Pith. sign in

REVIEW 3 major objections 5 minor 46 references

photo-3x2-pt: Cosmology from cosmic shear and galaxy clustering with a single photometric galaxy catalog

T0 review · 3 major / 5 minor · reviewed 2026-08-08 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗ Review JSON

Pith's one-line read Combining galaxy clustering, galaxy-shear cross-correlation, and cosmic shear from the same photometric galaxy catalog tightens the S8 constraint by about 25% while remaining consistent with shear-only results.

desk verdict A careful first HSC-Y3 photo-3x2-pt measurement whose 25% S8 tightening depends on clustering systematics not exercised by the mocks; worth refereeing with a request for end-to-end validation. read the letter →

arxiv 2608.05530 v1 pith:DAJRUXP5 submitted 2026-08-06 astro-ph.CO

Takashi Hamana (NAOJ) This is my paper · ORCID
classification astro-ph.CO
keywords cosmology:observationsdarkmattercosmologicalparameterslarge-scalestructureofuniversecosmicsheargalaxyclusteringgalaxy-galaxylensingintrinsicalignment
topics Dark Matter
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 seeks to establish that a joint analysis of cosmic shear, galaxy-shear cross-correlation, and galaxy clustering measured from a single photometric galaxy catalog recovers the growth-of-structure parameter $S_8 = \sigma_8\sqrt{\Omega_m/0.3}$ more tightly than cosmic shear alone. Using the HSC-Y3 weak lensing shape catalog, the author measures the three angular power spectra with the pseudo-$C_\ell$ method and removes systematics from the galaxy density maps through area cuts and template deprojection. The reported 68% credible interval is $0.76 \le S_8 \le 0.81$, consistent with the HSC-Y3 cosmic shear analyses but about 25% tighter. A mock-catalog performance test is presented to show that the key cosmological and nuisance parameters are recovered without bias.

What carries the argument

The data vector consists of 96 band-power measurements: ten shear-shear, ten galaxy-shear, and four galaxy clustering auto-spectra, with four band powers each; the scale cuts are $317 \le \ell \le 1000$ for shear-shear and $178 \le \ell \le 562$ for the other two. The power spectra are computed with the pseudo-$C_\ell$ formalism, and the galaxy density maps are cleaned by cutting about 29.5% of the survey area where observing conditions correlate with galaxy density and then deprojecting contaminant template maps. The load-bearing mechanism for the improved $S_8$ is the self-calibration: because the galaxy clustering kernel is directly proportional to the redshift distribution, the clustering auto-spectra constrain the $\Delta z_i$ shift parameters that otherwise inflate shear-only errors, while the galaxy-shear spectra constrain the intrinsic alignment amplitudes.

What would settle it

Apply the same photo-3x2pt pipeline to mock catalogs that include realistic spatial maps of seeing, depth, extinction, and sky level, impose the same area cuts and deprojection, and check whether the mean recovered $S_8$ over many realizations equals the input value within the quoted error; a shift larger than the statistical uncertainty would show the mitigation is biased.

Watch

Extended reading notes

Core claim

The central claim is that the photo-3x2-pt data vector, built from the same photometric galaxy catalog that supplies the shear sample, constrains $S_8$ to $0.76 \le S_8 \le 0.81$ at 68% credibility. This interval overlaps the results of the HSC-Y3 cosmic shear studies but is about 25% narrower. The improvement is attributed to the added sensitivity to the two nuisance parameters that dominate shear-only errors: the intrinsic alignment amplitude, which the galaxy-shear spectra help pin down, and the shift parameters of the source redshift distributions, which the galaxy clustering auto-spectra effectively self-calibrate. The paper also reports that the measured B-mode power spectra are consistent with zero, and that mock-catalog inferences recover unbiased values of $S_8$, intrinsic alignment parameters, galaxy clustering bias, and redshift shift parameters.

Load-bearing premise

The result stands or falls on whether the area cuts and template deprojection remove observing-condition contaminants from the galaxy density maps without biasing the cosmological clustering signal, a step the mock test does not exercise because it omits observational condition variations and area cuts.

Editorial extensions

If this is right

  • The $S_8$ credible interval narrows by roughly 25% relative to the HSC-Y3 cosmic shear-only analyses, with a consistent central value.
  • The shift parameters $\Delta z_3$ and $\Delta z_4$ for the two highest redshift bins are constrained about 30% more tightly, removing the main nuisance-driven error of shear-only analyses.
  • No significant B-mode signal is found in the galaxy-shear or shear-shear spectra, supporting the adopted scale cuts.
  • Because the extra information comes from the same galaxies already used for the shear catalog, the method requires no separate spectroscopic lens sample and can be applied to other photometric surveys.

Reading between the lines

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

  • If this result holds, photo-3x2pt analyses could reduce the reliance of Stage-IV weak lensing surveys on external photometric redshift calibration, since the clustering spectra self-calibrate the relevant shifts.
  • Beyond the paper, the same single-catalog strategy could be combined with a spectroscopic lens sample in a 6x2pt analysis; the paper's mock validation gives partial empirical support for that extension.
  • A testable prediction of the mechanism is that adding clustering and galaxy-shear spectra should shrink the $S_8$ posterior mainly by narrowing the $\Delta z_3$ and $\Delta z_4$ and intrinsic alignment directions, which could be verified by inspecting posterior covariances.
  • The area-cut thresholds in this paper are chosen from the data; a stronger validation would be to inject simulated systematics into mocks with realistic observing conditions and confirm that the recovery remains unbiased.
Share X Bluesky LinkedIn Reddit HN

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

3 major / 5 minor

Summary. This paper presents a joint "photo-3x2-pt" cosmological analysis using the HSC-Y3 weak lensing shape catalog: it measures shear-shear, galaxy-shear, and galaxy clustering angular power spectra with the pseudo-C_ell method, mitigates systematics in the galaxy density maps via area cuts and template deprojection, and performs a Bayesian parameter inference with nuisance parameters for intrinsic alignments, galaxy bias, lensing magnification, baryonic feedback, and redshift distribution shifts. For a flat LCDM model the paper reports a 68% credible interval 0.76 <= S8 <= 0.81, which it states is consistent with the HSC-Y3 cosmic shear results of Dalal et al. (2023) and Li et al. (2023) but about 25% tighter. The analysis is supported by mock catalogs built from N-body and ray-tracing simulations, with 64 realizations, which are used to test unbiased recovery of S8, IA amplitudes, galaxy bias, and redshift shift parameters.

Significance. If the central claim holds, the paper demonstrates an important practical result: adding galaxy clustering and galaxy-shear spectra from the same photometric catalog used for cosmic shear can self-calibrate nuisance parameters such as intrinsic alignment amplitudes and redshift distribution shifts, yielding a tighter and apparently unbiased S8 constraint than cosmic shear alone. This is relevant for current Stage-III analyses and for the design of Stage-IV 3x2-pt and 6x2-pt analyses. The paper has clear strengths: it uses public, widely used software (NaMaster, CAMB, MultiNest, OneCovariance); it reports B-mode null tests for the new galaxy-shear and shear-shear combinations; it performs a non-trivial mock validation with 64 realizations; and it checks robustness of the S8 result against several modeling choices (IA model variants, baryonic feedback, galaxy bias redshift dependence). The main weakness is that the most aggressive systematics-mitigation steps applied to the real galaxy density maps, namely the 29.5% area cut and the template deprojection, are not exercised by the mock validation, which leaves a gap in the evidence for the central claim.

major comments (3)
  1. [Appendix 2 and Section 3.2.3] The end-to-end validation of the galaxy clustering systematics mitigation is missing, and this is load-bearing for the central claim. The real clustering spectra are produced after two steps: data-driven area cuts that remove 29.5% of the survey area (Table 3) and template deprojection of six contaminant maps (Section 3.2.3). The thresholds in Table 3 are chosen by inspecting the relation between galaxy number density and the systematics maps in the same data; for example, the seeing cut includes a lower threshold set because "the slope of the correlation fluctuated erratically" (Appendix 2). The mock validation explicitly does not exercise these steps: Appendix A.1.3 states "No area cut by observational conditions was made for galaxy density map as any variations of observational conditions were not considered in creating mock data." The template deprojection is likewise not tested in the mocks. If the area cuts preferentially remove over- or underdense regions, or if the deprojection subtracts modes that are correlated with the true density field, the galaxy clustering auto-spectra are biased. Because Section 6.1 uses these clustering spectra to self-calibrate Delta_z3, Delta_z4 and the galaxy biases, such a bias would propagate directly into S8, not merely into an uninteresting nuisance parameter. I recommend that the authors add a validation test in which mock density maps are populated with realistic observational-condition templates (depth, seeing, sky level, coverage) and the same area-cut and deprojection pipeline is applied, checking that the recovered S8 and Delta_z values remain unbiased. At minimum, the real-data analysis should report how the S8 result shifts when the Table 3 thresholds are varied within plausible ranges.
  2. [Section 6.4 and Figure 8] The headline comparison that the result is "~25% tighter than the HSC-Y3 cosmic shear studies" is not an apples-to-apples comparison, and the paper should either qualify it or provide a matched comparison. The HSC-Y3 analyses of Dalal et al. (2023) and Li et al. (2023) use different scale cuts (their cosmic shear extends to ell ~ 1800), different treatment of PSF systematics and shear calibration (marginalized over, as stated in Sections 5.3.2 of this paper), and different covariance choices. This paper's own "gamma-gamma-only" reference analysis uses the more conservative scale cut 317 <= ell <= 1000, so the relative tightening shown in Figure 8 conflates the effect of adding the new probes with the effect of changing scale cuts and systematics treatments. The paper does note some of these caveats, but the abstract and Section 6.4 nevertheless present the 25% figure as a headline. I suggest reporting the fractional width improvement from a matched analysis, e.g., the ratio of the S8 interval from the full photo-3x2-pt data vector to that from the same pipeline applied to the shear-shear spectra alone with identical scale cuts and systematics treatment.
  3. [Section 6.2 and footnote 5] The goodness-of-fit statistic chi2 = 70.5 for "effective" 85 degrees of freedom, with p = 0.87, is based on a post-hoc selection of the 11 parameters that the data happen to constrain more tightly than their priors. This procedure is not a standard chi2 test: the full model has 26 varied parameters, and selecting the effective number of degrees of freedom from the width of the posteriors makes the reported p-value optimistic. The unusually high p-value could also indicate that the covariance is somewhat overestimated. This does not directly invalidate the S8 constraint, but the paper should either report the chi2 and p-value for the full 96-26 = 70 degrees of freedom, or present the effective-dof calculation as an approximate diagnostic rather than a formal goodness-of-fit test.
minor comments (5)
  1. [Appendix 2, Table 3] The table reports a cut of "Seeing >= 0.5 and <= 0.75" removing 10.2% of the area, but the lower threshold motivation is only described qualitatively. Since this is one of the largest area cuts, a quantitative stability test (e.g., how the inferred clustering amplitudes change when the lower threshold is varied by +/- 0.05 arcsec) would be valuable.
  2. [Appendix 2, Table 2] In the third row of Table 2, the dumped-redshift list "0.449, 0.923, 0.538, ..." contains a value 0.923 that is not in monotonic order with the neighboring entries; this is presumably a typo for something like 0.492 and should be corrected.
  3. [Section 3.2.3] The text says "in summery we cut ~30 percent of the survey area"; "summery" should be "summary".
  4. [Section 6.2] The sentence "the constraints on alpha_mu for all the bins are very week" contains a typo: "week" should be "weak".
  5. [Section 6.4] The sentence "our credible intervals are ~30% tiger" contains a typo: "tiger" should be "tighter".

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity: the photo-3x2-pt S8 constraint is an independent combination of measured spectra, and the mock-validation gap is a robustness limitation, not a circular step.

full rationale

The paper's central result (0.76 ≤ S8 ≤ 0.81) is obtained by a standard Bayesian likelihood analysis of 96 measured band powers (10 shear-shear, 10 galaxy-shear, and 4 galaxy clustering spectra, each with four band powers). The added spectra are independent data vectors: galaxy clustering and galaxy-shear depend on galaxy density fields, while cosmic shear depends on shear fields, and both enter the model through separate kernels (Eqs. 4–10). They are not constructed from the target S8. Nuisance parameters (A1, bg, Δz, αμ) are marginalized with priors given in Table 1; they are not fitted to S8 and then renamed as predictions. The 'self-calibration' of Δz3/Δz4 via galaxy clustering is an inference from new measurements, not an identity: clustering auto-spectra constrain p(z) with a free bias bg, and the galaxy-shear cross-spectra help break the degeneracy; no equation sets the clustering spectrum equal to a fitted S8 value. The mock validation in Appendix 1 is external: mock catalogs are built from N-body and ray-tracing simulations with known inputs (σ8 = 0.83, A1 = 0.5, αμ = (0.3, 0.3, 0.7, 1.2)) and the pipeline recovers them, providing independent support. The only notable gap is stated by the paper itself in Appendix A.1.3: 'No area cut by observational conditions was made for galaxy density map as any variations of observational conditions were not considered in creating mock data.' This means the 29.5% area cut and template deprojection are not end-to-end validated in mock, but that is a robustness or correctness concern, not circularity: the thresholds are chosen by inspecting systematics–density relations (Appendix 2), not by fitting the S8 that is later reported. Citations to prior HSC analyses and to Nicola et al. (2020) / Elsner et al. (2016) supply methods and benchmarks; none is used as a uniqueness theorem or as the sole justification for the S8 interval. No circular step can be exhibited from the paper's equations or quoted text.

Assumptions & free parameters 11 free parameters · 9 assumptions · 0 invented entities

The analysis rests on standard cosmological and astrophysical modeling assumptions (flat LambdaCDM, Limber, linear bias, NLA IA, HMcode baryonic model, template deprojection, shift-only photo-z uncertainties) and 26 fitted model parameters, of which 11 are said to be constrained by the data. No new particles or entities are introduced. The most fragile assumptions are the data-driven area-cut selection and the shift-only model for redshift distribution uncertainty.

free parameters (11)
  • Omega_c (CDM density parameter) = Omega_m 68% CI 0.18-0.25
    Flat prior (0.1,0.7) in Section 5.2.1. Constrained by the full data vector and drives S8.
  • A_s (or sigma8) = sigma8 68% CI 0.83-1.01
    Flat prior A_s*1e9 in (0.5,10). Dominant amplitude parameter in the S8 measurement.
  • omega_b = prior flat(0.02,0.025), weakly constrained
    Prior bracketing external values; Section 5.2.1.
  • h = prior flat(0.62,0.80)
    Weakly constrained by photo-3x2-pt; prior from external experiments.
  • n_s = prior flat(0.87,1.07)
    Weakly constrained; prior from external experiments.
  • Intrinsic alignment amplitudes A1^i (i=1-4) = inferred in Figure 5; lower bins constrained, highest bin poorly constrained
    Flat prior (-3,3). Galaxy-shear spectra are meant to tighten these; Section 5.2.2.
  • Intrinsic alignment tidal biases bT^i (i=1-4) = posteriors broad, truncated at prior edges
    Flat prior (0,2); paper states data have no practical sensitivity, Section 6.3.
  • Galaxy clustering biases bg^i (i=1-4) = posterior means in Figure 5; mock check in Figure 12
    Flat prior (0.5,3.5); needed because clustering spectra are the new data vector.
  • Lensing magnification slopes alpha_mu^i (i=1-4) = poorly constrained in real data; mock unbiased except alpha_mu^1
    Flat prior (0,2); estimated slopes from observed counts are ~0, 0.3, 0.6, 0.9 but posteriors are weak.
  • Baryonic feedback amplitude Abary = posterior truncated at lower bound
    Flat prior (2,3.13); no useful constraint, but S8 shifts only 0.38 sigma when fixed at 3.13, Section 6.3.
  • Redshift distribution shifts Delta_z_i (i=1-4) = Delta_z1,z2 prior dominated; Delta_z3,z4 about 30 percent tighter than HSC-Y3
    Gaussian priors for bins 1-2, flat for bins 3-4; Section 5.3.1.
assumptions (9)
  • domain assumption Flat LambdaCDM with fixed neutrino mass sum 0.06 eV
    Section 5.2.1 sets five cosmological parameters and fixes neutrino mass from oscillation results; the central S8 result is only defined within this model.
  • standard math Limber approximation for all angular power spectra
    Equation (3) uses Limber; Section 5.1 notes it is inaccurate below ell ~ 100, hence scale cuts start at 178.
  • domain assumption Scale-independent linear galaxy bias per tomographic bin
    Equations (2) and (6) and Section 5.2.3; high-ell cuts chosen to preserve validity.
  • domain assumption Nonlinear alignment (NLA) intrinsic alignment model extended to 1-loop from Blazek et al. 2015
    Section 4.1 equations (8) and (9); the tidal bias bT terms contribute little at the adopted ell range.
  • domain assumption HMcode nonlinear matter power spectrum and Mead et al. 2015 baryonic feedback model
    Section 4.1 and 5.2.5; baryonic parameter Abary posterior is truncated, no useful constraint.
  • domain assumption Template deprojection assumes contaminants add linearly to the galaxy overdensity
    Section 3.2.3, from Elsner et al. 2016 and Nicola et al. 2020; no direct validation on HSC-Y3, only transferred from PDR1.
  • domain assumption Source redshift distributions from Rau et al. 2023 with uncertainties modeled only as overall shifts
    Section 5.3.1; cross-spectra between tomographic bins are excluded because this model does not capture tails.
  • domain assumption Covariance is Gaussian from NaMaster plus connected non-Gaussian and super-sample terms scaled by fsky
    Section 4.2; approximation justified by smallness at the adopted ell ranges but not exact.
  • ad hoc to paper The 11 constrained parameters are the effective degrees of freedom for the chi-square test
    Section 6.2 footnote; this is a conservative ad hoc choice, not a rigorous model-selection statistic.

how reviews work

0 comments
Cite this review

Pith. "Pith review of photo-3x2-pt: Cosmology from cosmic shear and galaxy clustering with a single photometric galaxy catalog." pith.science (2026). https://pith.science/paper/DAJRUXP5

@misc{pith2026260805530,
  author       = {Pith},
  title        = {Pith review of: photo-3x2-pt: Cosmology from cosmic shear and galaxy clustering with a single photometric galaxy catalog},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/DAJRUXP5}},
  note         = {Machine review of arXiv:2608.05530}
}
abstract

We perform a joint cosmological analysis using angular power spectra of galaxy clustering, galaxy-shear cross correlation, and cosmic shear (hereafter referred to as photo-3x2-pt) measured from the Hyper Suprime-Cam year-3 (HSC-Y3) weak lensing shape catalog. We employ the pseudo-$C_\ell$ method to measure these power spectra and use the template deprojection method to mitigate systematics in the galaxy density maps. We perform a standard Bayesian likelihood analysis for cosmological inference based on the measured photo-3x2-pt, including contributions from intrinsic alignments of galaxies, galaxy clustering bias, lensing magnification effect, baryonic feedback effect, and source redshift distribution errors. For a flat cold dark matter model, we find a 68% credible interval of $0.76 \le S_8 \le 0.81$. This result is consistent with those of the HSC-Y3 cosmic shear analyses (Dalal et al. 2023, Li et al. 2023), but is $\sim 25$% tighter than theirs. We also perform a performance test using mock catalogs that mimic the HSC-Y3 data to validate our photo-3x2-pt analysis. Through Bayesian parameter inference of mock data, we verify that unbiased estimates can be obtained for the key cosmological and nuisance parameters, including $S_8$, model parameters of intrinsic alignment, galaxy clustering bias, and shift parameters of the source redshift distributions.

Figures

Figures reproduced from arXiv: 2608.05530 by the authors.

Figure 1
Figure 1. Galaxy clustering power spectra for ten combinations of tomo￾graphic redshift bins (indicated in each panel). Error bars represent the square-root of the diagonal elements of the covariance matrix. Note that only four ℓ-bins within the range 178 ≤ ℓ ≤ 562 of the auto-power spectra are used for parameter inference. The cross-spectra are also presented to show levels of detections. The solid lines show the theoretical… view at source ↗
Figure 2
Figure 2. Galaxy-shear power spectra for ten combinations of tomographic redshift bins (indicated in each panel). Error bars represent the square￾root of the diagonal elements of the covariance matrix. Note that only four ℓ-bins within the range 178 ≤ ℓ ≤ 562 are used for parameter infer￾ence. The solid lines show the theoretical prediction based on a repre￾sentative ΛCDM model with S8 = 0.78, where other model parameters are… view at source ↗
Figure 3
Figure 3. Normalized number counts of galaxies in four tomographic samples as a function of i-band magnitude. Top and bottom panels show accumu￾lated and differential counts, respectively. Inserted plot shows the slope of the counts in flux α i µ = d ln N(> f)/d ln f, a key factor determining the strength of the gravitational lensing magnification effect (see section 5.2.4). to a turnover at a brighter magnitude. 5.2.5 Baryon… view at source ↗
Figures from the paper (14 more)
Figure 4
Figure 4. Figure 4: shows marginalized posterior contours in the Ωm-σ8 and Ωm-S8 planes, along with the marginalized one-dimensional posterior distributions for each parameter. We find marginalized 68% confidence intervals of 0.18 < Ωm < 0.25, 0.83 < σ8 < 1.01, and 0.76 < S8 < 0.81. We wi…
Figure 5
Figure 5. Figure 5: The marginalized one-dimensional posterior distributions for the fiducial ΛCDM model. From the top to bottom rows, the panels display the intrinsic alignment amplitude parameters, the galaxy clustering bias parameters, the shift parameters of the galaxy redshift distri…
Figure 6
Figure 6. Figure 6: Marginalized two-dimensional posterior contours (68% and 95% credible levels) in the Abary-S8 plane for the fiducial ΛCDM model are shown. The corresponding marginalized 1D posterior distributions are shown alongside the 2D plots. The dashed line in the right panel is …
Figure 8
Figure 8. Figure 8: Same as [PITH_FULL_IMAGE:figures/full_fig_p010_8.png]
Figure 9
Figure 9. Figure 9: shows distributions of inferred values of key cosmologi￾cal parameters (Ωm, σ8 and S8). It is found from this Figure that unbiased estimates for those cosmological parameters can be ob￾tained from the photo-3 × 2-pt analysis. IA parameters Results for IA amplitude para…
Figure 10
Figure 10. Figure 10: Bottom panels: Scatter plots showing inferred values in A i 1 -S8 plane. Error bars show averaged 68- and 95-percents credible intervals centered at averaged means over 64 realizations. Top panels: Frequency distributions of inferred values. The dashed lines show the …
Figure 11
Figure 11. Figure 11: Same as [PITH_FULL_IMAGE:figures/full_fig_p015_11.png]
Figure 12
Figure 12. Figure 12: It is found from the figure that unbiased estimates [PITH_FULL_IMAGE:figures/full_fig_p015_12.png]
Figure 14
Figure 14. Figure 14: Top panel: The area fraction as a function of 5σ point source sur￾vey depth. The thin and thick lines are for the differential and accumulated fractions, respectively. Bottom panel: Filled squares with error bars show the mean number density of galaxies from all four …
Figure 15
Figure 15. Figure 15: Same as [PITH_FULL_IMAGE:figures/full_fig_p016_15.png]
Figure 16
Figure 16. Figure 16: Same as [PITH_FULL_IMAGE:figures/full_fig_p017_16.png]
Figure 19
Figure 19. Figure 19: Same as [PITH_FULL_IMAGE:figures/full_fig_p017_19.png]
Figure 22
Figure 22. Figure 22: Same as [PITH_FULL_IMAGE:figures/full_fig_p018_22.png]
Figure 21
Figure 21. Figure 21: Same as [PITH_FULL_IMAGE:figures/full_fig_p018_21.png]

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

46 extracted references · 36 canonical work pages

  1. [1]

    Alonso, D., Sanchez, J., & Slosar, A. a. 2019, MNRAS, 484, 412 7

    work page 2019

  2. [2]

    R., & Brenneman, W

    Ba, S., Myers, W. R., & Brenneman, W. A. 2015, Technometrics, 57, 479

    work page 2015

  3. [3]

    M., d’Assignies, W., Troxel, M

    Bernstein, G. M., d’Assignies, W., Troxel, M. A., et al. 2026 , ApJ, 1002, 95

    work page 2026

  4. [4]

    2015, Journal of Cosmology and Astroparticle Physics, 2015, 015

    Blazek, J., Vlah, Z., & Seljak, U. 2015, Journal of Cosmology and Astroparticle Physics, 2015, 015

    work page 2015

  5. [5]

    A., MacCrann, N., Troxel, M., & Fang, X

    Blazek, J. A., MacCrann, N., Troxel, M., & Fang, X. 2019, Phys ical Review D, 100, 103506

    work page 2019

  6. [6]

    2007, New Journal of Physics, 9, 444

    Bridle, S., & King, L. 2007, New Journal of Physics, 9, 444

    2007

  7. [7]

    Chisari, N. E. 2025, A&AR, 33, 1

    work page 2025

  8. [8]

    2023, Physical Review D, 108, 123519 Dark Energy Survey Collaboration, Abbott, T., Abdalla, F

    Dalal, R., Li, X., Nicola, A., et al. 2023, Physical Review D, 108, 123519 Dark Energy Survey Collaboration, Abbott, T., Abdalla, F. B ., et al. 2016, MNRAS, 460, 1270 de Jong, J. T. A., V erdoes Kleijn, G. A., Kuijken, K. H., & V ale ntijn, E. A. 2013, Experimental Astronomy, 35, 25 de Souza, D. H. F., Yin, B., Eifler, T., et al. 2026, Journal of C osmolo...

    arXiv 2023

Show all 46 references
  1. [9]

    Elsner, F., Leistedt, B., & Peiris, H. V . 2016, MNRAS, 465, 1847

    2016

  2. [10]

    T., Springel, V ., et al

    Ferlito, F., Davies, C. T., Springel, V ., et al. 2024, MNRAS, 533, 3209

    2024

  3. [11]

    Feroz, F., & Hobson, M. P . 2008, MNRAS, 384, 449

    2008

  4. [12]

    P ., & Bridges, M

    Feroz, F., Hobson, M. P ., & Bridges, M. 2009, MNRAS, 398, 1601

    2009

  5. [13]

    P ., Cameron, E., & Pettitt, A

    Feroz, F., Hobson, M. P ., Cameron, E., & Pettitt, A. N. 2019, T he Open Journal of Astrophysics, 2, 10 García-García, C., Alonso, D., & Bellini, E. 2019, Journal o f Cosmology and Astroparticle Physics, 2019, 043

    2019

  6. [14]

    M., Hivon, E., Banday, A

    Gorski, K. M., Hivon, E., Banday, A. J., et al. 2005, ApJ, 622, 759

    2005

  7. [15]

    M., & Seljak, U

    Hirata, C. M., & Seljak, U. 2004, Physical Review D, 70, 06352 6

    2004

  8. [16]

    2000, Physical Review D, 62, 043007

    Hu, W. 2000, Physical Review D, 62, 043007

    2000

  9. [17]

    2019 , MNRAS, 488, 1652

    Huang, H.-J., Eifler, T., Mandelbaum, R., & Dodelson, S. 2019 , MNRAS, 488, 1652

    2019

  10. [18]

    2016, PASJ, 68, 54

    Iwasawa, M., Tanikawa, A., Hosono, N., et al. 2016, PASJ, 68, 54

    2016

  11. [19]

    D., et al

    Joachimi, B., Cacciato, M., Kitching, T. D., et al. 2015, Spa ce Sci. Rev., 193, 1

    2015

  12. [20]

    A., Asgari, M., et al

    Joachimi, B., Lin, C. A., Asgari, M., et al. 2021, A&A, 646, A1 29

    2021

  13. [21]

    2025, A& A, 699, A127

    Johnston, H., Elisa Chisari, N., Joudaki, S., et al. 2025, A& A, 699, A127

    2025

  14. [22]

    2017, MNRAS, 4 72, 2126

    Kilbinger, M., Heymans, C., Asgari, M., et al. 2017, MNRAS, 4 72, 2126

    2017

  15. [23]

    2011, ArXiv e-p rints, arXiv:1110.3193

    Laureijs, R., Amiaux, J., Arduini, S., et al. 2011, ArXiv e-p rints, arXiv:1110.3193

    2011 arXiv

  16. [24]

    D., Ferreira, T., Fang, X., et al

    Leonard, C. D., Ferreira, T., Fang, X., et al. 2023, The Open J ournal of Astrophysics, 6, 8

    2023

  17. [25]

    2013, N eutrino Cosmology (Cambridge, UK: Cambridge University Press)

    Lesgourgues, J., Mangano, G., Miele, G., & Pastor, S. 2013, N eutrino Cosmology (Cambridge, UK: Cambridge University Press)

    2013

  18. [26]

    2000, ApJ, 538, 473

    Lewis, A., Challinor, A., & Lasenby, A. 2000, ApJ, 538, 473

    2000

  19. [27]

    2022, PASJ, 74, 421

    Li, X., Miyatake, H., Luo, W., et al. 2022, PASJ, 74, 421

    2022

  20. [28]

    2023, Physical Review D, 108, 123518 LSST Science Collaboration, Abell, P

    Li, X., Zhang, T., Sugiyama, S., et al. 2023, Physical Review D, 108, 123518 LSST Science Collaboration, Abell, P . A., Allison, J., et al . 2009, ArXiv e-prints, arXiv:0912.0201

    2023 arXiv

  21. [29]

    J., Heymans, C., Lombriser, L., et al

    Mead, A. J., Heymans, C., Lombriser, L., et al. 2016, MNRAS, 4 59, 1468

    2016

  22. [30]

    J., Peacock, J

    Mead, A. J., Peacock, J. A., Heymans, C., Joudaki, S., & Heave ns, A. F. 2015, MNRAS, 454, 1958

    2015

  23. [31]

    2023, Physica l Review D, 108, 123517

    Miyatake, H., Sugiyama, S., Takada, M., et al. 2023, Physica l Review D, 108, 123517

    2023

  24. [32]

    2018, PASJ, 7 0, 70

    Namekata, D., Iwasawa, M., Nitadori, K., et al. 2018, PASJ, 7 0, 70

    2018

  25. [33]

    2021, Jour nal of Cosmology and Astroparticle Physics, 2021, 067

    Nicola, A., García-García, C., Alonso, D., et al. 2021, Jour nal of Cosmology and Astroparticle Physics, 2021, 067

    2021

  26. [34]

    2020, Journal of C osmology and Astroparticle Physics, 2020, 044

    Nicola, A., Alonso, D., Sánchez, J., et al. 2020, Journal of C osmology and Astroparticle Physics, 2020, 044

    2020

  27. [35]

    2026, ArXiv e-pr int, arXiv:2605.28581

    Nishimichi, T., Tanaka, S., & Y oshikawa, K. 2026, ArXiv e-pr int, arXiv:2605.28581

    2026 arXiv

  28. [36]

    2014, MNRAS, 444, 147

    Oguri, M. 2014, MNRAS, 444, 147

    2014

  29. [37]

    2017, PASJ, 70, S20 Planck Collaboration, Ade, P

    Oguri, M., Lin, Y .-T., Lin, S.-C., et al. 2017, PASJ, 70, S20 Planck Collaboration, Ade, P . A. R., Aghanim, N., et al. 2016 , A&A, 594, A13 Planck Collaboration, Aghanim, N., Akrami, Y ., et al. 2020, A&A, 641, A6

    2017

  30. [38]

    M., Dalal, R., Zhang, T., et al

    Rau, M. M., Dalal, R., Zhang, T., et al. 2023, MNRAS, 524, 5109

    2023

  31. [39]

    2025, A&A, 699, A1 24

    Reischke, R., Unruh, S., Asgari, M., et al. 2025, A&A, 699, A1 24

    2025

  32. [40]

    J., Finkbeiner, D

    Schlegel, D. J., Finkbeiner, D. P ., & Davis, M. 1998, ApJ, 500 , 525

    1998

  33. [41]

    2015, MNRAS, 453, 30 44

    Shirasaki, M., Hamana, T., & Y oshida, N. 2015, MNRAS, 453, 30 44

    2015

  34. [42]

    2023, Physical R eview D, 108, 123521

    Sugiyama, S., Miyatake, H., More, S., et al. 2023, Physical R eview D, 108, 123521

    2023

  35. [43]

    2017, ApJ, 8 50, 24

    Takahashi, R., Hamana, T., Shirasaki, M., et al. 2017, ApJ, 8 50, 24

    2017

  36. [44]

    2018, PASJ, 70, S 9

    Tanaka, M., Coupon, J., Hsieh, B.-C., et al. 2018, PASJ, 70, S 9

    2018

  37. [45]

    A., & Ishak, M

    Troxel, M. A., & Ishak, M. 2015, Phys. Rep., 558, 1

    2015

  38. [46]

    H., Stölzner, B., Asgari, M., et al

    Wright, A. H., Stölzner, B., Asgari, M., et al. 2025, A&A, 703 , A158

    2025

Pith tools

Reviewed August 8, 2026 · model on record in the stance chip above.