the reported bias fractions. Our work targets the leading linear-order relativistic RSDs, which dominate the finger-of-the-observer effect on the ultra-large scales considered. The existing validation confirms consistency with linear theory for these effects. In the revised manuscript we will add a dedicated paragraph estimating the expected size of second-order relativistic corrections from the literature and arguing that they remain sub-dominant for the f_nl bias at the precision of our results; we will also flag a full non-linear treatment as future work. revision: partial

  2. Referee: [Power spectrum multipole measurements and f_nl impact assessment] The assessment of bias relative to sigma_fnl is obtained from the with/without power-spectrum comparison, yet the manuscript provides no error bars on the reported percentages, no convergence tests with respect to simulation volume or resolution, and no explicit comparison against analytic expectations for the relativistic correction. These omissions make it difficult to judge the statistical significance of the 40% and 80% figures.

    Authors: We acknowledge these omissions. In the revised manuscript we will add bootstrap-derived error bars on the 40% and 80% fractions. We will also report convergence tests using sub-volumes of the Huge MultiDark Planck simulation. Finally, we will include a direct comparison of the simulated power-spectrum multipoles (with and without the finger-of-the-observer term) against the corresponding analytic expressions, confirming consistency at linear order. revision: yes

Circularity Check

0 steps flagged

No significant circularity: bias fractions obtained via direct simulation comparison

full rationale

The central result (40% of realizations exceeding 1 sigma_fnl bias when omitting finger-of-the-observer) is obtained by explicit with/without measurement of power spectrum multipoles on the same DESI-like LRG sample generated from the Huge MultiDark Planck simulation using LIGER4GAL. This is a direct numerical comparison rather than a derivation, fit, or self-referential equation. No load-bearing step reduces to a fitted parameter renamed as prediction, self-citation chain, or ansatz smuggled via prior work. The linear-order RSD implementation is an input assumption whose adequacy is an external validity question, not a circularity issue. The paper remains self-contained against its own simulation benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

Central claim rests on validity of linear relativistic RSD modeling and simulation fidelity for the chosen k-range and galaxy sample.

axioms (1)
  • domain assumption Linear-order relativistic RSDs dominate the observer-motion imprint on ultra-large scales
    Incorporated directly at tracer level to assess PNG bias

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