Joint Geometric and Dynamical Constraints on Cosmology from Anisotropies in Galaxy Intrinsic-Alignment Correlations

Teppei Okumura

REVIEW 4 major objections 6 minor 97 references

Joint Geometric and Dynamical Constraints on Cosmology from Anisotropies in Galaxy Intrinsic-Alignment Correlations

T0 review · 4 major / 6 minor · reviewed 2026-08-10 · deepseek-v4-flash

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Pith's one-line read Joint use of anisotropic galaxy intrinsic alignments with clustering gives the first IA-based geometric and dynamical constraints, cutting fractional errors on growth and distance by up to 32%.

desk verdict First real AP-from-IA measurement, honestly presented; the headline improvement fractions are scale-cut dependent and not yet robust, but the qualitative result deserves a serious referee. read the letter →

arxiv 2608.06927 v1 pith:HBQYZKPZ submitted 2026-08-07 astro-ph.CO astro-ph.GAgr-qc

Teppei Okumura This is my paper · ORCID

classification astro-ph.COastro-ph.GAgr-qc

keywords galaxyintrinsicalignmentredshift-spacedistortionsAlcock-PaczynskieffectbaryonacousticoscillationsellipticitycorrelationsBOSSsurveyDESILegacyImagingSurveysassociatedLegendremultipoles

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

This paper tries to establish that the anisotropic, spin-dependent correlations of galaxy intrinsic alignments, not just galaxy positions, carry usable cosmological information about both cosmic expansion and structure growth. Using BOSS galaxy positions with shape measurements from DESI imaging, it measures the GI and II multipoles and models them jointly with galaxy clustering under redshift-space and Alcock-Paczynski distortions. Adding these IA statistics reduces the fractional uncertainties on f sigma_8, D_A, and H by 32%, 18%, and 29%, whereas an RSD-only version improves f sigma_8 by only 6%, showing that the gain is geometric. The paper argues this makes anisotropic galaxy shapes a new source of geometric and dynamical information for spectroscopic cosmology.

What carries the argument

The central object is the associated Legendre multipole expansion of the GI and II correlation functions (Theta^m_l with m = 2 for GI and m = 4 for II), which captures their spin-dependent anisotropy. The model combines the nonlinear alignment (NLA) assumption, that intrinsic ellipticity is proportional to the tidal field, with a Gaussian Finger-of-God damping and the standard AP rescaling applied to the IA power spectra. This lets the same anisotropic multipoles that carry RSD growth information also encode the angular-diameter distance and Hubble rate through the shape of the BAO feature.

What would settle it

Repeat the joint fit with r_min = 40 $h^{-1}$ Mpc; the paper itself finds the w0 gain vanishes there, so if the f sigma_8, alpha_perp, and alpha_parallel improvements also drop toward the RSD-only 6% level, the central result is driven by small-scale modeling. A stronger test: run the identical pipeline on mock catalogs with known cosmology and check that the recovered parameters stay unbiased and the reported error gains are reproduced.

Watch

Extended reading notes

Core claim

The paper claims that anisotropic galaxy intrinsic-alignment correlations, measured through associated Legendre multipoles of the GI and II statistics, are a new cosmological observable carrying both geometric and dynamical information. In a joint RSD+AP fit to BOSS galaxies with DESI shapes at 0.43 < z < 0.7, adding IA to galaxy clustering yields f sigma_8 = 0.468 +/- 0.024, alpha_perp = 1.004 +/- 0.011, and alpha_parallel = 1.031 +/- 0.016, cutting their fractional uncertainties by 32%, 18%, and 29% relative to clustering alone. The author argues the gain is genuinely geometric because an RSD-only version improves f sigma_8 by only 6%. The paper further claims that mapping these constraints to flat w0CDM tightens Omega_m, H0, and w0, while cautioning that the w0 improvement depends on the minimum scale included and should not be read as evidence against Lambda CDM.

Load-bearing premise

The load-bearing premise is that the nonlinear alignment model with Gaussian Finger-of-God damping accurately describes the GI and II multipoles down to r_min = 10 $h^{-1}$ Mpc, and that the same Alcock-Paczynski transformation applies to IA spectra; if small-scale nonlinear IA modeling is wrong, the reported improvements and the w0 preference could be artifacts.

Editorial extensions

If this is right

Adding GI and II statistics to galaxy clustering tightens f sigma_8, alpha_perp, and alpha_parallel by 32%, 18%, and 29%.
Because the RSD-only gain is only 6%, the improvement is geometric: IA anisotropies carry Alcock-Paczynski information.
The GI correlation shows the expected BAO feature, so IA provides an independent BAO-based distance probe.
Mapping to flat w0CDM tightens Omega_m by 33% and H0 by 27%, and reduces the absolute w0 uncertainty by about 13%.
The w0 > -1 preference and much of the w0 gain disappear at r_min >= 40 h^-1 Mpc, so small scales drive both the gain and the shift.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

If the small-scale NLA model is validated, this opens multi-bin full-shape IA analyses where broadband power, not just the BAO peak, contributes to geometry and growth constraints.
The scale-cut sensitivity suggests a decisive near-term test: calibrate the NLA model on high-resolution simulations before trusting IA multipoles at r < 40 h^-1 Mpc.
The same anisotropic IA statistics could be cross-correlated with cosmic shear or with other tracers to separate tidal-alignment physics from cosmology.
Larger imaging-plus-spectroscopic samples should reproduce the 32/18/29% gains at higher significance if the model is correct.

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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Desk Editor's Note

read the letter

Okumura has done something genuinely new: measured Alcock–Paczynski information from galaxy intrinsic-alignment anisotropies, not just the usual RSD. On data, this is the first time. He uses BOSS galaxies with DESI shapes, expands the GI and II correlations in associated Legendre multipoles, and fits them jointly with clustering over scales including BAO. The controls are the right ones. The RSD-only analysis (Appendix B) shows the fσ8 gain from IA is only 6% when AP is fixed, and the r_min scan (Appendix A) shows the extra constraining power comes from small scales. That combination supports the claim that the geometric information is real, even if the exact size of the gain is uncertain.

Soft spots, in proportion. The headline numbers—32%, 18%, 29% fractional-uncertainty reductions—come from the fiducial r_min = 10 h^-1 Mpc fit. At r_min = 40 h^-1 Mpc they fall to roughly 13%, 6%, 16%, and the w0 improvement essentially disappears. The paper says it cannot tell a modeling systematic from a statistical fluctuation; that is the honest reading. The NLA model with Gaussian FoG damping is trusted below ~40 h^-1 Mpc without mock or simulation validation, and the jackknife covariance is acknowledged to be not unbiased. So the specific improvement fractions in the abstract are provisional. What survives is qualitative: some tightening of fσ8 and α∥ persists at r_min = 40, and the RSD-only control rules out the alternative explanation that the better shape catalog alone is doing the work. I read the w0 shift toward > -1 as a scale-cut artifact, and the paper says the same.

The formalism—associated Legendre multipoles, the AP transformation of IA spectra, the NLA model—is drawn from his own prior work and is coherent; the math is not the weak point. Pipeline details like covariance estimation, shape cross-matching, and the likelihood cannot be independently reproduced from the preprint. That is normal for a first measurement, but it means the quantitative claims should be treated as provisional until mocks validate the covariance and the IA model. The citation pattern is fine: heavy self-citation, but to the papers that built this model, which is appropriate. No obvious missing references.

Who gets value: the LSS and IA community, and DESI/PFS/Euclid planners interested in whether shapes can complement clustering for full-shape analyses. I would cite it as the first AP-from-IA measurement, and I would bring it to reading group. It deserves a serious referee. The referee brief should require mock-based validation of the covariance and IA model, and a presentation that gives the r_min = 40 numbers the same prominence as the fiducial ones.

Referee Report

4 major / 6 minor

Summary. The paper measures anisotropic galaxy density–intrinsic ellipticity (GI) and intrinsic ellipticity–ellipticity (II) correlations for BOSS galaxies using DESI Legacy Imaging shapes, decomposes them into associated Legendre multipoles, and jointly fits them with the galaxy clustering multipoles to constrain the growth rate fσ8, the angular-diameter distance parameter α⊥ = DA/DA_fid, and the Hubble parameter α∥ = H/H_fid through redshift-space and Alcock–Paczynski distortions. The fiducial analysis over 10–140 h−1 Mpc reports that adding the IA statistics reduces the fractional uncertainties on fσ8, α⊥, and α∥ by 32%, 18%, and 29%, respectively, relative to clustering alone. The paper also maps these constraints to a flat w0CDM model and finds improved Ωm and H0 constraints, while the w0 constraint is explicitly shown to be sensitive to the minimum fitting scale. Appendices provide scale-cut dependence and an RSD-only comparison that shows only a 6% improvement in fσ8 when the AP parameters are fixed.

Significance. If the central claims are upheld, this would be the first demonstration that anisotropic galaxy intrinsic-alignment correlations carry both geometric (AP) and dynamical (RSD) cosmological information, complementing standard galaxy clustering. The paper is commendably transparent: it reports the scale dependence of the improvements, honestly states that the w0 preference for w0 > −1 disappears at larger r_min and is not interpreted as evidence against ΛCDM, and isolates the AP contribution by contrasting the 32% improvement with the 6% RSD-only improvement. These strengths are substantial. However, the quantitative headline numbers rest on small scales (r_min = 10 h−1 Mpc) where the nonlinear alignment model is unvalidated, and the covariance is jackknife-only with no mock-based verification. The qualitative claim that IA anisotropies add geometric information is plausible and partially supported by the persistence of some improvement at r_min = 40 h−1 Mpc, but the specific improvement fractions in the abstract and Table I are not yet robust.

major comments (4)

[Table I and Appendix A (Fig. 4)] The advertised reductions of 32%, 18%, and 29% in the fractional uncertainties of fσ8, α⊥, and α∥ are obtained at the fiducial r_min = 10 h−1 Mpc. Appendix A shows that these improvements drop to roughly 13%, 6%, and 16% when r_min = 40 h−1 Mpc, and the text states that the analysis cannot distinguish a modeling systematic from a statistical fluctuation. Since the NLA model has not been validated on these small scales, the quantitative headline numbers are scale-dependent and potentially inflated. I recommend either validating the small-scale model (e.g., with mocks or N-body-based IA catalogs) or moving the conservative r_min ≥ 40 results to the headline claims.
[Covariance estimation paragraph in 'Measurements of IA correlation functions'] The error bars and all uncertainty improvements depend entirely on the jackknife covariance matrix, which the paper acknowledges is not unbiased. No mock-based validation of this covariance is presented, and the number of jackknife regions or the effective rank of the 117×117 covariance matrix is not reported. Because the central claim is about uncertainty reduction, the covariance must be verified, at least with approximate mocks (e.g., log-normal realizations) or by comparing to an analytic covariance. Please add this validation and report the jackknife configuration.
[Appendix B vs. main analysis in 'Constraints on growth and expansion rates'] The comparison that isolates the AP contribution is confounded by different analysis choices. The main joint analysis uses linearly binned correlation functions over 10 ≤ r ≤ 140 h−1 Mpc, while the RSD-only analysis in Appendix B uses logarithmically binned functions over 10 ≤ r ≤ 100 h−1 Mpc. The claim that 'the substantial gain in the joint analysis therefore arises from the geometric information' would be cleaner if the RSD-only test used the same linear binning and r_max = 140 h−1 Mpc. Please repeat the RSD-only analysis with the same binning and fitting range to ensure the 6% vs. 32% contrast is not partly due to these differences.
[Modeling section, Eqs. (5), (9), (10), and (11)] The NLA model with a Gaussian Finger-of-God damping is assumed to describe the GI and II multipoles down to 10 h−1 Mpc, and the same AP transformation as for galaxy density is applied to the IA spectra. The new multipoles (m = 2 for GI and m = 4 for II) have not been tested against simulations or higher-order perturbation theory. Given that the paper itself flags the possibility of a modeling systematic, a simulation-based validation of the IA model (e.g., with N-body catalogs that include intrinsic alignments) is necessary to support the small-scale information driving the headline improvements.

minor comments (6)

[Table I] The 5% improvement quoted for w0 in the flat w0CDM block is a fractional-error improvement, but the central value shifts toward smaller |w0|; the text explains this and quotes a 13% absolute-uncertainty improvement. A footnote in the table would prevent misinterpretation.
[Section 'Galaxy density and shape samples'] The abbreviation 'CMASSLOWZTOT' is used without definition; please state that it denotes the combined CMASS and LOWZ constant-mass sample from BOSS DR12.
[Eq. (2)] The density fluctuation δ_g(x) is used in the definition of ξ_X before it is defined in the following sentence; move the definition earlier or add a parenthetical.
[Eq. (4)] The factor of 2 in the expansion over 0 ≤ μ_r ≤ 1 is not explained; state that it accounts for the symmetry of the correlation function under μ → −μ.
[Introduction and Eq. (12)] The phrase 'spin-dependent angular structure' is used but the spin index m is not defined; a sentence connecting m in Θ_m^ℓ to the spin of the correlation would improve readability.
[Fig. 2] The axis labels in the contour plot are very small and the panel titles are cramped; increasing the font size or using separate panels would improve legibility.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the reported constraints are fits to external BOSS+DESI data; the author's prior IA-modeling papers are used as model inputs, not as self-fulfilling evidence.

full rationale

The paper's central quantities (f sigma8, DA, H, and the derived w0, Omega_m, H0) are estimated by fitting a six-parameter model to public BOSS spectroscopy and DESI Legacy shape catalogs, not derived from the model by construction. The claimed 32%, 18%, and 29% improvements are comparisons of posterior widths on the same data vector with and without the GI/II multipoles, so they are empirical statements about information content rather than predictions that reduce to their inputs. The NLA model of Eqs. (9)-(10) and the associated-Legendre expansion are taken from the author's prior papers (Refs. [36], [39], [49]), but these are model and basis choices applied to external data; they do not encode the recovered parameter values, and the paper explicitly treats them as assumptions, noting in Appendix A that it 'cannot distinguish a modeling systematic from a statistical fluctuation.' The RSD-only control analysis in Appendix B provides an internal check that the improvements are not automatically produced by the formalism. Self-citations are numerous but none imports a uniqueness theorem or a fitted parameter under a new name, so there is no load-bearing circular step.

Assumptions & free parameters 6 free parameters · 7 assumptions · 0 invented entities

The analysis uses standard cosmological probes and public data; no new particles, forces, or fields are introduced. The parameters listed above are fitted amplitudes and geometry, and the axioms are the phenomenological modeling choices on which the constraints rest. The main burden is the validity of the NLA plus FoG model at small scales and the unvalidated jackknife covariance.

free parameters (6)

fσ8 (growth rate times amplitude) = 0.468 ± 0.024 (GG+IA); 0.456 ± 0.035 (GG-only)
Primary cosmological target, jointly fitted to GG and IA multipoles; not a nuisance but a fitted free parameter.
α⊥ = D_A / D_A_fid = 1.004 ± 0.011 (GG+IA)
AP geometric parameter, free in the RSD+AP fit.
α∥ = H / H_fid = 1.031 ± 0.016 (GG+IA)
AP geometric parameter, free in the RSD+AP fit.
bσ8 (galaxy bias) = ~1.20 to 1.32 posterior range in Fig. 2
Nuisance parameter in the GG model, marginalized in the reported constraints.
b_K σ8 (shape bias) = -0.104 to -0.116 posterior range in Fig. 2
NLA amplitude, free nuisance parameter; the authors note its normalization differs from the literature because q is set to 0.
σv (velocity dispersion for FoG damping) = ~0.6 to 2.4 h^-1 Mpc posterior range in Fig. 2
FoG damping parameter in Eq. (5), fitted to the multipoles.

assumptions (7)

domain assumption Intrinsic ellipticity is linearly proportional to the nonlinear tidal field (NLA model), Eq. (7): γ ∝ k^-2 (k_x^2 - k_y^2, 2 k_x k_y) δm.
Central model for the GI and II spectra, cited to Refs [21,59,60]; assumed valid down to r_min = 10 h^-1 Mpc, and the paper flags the need for simulation-based validation.
domain assumption Gaussian Finger-of-God damping factorizes from the power spectra, Eq. (5): P_X = exp(-k^2 μ^2 σv^2) P_hat_X.
Phenomenological RSD model extended from Ref [56] to IA spectra; the velocity dispersion σv is fitted.
domain assumption Nonlinear matter and velocity power spectra from Halofit and the Hahn et al. fitting formulae, Eq. (6) and Refs [57,58], are accurate in the fitted range.
Used to compute the GG, gE, and EE spectra; no simulation validation is presented in this paper.
domain assumption The Alcock-Paczynski distortion model, Eq. (11), applies to IA power spectra with the same α∥ and α⊥ as galaxy clustering.
Geometric mapping of observed to comoving coordinates, assumed to be valid for the anisotropic IA multipoles.
domain assumption Fiducial flat ΛCDM cosmology from Planck [43] is used to convert redshifts to distances and as the reference for α∥ and α⊥.
The reported α values are relative to this fiducial; a different fiducial would shift them.
domain assumption The conditional mapping to flat w0CDM holds all other cosmological parameters and the broadband power-spectrum shape fixed at fiducial values.
The w0, Ωm, and H0 constraints come from projecting the three measured quantities onto this model, not from a full-shape fit.
domain assumption Jackknife resampling covariance, although 'not unbiased', is reliable in the shot-noise-dominated limit and on scales up to r_max = 140 h^-1 Mpc.
Used for all parameter contours; no mock covariance or Hartlap correction is presented.

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Cite this review

Pith. "Pith review of Joint Geometric and Dynamical Constraints on Cosmology from Anisotropies in Galaxy Intrinsic-Alignment Correlations." pith.science (2026). https://pith.science/paper/HBQYZKPZ

@misc{pith2026260806927,
  author       = {Pith},
  title        = {Pith review of: Joint Geometric and Dynamical Constraints on Cosmology from Anisotropies in Galaxy Intrinsic-Alignment Correlations},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/HBQYZKPZ}},
  note         = {Machine review of arXiv:2608.06927}
}

abstract

We present the first joint cosmological analysis to extract both geometric and dynamical information from galaxy intrinsic alignments (IAs). Using BOSS spectroscopy cross-matched with galaxy shape measurements from the DESI Legacy Imaging Surveys, we measure anisotropic galaxy density--intrinsic ellipticity (GI) and intrinsic ellipticity (II) correlations over $0.43\leq z\leq0.7$ and decompose their spin-dependent angular structure into associated Legendre multipoles. The measured GI correlation exhibits the expected baryon acoustic oscillation (BAO) structure, while its anisotropy provides geometric information complementary to galaxy clustering. By jointly modeling redshift-space and Alcock-Paczynski distortions, we constrain the growth rate parameter $f\sigma_8$, the angular-diameter distance $D_A$, and the Hubble expansion rate $H$. Relative to galaxy clustering alone, adding IA reduces their fractional uncertainties by 32\%, 18\%, and 29\%, respectively. By mapping these constraints onto a flat $w_0$CDM model, IA also tightens the constraints on $w_0$, $\Omega_m$, and $H_0$; however, the $w_0$ constraint is sensitive to the minimum scale included in the analysis. Our results establish anisotropic galaxy shapes as an additional source of geometric and dynamical information for spectroscopic cosmology.

Figures

Figures reproduced from arXiv: 2608.06927 by the authors.

**Figure 2.** shows the parameter constraints obtained from our galaxy sample. The blue and orange con1.20 1.24 1.28 1.32 bσ8 0.104 0.108 0.112 0.116 −bK σ8 0.6 1.2 1.8 2.4 σv 0.96 1.00 1.04 α ⊥ 0.32 0.40 0.48 0.56 fσ8 1.00 1.04 1.08 1.12 αk 1.20 1.24 1.28 1.32 bσ8 0.104 0.108 0.112 0.116 −bKσ8 0.6 1.2 1.8 2.4 σv 0.96 1.00 1.04 α⊥ 1.00 1.04 1.08 1.12 αk GG GG+IA FIG. 2: Constraints on (fσ8, α⊥, α∥, bσ8, bKσ8, σv), where α⊥ = DA/… view at source ↗

**Figure 1.** For the clustering-only analysis, the covariance is [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗

Figures from the paper (3 more)

**Figure 3.** Figure 3: FIG. 3: Constraints on the flat [PITH_FULL_IMAGE:figures/full_fig_p005_3.png]

**Figure 4.** Figure 4: FIG. 4: Dependence of the marginalized constraints on the minimum fitting scale, [PITH_FULL_IMAGE:figures/full_fig_p007_4.png]

**Figure 6.** Figure 6: FIG. 6: Scale-cut dependence of the RSD-only constraint on [PITH_FULL_IMAGE:figures/full_fig_p008_6.png]

Discussion (0). Continue with ORCID to comment.

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