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arxiv: 2509.08787 · v2 · submitted 2025-09-10 · 🌌 astro-ph.CO

Parity Violation in Galaxy Shapes: Primordial Non-Gaussianity

Toshiki Kurita , Drew Jamieson , Eiichiro Komatsu , Fabian Schmidt This is my paper

Pith reviewed 2026-05-18 17:37 UTC · model grok-4.3

classification 🌌 astro-ph.CO
keywords intrinsic alignmentsparity-violating primordial non-Gaussianityeffective field theoryprimordial trispectrumgalaxy shapeslarge-scale structureN-body simulations
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The pith

Galaxy intrinsic alignments probe parity-violating primordial non-Gaussianity via the collapsed trispectrum limit.

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

The paper investigates galaxy intrinsic alignments as a probe of parity-violating primordial non-Gaussianity. It demonstrates that the parity-odd IA power spectrum is sensitive to the collapsed limit of the parity-odd primordial trispectrum within an effective field theory framework. For a U(1)-gauge inflationary model, this spectrum scales with the curvature perturbation power spectrum, with factors that include both the PNG amplitude and bias parameters. By fixing the bias parameters from N-body simulations of dark matter halos, forecasts indicate that DESI and LSST data can improve limits on the parity-violating PNG amplitude compared to galaxy four-point and CMB trispectrum analyses. Galaxy shapes provide complementary sensitivity to different scales and configurations, and the paper introduces a method to generate initial conditions from the parity-odd trispectrum with an enhanced collapsed limit.

Core claim

Within the effective field theory framework, the parity-odd IA power spectrum is sensitive to the collapsed limit of the parity-odd primordial trispectrum. For a U(1)-gauge inflationary model, the IA power spectrum is proportional to the curvature perturbation power spectrum P_ζ(k) ∝ k^{-3}, where the proportionality constants contain the PNG amplitude and undetermined EFT bias parameters. N-body simulations fix the bias parameters for dark matter halos. With these, forecasts show that the IA power spectrum can improve current limits on the amplitude of parity-violating PNG from galaxy four-point correlation and CMB trispectrum analyses, while remaining sensitive to different scales and tris

What carries the argument

The parity-odd intrinsic alignment power spectrum in the EFT framework, which encodes sensitivity to the collapsed limit of the parity-odd primordial trispectrum and depends on both the PNG amplitude and bias parameters.

If this is right

  • The IA power spectrum provides constraints on parity-violating PNG that complement those from galaxy four-point correlations and CMB trispectra by accessing different scales and configurations.
  • Once bias parameters are fixed by simulations, IA data from DESI and LSST can tighten limits on the amplitude of parity-violating PNG.
  • Galaxy shapes serve as an independent observable for testing inflationary models that produce parity violation.
  • A new method for generating initial conditions allows forward modeling of the parity-odd trispectrum with enhanced collapsed limit in simulations.

Where Pith is reading between the lines

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

  • Cross-correlations between galaxy shapes and density fields could isolate parity-odd signals more effectively than shapes alone.
  • The framework might extend to testing other forms of early-universe parity violation beyond the specific U(1) model considered.
  • Dedicated shape analyses in future surveys could become standard for mapping symmetries in the primordial universe if the signal strength matches forecasts.

Load-bearing premise

The EFT bias parameters extracted from N-body simulations of dark-matter halos remain valid and unbiased when the parity-odd PNG signal is present at the amplitudes relevant for DESI and LSST observations.

What would settle it

A measurement of the parity-odd IA power spectrum in DESI or LSST data whose amplitude deviates significantly from the prediction using the simulation-calibrated bias parameters and existing PNG limits from four-point or CMB analyses.

Figures

Figures reproduced from arXiv: 2509.08787 by Drew Jamieson, Eiichiro Komatsu, Fabian Schmidt, Toshiki Kurita.

Figure 1
Figure 1. Figure 1: FIG. 1. A diagram of the parity-odd power spectrum sourced [PITH_FULL_IMAGE:figures/full_fig_p009_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Parity-odd power spectra of helicity-1 (left panel) and helicity-2 (right panel), as defined in Eq. ( [PITH_FULL_IMAGE:figures/full_fig_p012_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. A conceptual diagram illustrating why the single-hard limit dominates in the case of a squeezed trispectrum. The red [PITH_FULL_IMAGE:figures/full_fig_p013_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. Definitions of the polar and azimuthal angles [PITH_FULL_IMAGE:figures/full_fig_p015_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. The shape of a tetrahedron is determined by two [PITH_FULL_IMAGE:figures/full_fig_p016_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6. A validation test for our initial conditions, comparing the measurements of the parity-odd trispectrum in the initial [PITH_FULL_IMAGE:figures/full_fig_p018_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7. Comparison between the measured parity-odd power spectra of halo IA for different initial conditions and the corre [PITH_FULL_IMAGE:figures/full_fig_p019_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: FIG. 8. Relations among the measured bias parameters and results of polynomial fitting. The left panel shows the relation [PITH_FULL_IMAGE:figures/full_fig_p019_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: shows the dipole moment (ℓ = 1) of the EB cross-power spectrum measured from the projected shapes of dark matter halos, using the method introduced in Ref. [81]. We omit the octopole moment due to the low signal-to-noise ratio. The solid curve represents the EFT prediction, which is not obtained by directly fitting PEB, but instead derived by projecting the theoretical model from the previous section. Spec… view at source ↗
Figure 10
Figure 10. Figure 10: FIG. 10. Forecasted 1 [PITH_FULL_IMAGE:figures/full_fig_p024_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: FIG. 11. Angular [PITH_FULL_IMAGE:figures/full_fig_p026_11.png] view at source ↗
Figure 12
Figure 12. Figure 12: FIG. 12. Same as Fig [PITH_FULL_IMAGE:figures/full_fig_p027_12.png] view at source ↗
Figure 13
Figure 13. Figure 13: shows the contribution of the two shells to the power spectrum. The dominant contribution arises when one of the wave numbers, q or q ′ , equals k while the other is in the UV regime. This corresponds to the case where the two triangles, sharing the common edge k, consist of one equilateral triangle and one squeezed triangle. In other words, this situation represents the UV limit for one of the momenta, i… view at source ↗
Figure 14
Figure 14. Figure 14: FIG. 14. Contributions from each channel to the parity-odd power spectrum [PITH_FULL_IMAGE:figures/full_fig_p034_14.png] view at source ↗
Figure 15
Figure 15. Figure 15: shows a comparison between the parity-odd trispectrum measured from the initial conditions and the theoretical prediction computed from Eq. (E10). To highlight the structure of the theoretical prediction, we decompose [PITH_FULL_IMAGE:figures/full_fig_p041_15.png] view at source ↗
Figure 16
Figure 16. Figure 16: shows the bias parameters measured with this alternative shape definition, along with the corresponding best-fit curves. The best-fit parameters, assuming the same functional forms as Eqs. (124) and (127), are given by β = 2.61 ± 0.11, α2 = 4.16 ± 0.31, α4 = 14.69 ± 3.55. (F3) While β and α2 remain consistent within 1σ, the best-fit values of α4 differ from those obtained using the reduced inertia tensor … view at source ↗
read the original abstract

We present a comprehensive study of galaxy intrinsic alignment (IA) as a probe of parity-violating primordial non-Gaussianity (PNG). Within the effective field theory (EFT) framework, we show that the parity-odd IA power spectrum is sensitive to the collapsed limit of the parity-odd primordial trispectrum. For a $U(1)$-gauge inflationary model, the IA power spectrum is proportional to the power spectrum of the curvature perturbation, $P_\zeta(k) \propto k^{-3}$. However, the proportionality constants contain not only the PNG amplitude but also undetermined EFT bias parameters. We use $N$-body simulations to determine the bias parameters for dark matter halos. Using these bias parameters, we forecast IA's constraining power, assuming data from the Dark Energy Spectroscopic Instrument (DESI) and the Rubin Observatory Legacy Survey of Space and Time (LSST). We find that the IA power spectrum can improve the current limits on the amplitude of parity-violating PNG derived from galaxy four-point correlation and CMB trispectrum analyses. Moreover, galaxy shapes are complementary to these probes as they are sensitive to different scales and trispectrum configurations. Beyond galaxy shapes, we develop a new method to generate initial conditions for simulations and forward models from the parity-odd trispectrum with an enhanced collapsed limit.

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

1 major / 2 minor

Summary. The manuscript claims that the parity-odd intrinsic alignment (IA) power spectrum of galaxies provides a probe of parity-violating primordial non-Gaussianity (PNG), specifically sensitive to the collapsed limit of the parity-odd primordial trispectrum. Within the EFT framework, for a U(1)-gauge model the IA spectrum is proportional to P_ζ(k) ∝ k^{-3}, with the proportionality constants containing both the PNG amplitude and EFT bias parameters. These bias parameters are calibrated from N-body simulations of dark-matter halos, after which forecasts for DESI and LSST data are presented that claim an improvement over existing limits from galaxy four-point functions and CMB trispectra. A new method for generating initial conditions that incorporate an enhanced collapsed limit of the parity-odd trispectrum is also developed.

Significance. If the bias calibration remains valid, the result would supply a complementary observable sensitive to different scales and trispectrum configurations than four-point or CMB probes, with potential to tighten constraints on parity-violating PNG. The EFT derivation of the proportionality and the new initial-condition generation technique constitute clear technical strengths that could enable future simulation-based tests.

major comments (1)
  1. [simulation calibration and forecasting] Simulation calibration and forecasting section: the bias parameters entering the parity-odd IA power spectrum are extracted from standard N-body simulations that do not include the parity-odd PNG initial conditions. The forecast for improved PNG limits assumes these parameters remain unchanged at the amplitudes relevant for DESI/LSST; this independence is asserted rather than demonstrated and is load-bearing for the central claim of improved constraints.
minor comments (2)
  1. The abstract does not report error bars, covariance, or robustness tests on the fitted EFT bias parameters.
  2. Notation for the collapsed-limit trispectrum configuration could be clarified with an explicit equation reference when first introduced.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their thorough review and constructive feedback on our manuscript. The central concern regarding the simulation calibration of bias parameters and its implications for the forecasts is well taken. We address this point directly below and outline revisions that will clarify the assumptions while preserving the core claims of the work.

read point-by-point responses

  1. Referee: Simulation calibration and forecasting section: the bias parameters entering the parity-odd IA power spectrum are extracted from standard N-body simulations that do not include the parity-odd PNG initial conditions. The forecast for improved PNG limits assumes these parameters remain unchanged at the amplitudes relevant for DESI/LSST; this independence is asserted rather than demonstrated and is load-bearing for the central claim of improved constraints.

    Authors: We agree that the independence of the bias parameters from the PNG amplitude is an important assumption that merits explicit justification. Within the EFT framework, the bias parameters encode the response of halo shapes to the long-wavelength gravitational field and are determined by the nonlinear gravitational evolution and halo formation physics. These are captured accurately by standard N-body simulations. The parity-violating PNG contributes an additional term to the initial conditions that sources the parity-odd IA signal linearly in the PNG amplitude. Corrections to the bias parameters themselves would enter only at quadratic or higher order in the PNG strength. For the small amplitudes relevant to current and forecasted constraints (well below the values that would induce order-one changes in halo properties), these higher-order corrections are negligible. We will add a dedicated paragraph in the revised manuscript (in the simulation calibration and forecasting section) that spells out this perturbative argument, references the order counting in the EFT, and notes that the new initial-condition generation technique developed in the paper enables future direct numerical tests at larger amplitudes. With this clarification, the forecasts remain valid as a demonstration of the complementary constraining power of the IA observable. revision: yes

Circularity Check

0 steps flagged

No significant circularity; derivation relies on independent EFT and external simulation calibration

full rationale

The paper derives within the EFT framework that the parity-odd IA power spectrum is sensitive to the collapsed limit of the parity-odd primordial trispectrum, with the IA spectrum proportional to P_ζ(k) for the U(1) model. The proportionality constants include EFT bias parameters that are calibrated from separate N-body simulations of dark-matter halos; these simulations function as external inputs rather than outputs of the same fit. The subsequent forecasting for DESI and LSST constraints then applies the fixed biases to predict sensitivity, but this does not reduce the central sensitivity relation to a tautology by construction. No self-definitional loops, fitted inputs renamed as predictions, or load-bearing self-citations appear in the provided derivation chain. The new initial-conditions method is developed independently. The chain remains self-contained against external benchmarks, with the validity of biases under PNG treated as an assumption rather than a circular reduction.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

The central claim rests on the validity of the EFT framework for IA in the presence of parity-odd PNG and on the assumption that N-body simulations can calibrate the bias parameters without the PNG signal contaminating the calibration at the relevant amplitudes.

free parameters (1)
  • EFT bias parameters for IA
    Undetermined coefficients in the EFT expansion that are fitted from N-body simulations of dark-matter halos.
axioms (1)
  • domain assumption Effective field theory framework applies to galaxy intrinsic alignments in the presence of parity-violating PNG
    Invoked to relate the IA power spectrum to the collapsed trispectrum limit.

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Forward citations

Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

  1. How to augment cosmic shear measurements with radio polarimetry of galaxies?

    astro-ph.CO 2026-05 unverdicted novelty 7.0

    A Gaussian statistical model of galaxy shapes and radio polarizations yields unbiased, minimum-variance estimators for cosmic shear, intrinsic alignment, and line-of-sight rotation that are accurate to first order.

  2. Testing parity with composite-field spectra of BOSS and DESI luminous red galaxies

    astro-ph.CO 2026-04 accept novelty 7.0

    No evidence for cosmological parity violation is found in the first kurto-spectrum analysis of BOSS DR12 and DESI DR1 luminous red galaxies.

Reference graph

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