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A new redshift-fluctuation observable tightens the 2D bound on primordial non-Gaussianity to f_NL = -3 ± 14.

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2026-08-03 08:23 UTC pith:PJLRVX2U

load-bearing objection First real-data ARF measurement of fNL, but the ~25% gain hinges on ℓ>200 scales where halofit is doing unrecognized work; solid enough to referee, weak enough to force a rewrite. the 3 major comments →

arxiv 2601.16948 v2 pith:PJLRVX2U submitted 2026-01-23 astro-ph.CO

Improving constraints on primordial non-Gaussianity from Quaia with a new cosmological observable: angular redshift fluctuations

Jos\'e Ram\'on Bermejo-Climent , Carlos Hern\'andez-Monteagudo , Alba Crespo-P\'erez , Jorge Martin Camalich , David Alonso , Giulio Fabbian , Kate Storey-Fisher This is my paper
classification astro-ph.CO PACS 98.80.Es98.80.-k
keywords primordial non-Gaussianityangular redshift fluctuationsscale-dependent biasquasar catalogCMB lensing cross-correlationangular power spectraQuaiaf_NL
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.

This paper argues that angular redshift fluctuations—the small, direction-dependent variations in the average redshift of quasars across the sky—carry independent information about galaxy bias, and therefore about the scale-dependent bias imprinted by local primordial non-Gaussianity. It measures these fluctuations in the Quaia quasar catalog, combines them with the projected quasar density and CMB lensing cross-correlations, and obtains f_NL = -3 ± 14 at 68% confidence under the universality relation. This is about 25% tighter than the previous Quaia density-plus-lensing measurement and, the authors argue, the best f_NL constraint yet obtained from projected two-dimensional summary statistics. The paper also reports internal tensions between the bias parameters inferred from different observables, which it attributes to the ARF kernel's stronger sensitivity to nonlinear scales, and shows the headline f_NL is stable when separate effective biases are fitted.

Core claim

The central claim is that the angular redshift fluctuation (ARF) two-point spectra, C_zz, and their cross-correlation with CMB lensing, C_κz, are not just a theoretical curiosity but a practical cosmological observable for f_NL. Analyzing roughly 1.3 million Quaia quasars split into two redshift bins, the authors measure f_NL = -43 ± 50 from ARF alone (autocorrelation plus lensing cross-correlation) and f_NL = -3 ± 14 when combining ARF with the quasar density and lensing spectra. The ARF term drives most of the improvement, matching mock forecasts that predict about a 30% tightening. The paper stresses that the baseline result assumes the universality relation (p = 1) for the quasar bias re

What carries the argument

The central object is the ARF field, defined as δz(n̂) = Σ_i (z_i − z̄) w_i / ⟨Σ_i w_i⟩, which turns redshift into a 2D map whose harmonic kernel replaces the density window W(z) with W(z)(z − z̄). This makes ARF a radial gradient of the density field: it is sensitive to galaxy bias and to f_NL through the standard scale-dependent bias correction Δb(k,z) = 2(b_g − p) f_NL δ_crit / α(k), implemented in a modified Boltzmann solver with a nonlinear power-spectrum prescription. The ARF kernel has higher amplitude at high k than the density kernel and a sign flip at k ~ 0.07 Mpc⁻¹, which is why it carries complementary information but also why nonlinear modeling is the delicate part of the analys

Load-bearing premise

The analysis assumes that one linear bias parametrization, b(z) = b0(1+z)^α / D(z), describes both the density and ARF fields and that the universality relation (p = 1) sets the quasar response to f_NL, while the data show a ~2σ mismatch between bias parameters from C_zz and C_κz and the ARF signal is weighted toward nonlinear scales where the model is least secure.

What would settle it

Compute the same five power spectra from a spectroscopic quasar sample with true redshifts instead of photo-zs; if the C_zz and C_κz bias parameters remain ~2σ apart and the joint f_NL shifts by more than about 10, the shared-bias model is absorbing nonlinear ARF physics rather than measuring primordial non-Gaussianity. Alternatively, replace the nonlinear power-spectrum prescription in the mocks and check whether the recovered f_NL moves by more than the quoted error.

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

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If this is right

  • Adding ARF to 2D clustering analyses improves f_NL error bars by about 25% with current data and about 30% in mocks, without adding new sky area.
  • The combination of density, ARF, and CMB lensing gives a 68% interval f_NL = -3 ± 14, consistent with Gaussian initial conditions and with CMB bispectrum constraints.
  • ARF autocorrelation plus lensing cross-correlation alone already constrains f_NL to σ ≈ 50, so ARF can stand as an independent probe for all-sky quasar catalogs.
  • Future photometric surveys can add ARF to standard harmonic-space analyses, and spectroscopic surveys with much smaller redshift uncertainties should yield an even cleaner ARF signal.
  • Because the ARF kernel emphasizes nonlinear scales, improving nonlinear modeling is the main step needed to exploit ARF at higher multipoles and to reduce the reported bias tensions.

Where Pith is reading between the lines

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

  • Since ARF is essentially a radial derivative of the density field, it may be even more sensitive than projected clustering to the redshift evolution of bias within a bin; simulations that vary b(z) inside the shell could isolate this effect.
  • The paper excludes the density–ARF cross-spectrum C_gz because it deviates from the model even at high multipoles; if those systematics can be modeled, including C_gz could add further constraining power.
  • The reported ~2σ mismatch between bias parameters from C_zz and C_κz could serve as a diagnostic of nonlinear biasing: measuring ARF in N-body mocks with known bias would show whether an effective-bias parametrization absorbs the nonlinear signal or shifts f_NL.
  • If the tighter constraint survives in spectroscopic samples with negligible photo-z error, ARF could become a standard 2D complement to 3D power-spectrum analyses, offering competitive f_NL limits without full redshift-space modeling.

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

3 major / 4 minor

Summary. The paper presents the first application of angular redshift fluctuations (ARF) to constrain local primordial non-Gaussianity from real data, using the Quaia quasar catalog and Planck PR4 CMB lensing. The authors measure angular power spectra of galaxy density, ARF, and their cross-correlations with CMB lensing, model them with the ARFCAMB code including scale-dependent bias and halofit nonlinear corrections, and fit f_NL together with bias parameters b0 and alpha. The baseline joint analysis yields f_NL = -3 ± 14 (68% CL), which they report as a ~25% improvement over the previous Quaia-based density+lensing constraint and as the second-tightest LSS two-point constraint to date. The paper includes extensive robustness tests: scale cuts validated with systematics deprojection, independent bias parameters for density vs ARF, alternative bias evolution models, a p=1.6 universality response, 1000 mocks for covariance, and a filtered analysis removing 6 outlier points.

Significance. If the result holds, this is an interesting and timely demonstration that ARF can add constraining power to standard 2D clustering analyses. The first-real-data use of ARF for f_NL, the public ARFCAMB code, and the transparent treatment of systematics are strengths. However, the central claim of a ~25% improvement is conditional on the treatment of nonlinear scales in the ARF kernel, which the paper itself identifies as an open modeling issue. The paper is honest about the poor global chi-square and the ℓ_max sensitivity, but those caveats directly affect the headline constraint. The value is therefore real but the analysis needs additional validation before the precision claim can be taken at face value.

major comments (3)
  1. [§5, Table 4 and Fig. 7] The headline improvement is not robust to the maximum multipole choice for ARF. Table 4 shows that for C_zz^ℓ + C_κz^ℓ, reducing ℓ_max from 300/240 to 200 changes f_NL from -49+53-36 to 95+117-89, flipping the sign and degrading the constraint. This demonstrates that the ARF constraining power is concentrated at ℓ > 200, where Fig. 7 shows the ARF transfer function changes sign near k ~ 0.07 h/Mpc and where the model uses halofit, calibrated for the matter power spectrum rather than for the ARF kernel. The robustness test with independent bias parameters for density and ARF (Table 5) keeps the same halofit predictions and the same ℓ_max, so it only marginalizes over an amplitude/slope that cannot absorb a scale-dependent nonlinear error. The mocks in Appendix B use the same halofit plus the power-law excess, so they validate the pipeline, not the nonlinear model. I request (i) the joint
  2. [§5, Tables 2 and 4] The baseline C_zz^ℓ + C_κz^ℓ values in Table 4 (-49+53-36, b0 = 0.63, alpha = 0.60) do not match the same nominal configuration in Table 2 (-43+50-44, b0 = 0.67, alpha = 0.55). This is the control row against which the ℓ_max = 200 result is compared, so the discrepancy undermines the controlled comparison. The authors should reconcile the two runs or explicitly report the MCMC sampling noise and any differences in ℓ_min, binning, or chain settings.
  3. [§5 and Appendix A] The global fit has chi^2/dof = 338/217, corresponding to a very low PTE. The paper improves it to 236/211 by removing six points that are > 2.5 sigma from the best fit. This is a post-hoc, data-dependent outlier cut rather than a pre-specified robust statistic. Although the central value is stable, the statistical weight of the measurement is weaker than the nominal error bars suggest. The origin of the > 3 sigma point at ℓ ~ 12 in C_κz^ℓ (Fig. 4) should be investigated and discussed. Please present the posterior with and without the cut and consider reporting a goodness-of-fit measure that does not rely on post-hoc outlier removal.
minor comments (4)
  1. [§3.1] The statement that ~62% of sources satisfy |Δz/(1+z)| < 0.01 appears inconsistent with the quoted photo-z uncertainty σ_z ~ 0.06(1+z); please check whether this is a typo or refers to a different subsample.
  2. [§4.3, Eq. (20)] The power-law excess correction is applied only when generating mocks, not in the likelihood model. Since the fitted ℓ0 and β imply order-unity corrections at multipoles just above the adopted ℓ_min for some auto-spectra, the authors should clarify why this residual excess does not bias the best-fit parameters, or include a corresponding term in the theory model.
  3. [References] The CAMB references appear in inconsistent forms (Lewis & Challinor 2011 and Challinor & Lewis 2011a,b); unify the citation style.
  4. [Abstract and §6] The headline 'second tightest LSS two-point constraint' should be explicitly qualified as holding for p = 1 (universality relation), since the p = 1.6 test gives f_NL = 2+20-21 with substantially larger error bars.

Circularity Check

0 steps flagged

No significant circularity: f_NL enters through the standard scale-dependent bias formula and is compared directly to the Quaia data; self-citations provide the ARF formalism/code but are not load-bearing.

full rationale

The f_NL measurement is not circular. f_NL enters the theory through the standard scale-dependent bias expression, Eq. (2)-(3), and the ARF/density/lensing kernels are computed from the same bias model via Eqs. (10)-(15) using the ARFCAMB code. The likelihood in Eq. (21) compares the measured Quaia power spectra directly to this model, so the reported f_NL is not defined in terms of a fitted parameter that already contains f_NL. The mocks are used only for covariance estimation and pipeline validation; they are not used to set the f_NL value. The low-multipole excess correction in Eq. (20) is fitted to the data and injected into mocks, but it is not part of the theory model in the likelihood, so it cannot by itself force the f_NL result. The self-citations to Hernández-Monteagudo et al. (2020a,b) and Lima-Hernández et al. (2022) introduce the ARF observable and its code, but the essential kernel is re-defined in Eqs. (12)-(15), and no uniqueness theorem or exclusive self-citation is used to forbid alternatives. The robustness tests, including separate bias parameters for density and ARF, further show that the f_NL constraint does not reduce to the shared-bias assumption. The main limitations—ℓ_max sensitivity (Table 4), the ARF sign flip at k~0.07 Mpc^-1 (Fig. 7), and the need for improved nonlinear ARF modeling—are correctness/systematics concerns, not circularity. Overall, the derivation is self-contained for the central claim, with only minor self-citation heritage that is not load-bearing.

Axiom & Free-Parameter Ledger

4 free parameters · 5 axioms · 1 invented entities

The paper's central claim rests on (i) the p=1 universality assumption for f_NL interpretation, (ii) an ARF kernel model that uses the same linear bias as density, (iii) a Gaussian photo-z approximation with a single σ_z, and (iv) halofit for nonlinear scales in a regime where the ARF kernel is shown to be sensitive. The mock covariance uses a phenomenological excess-power fit, which is a data-informed free parameter.

free parameters (4)
  • p (universality response parameter) = p=1 baseline; p=1.6 test
    Eq. 2: Δb = 2(bg - p) f_NL δcrit/α(k). p=1 is assumed as baseline; the p=1.6 assumption changes the result to f_NL = 2+20-21, nearly doubling the error bar. Thus the headline number is tied to this parameter.
  • b0 and α (bias evolution parameters) = b0=0.83±0.06, α=0.37±0.08 (baseline)
    Eq. 22: b(z) = b0/D(z)(1+z)^α. Fitted in the MCMC jointly with f_NL for density and ARF.
  • ℓ0 and β (excess power parameters for mocks) = ℓ0 ∈ {5,...,32}, β ∈ {1.19,...,3.59} (Table 1)
    Eq. 20: C_ℓ,measured ≈ C_ℓ,theory [1 + (ℓ0/ℓ)^β]. Fit to the data to generate the mock covariance. This injects observed excess power into the error model.
  • A1 and A2 (per-bin bias amplitudes in P24/L17 tests) = A1≈1.05, A2≈1.24 (P24); A2≈0.97 (L17)
    Alternative bias modeling in Table 5, only for robustness checks.
axioms (5)
  • domain assumption Universality relation for the halo mass function (bg - p) in the scale-dependent bias formula (Slosar et al. 2008)
    Eq. 2: the f_NL signal is proportional to (bg - p). The paper notes Barreira (2020, 2022) argue only b_phi f_NL is actually constrained; p=1 is a strong model assumption.
  • domain assumption Quaia photo-z errors are Gaussian with σz≈0.06(1+z)
    Section 3.1 and 4.2: the ARF theory needs the photo-z PDF; the paper uses a single average value rather than per-QSO uncertainties.
  • domain assumption The ARF field follows the linear-bias kernel W(z, z̄) = W(z)(z - z̄) with the same bias as the density field.
    Eq. 15 and Section 4.2: the ARF kernel is computed with the same bias evolution as density. The data show this assumption is internally inconsistent at ~2σ, so the ARF kernel is the fragile part.
  • domain assumption GR corrections to number counts are negligible for f_NL when magnification bias s≈0.4.
    Section 2.2: they cite Alonso et al. 2015 and Guedezounme et al. 2025; s≈0.4 is the value at which magnification vanishes, but it is a measured value.
  • domain assumption halofit is valid for ARF at ℓmax=240-300
    Section 4.2 and Fig. 7: the ARF transfer function has a sign flip at k≈0.07 Mpc^-1 and gains sensitivity at high k, yet halofit was used without a dedicated ARF nonlinear model. The ℓmax=200 test shows ARF bias is not robust.
invented entities (1)
  • None beyond the already-published ARF observable no independent evidence
    purpose: No new particles, forces, or dimensions.
    The ARF field was introduced in Hernández-Monteagudo et al. 2020a,b. This paper applies it to f_NL.

pith-pipeline@v1.3.0-alltime-deepseek · 20363 in / 8806 out tokens · 69700 ms · 2026-08-03T08:23:51.316289+00:00 · methodology

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Cite this review

Pith. "Pith review of Improving constraints on primordial non-Gaussianity from Quaia with a new cosmological observable: angular redshift fluctuations." pith.science (2026). https://pith.science/paper/PJLRVX2U

@misc{pith2026260116948,
  author       = {Pith},
  title        = {Pith review of: Improving constraints on primordial non-Gaussianity from Quaia with a new cosmological observable: angular redshift fluctuations},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/PJLRVX2U}},
  note         = {Machine review of arXiv:2601.16948}
}
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read the original abstract

Angular redshift fluctuations (ARF) are a new cosmological observable, recently proposed in the literature. It measures the 2D angular deviations of the average redshift of a given matter tracer under an input redshift shell. Since it depends on the galaxy bias, it can be used to constrain primordial non-Gaussianity through the scale-dependent bias effect. We analyze a sample of quasars built upon the Gaia satellite and unWISE data, Quaia, to measure the local non-Gaussianity parameter $f_{\rm NL}$. This sample is particularly suitable for measuring $f_{\rm NL}$ due to its large volume coverage. We measure the ARF power spectra from the Quaia catalog and combine their information with the 2D (projected) galaxy density and their cross-correlation with the $Planck$ PR4 CMB lensing maps lensing to jointly constrain $f_{\rm NL}$. Assuming the universality relation, we measure $f_{\rm NL} = -3 \pm 14$ at 68% confidence level by combining Quaia quasar angular density and ARF with the CMB lensing. This result is the second tightest constraint on $f_{\rm NL}$ using LSS two-point statistics to date and the best measurement achieved using two-point projected summary statistics, improving by $\sim$25% the previous measurement from Quaia. Our results motivate the inclusion of ARF as an additional cosmological observable in future 2D analysis of upcoming datasets from large surveys.

Figures

Figures reproduced from arXiv: 2601.16948 by Alba Crespo-P\'erez, Carlos Hern\'andez-Monteagudo, David Alonso, Giulio Fabbian, Jorge Martin Camalich, Jos\'e Ram\'on Bermejo-Climent, Kate Storey-Fisher.

Figure 1
Figure 1. Figure 1: Normalized redshift distribution of the Quaia QSO sample ana￾lyzed in this paper. The black dashed line corresponds to the full sam￾ple, while the blue and red lines correspond to the low and high redshift bins, respectively. 3.1. The Quaia QSO catalog Quaia (Storey-Fisher et al. 2024) is a QSO catalog constructed from the Gaia DR3 quasar candidates sample and unWISE (Schlafly et al. 2019) infrared data. I… view at source ↗
Figure 2
Figure 2. Figure 2: Upper panels: normalized masks from the Quaia selection functions applied in our analysis after applying a 0.5 threshold for the low-z and high-z redshift bins. Middle panels: Quaia density maps for the low-z and high-z redshift bins. Lower panels: Quaia ARF maps for the low-z and high-z redshift bins. The density and ARF maps are represented with a 1 degree beam smoothing. correlations with the Planck len… view at source ↗
Figure 3
Figure 3. Figure 3: Measured angular power spectra of the Quaia density and ARF autocorrelations for the low redshift (left panel) and high redshift (right panel) bins. The dots represent the binned angular power spectra with errorbars, the dashed lines the theoretical model with fNL = 0, and the dotted lines the same model after the parametrization of the measured excess of power. 10 1 10 2 1.0 0.5 0.0 0.5 1.0 1.5 C X 1e 6 L… view at source ↗
Figure 4
Figure 4. Figure 4: Measured angular power spectra of the Quaia density and ARF cross-correlations with the Planck CMB lensing for the low redshift (left panel) and high redshift (right panel) bins. The dots represent the binned angular power spectra with errorbars and the dashed lines the theoretical fiducial model with fNL = 0. 4.4. Systematics deprojection and scale cuts We perform systematics deprojection tests on the dat… view at source ↗
Figure 5
Figure 5. Figure 5: Comparison of the shift on the ℓ = 6 and ℓ = 10 angular power spectra of the Quaia high-z sample after applying systematics deprojection to the mocks and data for C zz ℓ (left panels) and C κz ℓ (right panels), used to validate the scale cuts in our analysis. The blue bars represent the distribution of the shift on the 1000 mock realizations and the red lines the shift found in real data. pixel, but also o… view at source ↗
Figure 6
Figure 6. Figure 6: 1σ and 2σ confidence ellipses for fNL and the b0 and α bias parameters measured from Quaia and Planck data, assuming the same bias parameterization for density and ARF (baseline case). The grey contours represent the constraints from ARF plus their CMB lensing cross-correlation, the red contours represent the density plus their CMB lensing cross-correlation, and the blue contours the combination of den￾sit… view at source ↗
Figure 7
Figure 7. Figure 7: Transfer function for the density (blue line) and ARF (orange line) fields obtained assuming the high-z Quaia sample for ℓ = 300, as a function of the k scale. with ℓmax; instead, the bias parameters measured from C zz ℓ + C κz ℓ vary when adopting a lower ℓmax and the tension between ob￾servables is alleviated. This suggests that the discrepancy on the bias measurement is related to the higher impact of s… view at source ↗
Figure 8
Figure 8. Figure 8: 1σ and 2σ confidence ellipses for fNL and the b0 and α bias parameters measured from Quaia and Planck data, assuming two independent bias parameterizations for density and ARF. The grey contours represent the constraints from ARF plus their CMB lensing cross-correlation, the red contours represent the density plus their CMB lensing cross-correlation, and the blue contours the combination of density, ARF an… view at source ↗

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Forward citations

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Works this paper leans on

2 extracted references · 1 linked inside Pith · cited by 2 Pith papers

  1. [1]

    G., Avila, S., Gonzalez-Perez, V ., et al

    Adame, A. G., Avila, S., Gonzalez-Perez, V ., et al. 2024, Astron. Astrophys., 689, A69 Afshordi, N. & Tolley, A. J. 2008, Physical Review D, 78 Akrami, Y ., Andersen, K. J., Ashdown, M., et al. 2020, Astron. Astrophys., A42 Alonso, D., Bull, P., Ferreira, P. G., Maartens, R., & Santos, M. G. 2015, The Astrophysical Journal, 814, 145 Alonso, D., Fabbian, ...

    2024

  2. [3]

    Low-z" sample,ℓ=30.5 for theC κg ℓ “High-z

    Constraints on Inflation from Galaxy Power Spectra & Bispectra Dalal, N., Doré, O., Huterer, D., & Shirokov, A. 2008, Phys. Rev. D, 77, 123514 D’Amico, G., Lewandowski, M., Senatore, L., & Zhang, P. 2023, Limits on pri- mordial non-Gaussianities from BOSS galaxy-clustering data Fabbian, G., Alonso, D., Storey-Fisher, K., & Cornish, T. 2025, Constraints on...

    Pith/arXiv arXiv 2008