Squeezing Full-Shape Dynamical Dark Energy Constraints with Galaxy Alignments

Atsushi Taruya; Junsup Shim; Teppei Okumura

REVIEW 2 major objections 5 minor 77 references

Squeezing Full-Shape Dynamical Dark Energy Constraints with Galaxy Alignments

T0 review · 2 major / 5 minor · reviewed 2026-08-11 · deepseek-v4-flash

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Pith's one-line read Adding galaxy intrinsic alignments to full-shape clustering forecasts sharpens dark energy constraints by up to 57 percent.

desk verdict A clean Fisher forecast showing IA can add 42-57% to DE FoM for PFS-like surveys, with the main caveat being an uncalibrated IA amplitude — but the paper's own sensitivity checks keep it honest. read the letter →

arxiv 2412.08150 v2 pith:62SKRA6G submitted 2024-12-11 astro-ph.CO

Junsup Shim , Teppei Okumura , Atsushi Taruya This is my paper · ORCID

classification astro-ph.CO

keywords intrinsicalignmentsfull-shapegalaxyclusteringdarkenergyequationofstateFisherforecastfiguremeritprimordialamplitudedynamicalmodifiedgravity

topics Dark Energy

open problems Dark Energy

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

Recent full-shape galaxy clustering analyses hint at $2$–$4\sigma$ deviations from a cosmological constant, but confirming dynamical dark energy needs sharper measurements of both expansion and growth. This paper asks whether galaxy intrinsic alignments — the tendency of galaxy shapes to line up with the surrounding tidal field — can extract extra information from the same surveys used for clustering. Running Fisher forecasts for a deep spectroscopic survey like PFS, it finds that adding the alignment power spectra $P_{gE}$ and $P_{EE}$ to the clustering spectrum $P_{gg}$ improves the dark-energy Figure-of-Merit by $42$–$57\%$ and tightens the primordial amplitude $\ln(10^{10}A_s)$ by $17$–$19\%$, across $w_0w_a$CDM and its extensions with curvature, massive neutrinos, and modified gravity. The reader should care because intrinsic alignments are already measured as a contaminant in weak lensing, and if this forecast holds they become a nearly free additional probe of dark energy.

What carries the argument

The central object is the triplet of power spectra built from the galaxy density field and the $E$-mode ellipticity field: $P_{gg}$ (clustering auto), $P_{gE}$ (density-shape cross), and $P_{EE}$ (shape auto), each written as a function of wavenumber $k$ and line-of-sight angle $\mu$. The linear alignment model gives $\gamma_E(k,z) = b_K(z)(1-\mu^2)\delta_m(k,z)$ with $b_K = -0.01344 A_{IA}\Omega_m/D(z)$, so IA carries the same matter power spectrum through a different geometric weight. The Fisher matrix over these spectra, with Gaussian covariance containing shot noise $1/n_g$ and shape noise $\sigma_\gamma^2/n_g$, plus the Alcock–Paczynski rescaling that makes all three spectra sensitive to $H(z)$ and $D_A(z)$, is what turns IA from a nuisance into a degeneracy breaker.

What would settle it

Measure the effective intrinsic-alignment amplitude of the emission-line galaxy sample from early imaging data; if the measured $A_{IA}$ is $12$ or lower, or the shape noise exceeds $\sigma_\gamma=0.3$, the forecast's headline improvement drops to $21$–$26\%$ or roughly half, falsifying the quoted $42$–$57\%$ gain for that survey.

Watch

Extended reading notes

Core claim

The paper's central claim is that the full shape of the galaxy clustering spectrum and the full shapes of the intrinsic-alignment spectra trace the same linear matter power spectrum through different line-of-sight angle factors, so combining them breaks parameter degeneracies that clustering alone leaves partly open. Under the linear alignment model, with Gaussian covariance including shot noise and shape noise, the joint analysis beats clustering alone in every dynamical dark energy model considered: the DE Figure-of-Merit rises by $42$–$57\%$, and the marginalized error on the primordial amplitude $\ln(10^{10}A_s)$ shrinks by $17$–$19\%$ in models without modified gravity. The improvement is largest in the most extended model, and it weakens when curvature, massive neutrinos, or modified gravity are added because IA strengthens specific cross-parameter correlations even while shrinking the overall error volume.

Load-bearing premise

The forecast assumes the PFS emission-line galaxies will have an effective intrinsic-alignment amplitude $A_{IA}=18$ and shape noise $\sigma_\gamma=0.2$, under the linear alignment model out to $k=0.2\,h\,\mathrm{Mpc}^{-1}$; if the real signal is weaker or noisier, the headline $42$–$57\%$ FoM gain shrinks accordingly, down to $21$–$26\%$ at $A_{IA}=12$.

Editorial extensions

If this is right

For the PFS-like setup, the joint forecast reaches about $10\%$ error on $w_0$ in the simplest flat $w_0w_a$CDM model, and about $19\%$ in the most extended model with curvature, massive neutrinos, and modified gravity.
The $w_a$ error improves by at least $25\%$ in every model, with the largest gains near $29\%$, and the $A_s$ error becomes percent-level across all models.
When modified gravity is added, the $A_s$ gain weakens to $1$–$7\%$, showing that IA helps most when the gravity model is kept standard.
For a wider survey with larger shape noise ($\sigma_\gamma=0.3$, $A_{IA}=18$), the FoM gain drops to $21$–$24\%$, but the absolute DE errors are still smaller because of the larger volume.
Restricting to $k_{\max}=0.1\,h\,\mathrm{Mpc}^{-1}$ raises the FoM improvement to $75$–$82\%$, so IA matters most when the analysis stays safely inside linear theory.

Reading between the lines

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

If the fiducial IA amplitude holds, the same Fisher framework should also sharpen constraints on the growth rate and the neutrino mass sum, since IA and clustering respond differently to redshift-space distortions; the paper does not report those full joint errors, so this is an inference.
A concrete near-term test is to measure $A_{IA}$ from early PFS/HSC data; the paper's own scaling predicts the FoM gain should be roughly $21$–$26\%$ if $A_{IA}=12$, so a measurement near that value would immediately downgrade the headline improvement.
Because IA is insensitive to RSD, combining it with clustering may separate growth from geometry without external lensing data, which could be especially valuable for modified-gravity models where the paper finds IA's $A_s$ gain is weakest.
The oscillatory dependence of the FoM gain on $k_{\max}$ is probably a small-sample Fisher artifact; a full likelihood or simulation-based covariance would either confirm or smooth it, so the exact gain at $k_{\max}=0.2\,h\,\mathrm{Mpc}^{-1}$ should be read as indicative until checked.

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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

The paper is a straightforward Fisher forecast showing that adding galaxy intrinsic alignments (IA) to full-shape galaxy clustering can improve dark energy FoM by 42–57% and As errors by 17–19% for a PFS-like survey. It's the first to combine full-shape information from IA (PEE and PgE) with full-shape GC across w0waCDM and extensions with curvature, massive neutrinos, and modified gravity. The math is standard and clearly laid out; the Gaussian covariance in Eq. (10) correctly includes the cross-terms. The robustness checks are genuinely useful: varying kmax, shape noise, and IA amplitude, and showing that gains get larger at smaller kmax, which supports the linear-theory credibility of the result.

The main soft spot is the fiducial choice A_IA=18, sigma_gamma=0.2. The paper relies on an estimator from Shi et al. (2021b) for ELG shapes and HSC photometry; there is no direct measurement that this combination will hold for the PFS sample. The stress-test concern that the gain evaporates at more conservative values is overstated. The paper's own grid shows that at A_IA=12 the FoM gain is still 21–26%, and at sigma_gamma=0.3 it halves. So the improvement shrinks but does not vanish unless you move to an extreme combination like A_IA=5 and sigma_gamma=0.3, which is not suggested by current data. Still, the abstract's clean percentage would be more accurate as 'up to 42–57%' with the fiducial explicitly stated.

A second, more minor, caveat: linear alignment at k=0.2 h/Mpc is a stretch, but the fact that the gain increases when kmax is reduced to 0.1 (75–82%) tells me the effect is coming from large scales where the model is safe. Also, it's a forecast, so no systematic errors from photo-z, calibration, or IA modeling uncertainty are included. That's normal for this genre, but worth remembering when comparing to DESI's actual constraints.

Bottom line: this is a solid forecast that will be useful for survey strategy. It deserves a serious referee; the main things to check are the IA amplitude calibration and whether the covariance handles the B-mode properly. I'd cite it if I work on DESI/PFS forecasts.

Referee Report

2 major / 5 minor

Summary. The paper uses Fisher forecasting to ask whether galaxy intrinsic alignments (IA), combined with full-shape galaxy clustering (GC), can improve constraints on dynamical dark energy parameters (w0, wa) and the primordial amplitude As. For a PFS-like survey, it claims that adding IA improves the dark-energy Figure-of-Merit by 42–57% and tightens As by 17–19%, across w0waCDM and extensions with curvature, massive neutrinos, and modified gravity. The analysis uses the linear alignment model, Gaussian covariances for the Pgg, PgE, and PEE power spectra, and a Planck CMB prior. The paper also reports sensitivity tests to shape noise, IA amplitude, survey geometry, and kmax.

Significance. If the forecasts are reliable, IA would provide a relatively inexpensive complement to full-shape galaxy clustering, because IA spectra can be measured from shape data that already accompany imaging surveys. The paper's formalism is explicit: it states the linear alignment model, gives the Gaussian covariance matrix, and includes a range of extended dark-energy models. It also performs its own robustness checks and honestly reports that the gains are strongly dependent on the IA amplitude and shape noise. The central idea is timely given current DESI results, and the quantitative claim, if robust, would be of interest to the community planning PFS and Euclid analyses.

major comments (2)

[§4 (Setup and Results); §5 (Conclusions)] The headline 42–57% DE-FoM gain is not robust to the assumed IA amplitude and shape-noise level. The fiducial choice AIA=18 and σγ=0.2 is motivated in §4 by an estimator from Shi et al. (2021b) and HSC shape information, but the manuscript does not establish that this particular (AIA, σγ) combination will hold for the PFS ELG sample. The §5 sensitivity tests show that the gain drops to 21–26% for AIA=12 and roughly halves when σγ increases to 0.3; since the IA signal-to-noise scales roughly as A_IA^2/σγ^2, a simultaneously lower amplitude (e.g., AIA≈5) and larger shape noise (σγ≈0.3) would reduce the effective IA signal by about an order of magnitude relative to the fiducial pair. Because the abstract-level claim is a percentage gain, this fiducial pair is load-bearing. Please either provide a direct calibration/measurement for the simultaneous values or reformulate the headline as explicitly conditional and present the gain as a function of (AIA, σγ).
[§2 (Eq. 4) and §4 (kmax = 0.2 h/Mpc)] The forecast applies the linear alignment model and linear matter power spectrum up to kmax = 0.2 h/Mpc. At these scales, nonlinear evolution and scale-dependent galaxy bias are non-negligible, and the linear tidal response of Eq. (4) has not been validated for the PFS ELG population. The manuscript's own kmax=0.1 robustness check gives a larger IA improvement, which supports the qualitative direction of the claim, but the absolute percentage gains quoted for kmax=0.2 may be affected by the absence of nonlinear modeling. Please quantify this sensitivity, for example by replacing the linear Pm with a nonlinear model and a simple bias treatment, or by explicitly reporting the kmax dependence for the extended dark-energy models.

minor comments (5)

[§1 (Title and text)] The title contains a stray space in 'F ull' and the abstract has a spacing issue in '0.6 ≤ z <2.4'; these should be corrected.
[§3 (Eq. 9)] The Fisher matrix expression says the analysis includes 'five fiducial parameters' plus curvature, neutrino mass, and modified-gravity parameters, but these parameters and their fiducial values are not listed in the Letter. A short table or appendix listing the full parameter vector and priors would make the forecasts reproducible.
[§4, Fig. 1] The contour labeled 'IA' in Fig. 1 is derived from both PEE and PgE, not from the IA auto-spectrum alone; the text should state this explicitly to avoid confusion about what the 'IA-only' probe contains.
[§4 and §5] The mapping from the estimator of Shi et al. (2021b) to the quoted AIA=18 is not explained; please specify the conversion, including any dependence on redshift or halo-mass definition, so that readers can judge whether the value is appropriate for PFS ELGs.
[General] No code or data-availability statement is included; for a Fisher forecast, releasing the pipeline or a table of the Fisher matrices would improve reproducibility and allow independent checks of the quoted FoM gains.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the Fisher forecast is self-contained; IA parameters are assumed and varied, not fitted, and the cited companion work is not load-bearing.

full rationale

The central claim is a Fisher forecast computed from the paper's own displayed equations (Eqs. 5-10) with stated survey parameters and explicitly quoted covariance structure. The IA amplitude and shape noise are fixed fiducial assumptions, not fitted to the quantity being predicted; their effect is directly quantified in Sec. 5 (AIA=12 vs 24, sigma_gamma=0.15/0.20/0.30, and kmax variations). The FoM gain is therefore a derived output of the model, not an input. Self-citations to Taruya & Okumura 2020, Okumura & Taruya 2022/2023, and to the companion paper Shim et al. 2024 are used for background or for details of the Fisher setup and additional parameter constraints, but the forecast here is recomputed with all relevant expressions included; none of these citations is invoked as an unverified uniqueness theorem or as a substitute for the calculation. The linear alignment model is attributed to Catelan et al. 2001 and Hirata & Seljak 2004, and the ELG IA amplitude assumption to Shi et al. 2021b, which has no overlap with the present authors. The forecast's main limitation, namely that the headline gain depends on the chosen AIA and sigma_gamma pair, is stated and quantified inside the paper, making the sensitivity transparent rather than circular. The '42-57%' improvement is thus a conditional forecast from an independent forward model, not a conclusion that reduces by construction to its own assumptions.

Assumptions & free parameters 3 free parameters · 4 assumptions · 0 invented entities

The forecast relies on a small number of assumed nuisance parameters, chiefly the IA amplitude, shape noise, and scale cutoff. These are not fitted to data in this paper and directly control the headline improvement. The axioms are standard modeling choices in galaxy clustering Fisher forecasts, but the linear alignment model at the chosen kmax is the least secure element.

free parameters (3)

A_IA = 18
Effective intrinsic alignment amplitude for the ELG shape estimator, fixed at 18 based on Shi et al. 2021b. The FoM improvement ranges from 21-26% at A_IA=12 to 74-98% at A_IA=24, so the headline number is sensitive to this choice.
sigma_gamma = 0.2 (PFS), 0.3 (Euclid)
Shape noise per galaxy. The authors show that reducing from 0.2 to 0.15 doubles the DE FoM while increasing to 0.3 halves it.
kmax = 0.2 h/Mpc
Maximum wavenumber in Fisher integral. The FoM improvement oscillates with kmax and rises to 75-82% at kmax=0.1 h/Mpc, indicating sensitivity to the chosen scale cutoff.

assumptions (4)

domain assumption Linear alignment model for intrinsic alignments (Eqs. 2-4)
IA is assumed to be a linear response to the tidal field, following Catelan et al. 2001 and Hirata & Seljak 2004. This neglects nonlinear and scale-dependent IA contributions that may matter at k up to 0.2 h/Mpc.
standard math Gaussian covariance for the three power spectra (Eq. 10)
The Fisher matrix assumes the power spectra are Gaussian-distributed with the given covariance; this is standard but ignores non-Gaussian terms and survey window effects.
domain assumption Linear matter power spectrum at k<=0.2 h/Mpc
The forecast uses the linear Pm. At z<1 and k=0.2 h/Mpc nonlinear corrections are non-negligible, which could change the constraining power.
domain assumption Planck-15 compressed likelihood as CMB prior
The CMB prior is taken from Planck 2015. Using more recent Planck 2018 or DESI data could shift the forecast, though the qualitative impact of IA would likely remain.

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Cite this review

Pith. "Pith review of Squeezing Full-Shape Dynamical Dark Energy Constraints with Galaxy Alignments." pith.science (2026). https://pith.science/paper/62SKRA6G

@misc{pith2026241208150,
  author       = {Pith},
  title        = {Pith review of: Squeezing Full-Shape Dynamical Dark Energy Constraints with Galaxy Alignments},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/62SKRA6G}},
  note         = {Machine review of arXiv:2412.08150}
}

abstract

Recent $2-4\sigma$ deviations from the Cosmological Constant $\Lambda$ suggest that dark energy (DE) may be dynamical, based on baryon acoustic oscillations and full-shape galaxy clustering (FS GC) analyses. This calls for even tighter DE constraints to narrow down its true nature. In this Letter, we explore how galaxy intrinsic alignments (IA) can enhance the FS GC-based DE constraints, using Fisher forecasts on various extensions of dynamical DE models, including scenarios with curvature, massive neutrinos, and modified gravity. Incorporating IA improves the DE Figure-of-Merit by $42-57\%$ and tightens the primordial power spectrum amplitude constraints by $17-19\%$. Our findings highlight IA's potential as a valuable cosmological probe complementary to GC.

Figures

Figures reproduced from arXiv: 2412.08150 by the authors.

**Figure 1.** 2D-confidence ellipses for DE EOS parameters of the most extended dynamical DE model, w0waCDM+(Ωk, mν, γ) assuming a PFS-like survey. Contours represent 1-σ confidence regions and CMB prior is included. Contour for ‘IA’ is obtained from PEE and PgE. 2011) to comment on how our results change depending on survey geometries, e.g., deep PFS-like and wide Euclid-like surveys. Parameters characterizing the PFSlike and … view at source ↗

**Figure 3.** Improvement in 1D-marginalized constraints with IA (left) and FS joint constraints (right), assuming a PFSlike survey with CMB prior included. Joint constraints as fractional errors, σi/θi, are shown. For wa, we show their actual errors, σi, since their fiducial values, θi, are zero. cacy of IA in constraining As. It is worth noting that IA significantly decreases correlation coefficients for w0- As and wa-As, like… view at source ↗

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