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Sample Variance Cancellation for Future Spectroscopic Surveys

T0 review · 4 major / 5 minor · reviewed 2026-08-10 · deepseek-v4-flash

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Pith's one-line read A second, clean galaxy tracer can cancel sample variance and expose hidden angular clustering dependence in Lyman-alpha emitters.

desk verdict A solid multi-tracer methods paper for diagnosing unknown angular clustering in LAEs; the packaged protocol is new and the derivations are careful, but the clean-tracer assumption and idealized mocks mean the quoted errorbars are conditional. read the letter →

arxiv 2608.07339 v1 pith:7NHGKJVM submitted 2026-08-07 astro-ph.CO

James M. Sullivan , Martin White This is my paper · ORCID
classification astro-ph.CO
keywords samplevariancecancellationmulti-tracergalaxyclusteringLyman-alphaemittersradiativetransferredshift-spacedistortionsquadraticestimatoroptimalfilterhigh-redshiftspectroscopicsurveys
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

High-redshift surveys of Lyman-$\alpha$ emitters (LAEs) may carry an angular clustering anisotropy from the radiative transfer of Ly$\alpha$ photons that linear theory does not predict, and if ignored it can bias growth-of-structure constraints. The paper argues that in a linear, Gaussian model this unknown angular dependence can be pinned down statistically rather than modeled astrophysically, provided a second tracer such as Lyman-break galaxies is available in the same volume and is free of the effect. Using sample-variance cancellation, the authors derive a three-step procedure: a conditional field-level reconstruction to test whether the assumed model is misspecified, an optimal Legendre-polynomial filter to recover the functional form of the angular dependence, and a corrected quadratic estimator to measure its amplitude with quantified uncertainty. Fisher forecasts indicate that even a modest 100 deg$^2$ pilot survey with LAEs and LBGs can constrain the simplest radiative-transfer parameter significantly better than LAEs alone when the model complexity is unknown. If correct, the approach gives observers a data-driven way to diagnose and remove unknown angular systematics before cosmological parameter inference.

What carries the argument

The load-bearing mechanism is multi-tracer sample-variance cancellation: two galaxy fields that trace the same underlying matter modes have a cross-correlation coefficient $r_{12}^2$ that approaches unity when shot noise and cross-stochasticity are small, so the residual field $r(\mu)=\hat\delta_g^{(1)}(\mu)-\alpha(\mu)\hat\delta_g^{(2)}(\mu)$ cancels the cosmic variance of shared modes and exposes any mismodeled angular dependence. The paper's three tools are built on this residual: the conditional normal distribution of Eq. (14) provides a field-level reconstruction whose error power spectrum $P_{\rm err}$ is $\mu$-flat when the model is right and rises at high $\mu$ when it is wrong; the optimal filter $\alpha(\mu)=\sum_\ell c_\ell L_\ell(\mu)$ minimizes the weighted residual in a Legendre basis; and the quadratic estimator uses the covariance derivatives $C_{,g}=2(b^{(2)}\mu^2+g\mu^4)P_m$ and $C_{,gg}=2\mu^4 P_m$ to estimate the RT amplitude with corrections for the parameter's quadratic entry into the covariance.

What would settle it

In a Gaussian mock at the paper's pilot densities, inject a large radiative-transfer amplitude (e.g. $g=5f$) into the LAE field only, keeping the LBG field exactly on the assumed linear model, and run the conditional reconstruction of Section III and the quadratic estimator of Section V; the paper's claim predicts a significant high-$\mu$ excess in the residual error power spectrum and an unbiased recovery of the injected amplitude within the quoted uncertainty, and a failure to see either would contradict the claim.

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Extended reading notes

Core claim

Within the restricted setting of linear, Gaussian tracer fields, the paper claims that the ratio of the two tracers' cross-spectrum to the clean tracer's auto-spectrum samples the same underlying cosmological modes, so the difference between the observed LAE field and a reconstruction from the LBG field is free of sample variance. Writing the LAE effective bias as $K^{(2)}(\mu)=b^{(2)}+g\mu^2$ (with optional higher $g_{2n}\mu^{2n}$ terms) and the LBG bias as $K^{(1)}(\mu)=b^{(1)}+f\mu^2$, the conditional distribution $\delta_g^{(2)}|\delta_g^{(1)}$ has mean $(\hat P_{12}/\hat P_{11})\,\hat\delta_g^{(1)}$ and covariance $\hat P_{22}-\hat P_{12}^2/\hat P_{11}$. A reconstruction residual with significant excess power at high $\mu$ signals that the assumed $g=f$ model is wrong. The paper then solves for the Legendre coefficients $c_\ell$ of an optimal filter $\alpha(\mu)=\sum_\ell c_\ell L_\ell(\mu)$ that minimizes the residual error power, and constructs a quadratic estimator with a parameter-dependent bias correction that recovers $g$ with near-Cramér–Rao variance in the multi-tracer case. Gaussian mocks at pilot number densities show the procedure identifies a large injected RT effect, and the multi-tracer estimator is less biased and closer to the bound than the single-tracer estimator.

Load-bearing premise

The method assumes the second tracer (the 'clean' population, e.g. Lyman-break galaxies) has no trace of the angular dependence being sought, has a perfectly known $\mu$-dependence $b^{(1)}+f\mu^2$, and has negligible cross-stochasticity with the LAEs; if the clean tracer is itself contaminated or its transfer function is mis-modeled, the diagnostics will attribute that contamination to the LAEs.

Editorial extensions

If this is right

  • A modest pilot survey of about 100 deg$^2$ can constrain the simplest radiative-transfer amplitude $g_2$ usefully even when $g_4$ and $g_6$ terms are marginalized over, whereas an LAE-only survey loses most of that constraining power.
  • The conditional-field reconstruction provides a model-misspecification test whose residual error power spectrum is flat in $\mu$ for a correct model and rises at high $\mu$ for a wrong one, so an observer can decide whether the fiducial angular model is adequate before estimating parameters.
  • The optimal filter recovers the relative angular transfer function between the two tracers with error power near the shot-noise floor, giving a model-agnostic measurement of the functional form without assuming a specific RT model.
  • The corrected quadratic estimator removes the leading bias and variance error caused by the RT parameter entering the covariance quadratically, bringing the multi-tracer uncertainty within roughly a percent of the Cramér–Rao bound.
  • Because the machinery applies to any angular dependence, not only Ly$\alpha$ radiative transfer, the same pipeline can diagnose other unmodeled line-of-sight systematics in 3D clustering data.

Reading between the lines

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

  • The paper leaves implicit that the conditional-reconstruction residual can serve as a per-$(k,\mu)$ goodness-of-fit map; such a map would show which scales and line-of-sight angles drive a model failure and could guide where an effective-field-theory bias expansion needs new operators.
  • Because the gain over single-tracer analyses grows roughly as $(1-r_{12}^2)^{-2}$, the real-world payoff depends on how small the LAE–LBG cross-stochasticity actually is; a targeted measurement in existing surveys would decide how much of the promised volume boost is available.
  • The same pipeline could be run on other tracer pairs, such as emission-line and continuum galaxies at lower redshift, to search for unknown angular selection effects rather than radiative transfer.
  • A natural stress test is the quasi-linear regime: the paper assumes Gaussianity, and at higher $k$ nonlinear evolution and non-Poisson stochasticity will violate that assumption, so applying the reconstruction to field-level effective-field-theory mocks would quantify how much sensitivity survives.
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Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

4 major / 5 minor

Summary. The paper proposes a three-step, multi-tracer strategy for detecting, characterizing, and estimating an unknown angular (μ-dependent) clustering signal, motivated by possible Lyman-α radiative-transfer (RT) effects in LAE samples. Step 1 (Sec. III) uses the conditional mean of the LAE field given a clean tracer (e.g., LBGs) to test for model misspecification. Step 2 (Sec. IV) estimates the functional form of the angular dependence through an optimal, Legendre-expanded filter. Step 3 (Sec. V) derives a quadratic estimator, with corrections for the nonlinear dependence of the covariance on the RT amplitude, to constrain that amplitude. The methods are demonstrated on linear Gaussian mocks and supplemented by Fisher forecasts for pilot and Stage-5 survey configurations, and by a simulation-based estimate of the LAE-LBG cross-stochasticity in Appendix A.

Significance. If validated, the framework would be a useful contribution to systematics mitigation for high-redshift spectroscopic surveys, showing how multi-tracer sample-variance cancellation can be applied at the field level to an unknown angular clustering component. The paper includes detailed derivations of the conditional-density test, the optimal filter, and the quadratic-estimator corrections, and it verifies the estimators' bias and variance behavior with Monte Carlo realizations. The use of EFT-based simulation measurements for cross-stochasticity (Appendix A) is a concrete strength. However, the demonstrations are deliberately idealized: they use linear Gaussian mocks, rely on a perfectly known clean-tracer μ-dependence, and, in the central QE demonstration, marginalize no other parameters. The headline claims in the abstract are therefore conditional in ways that the abstract does not fully convey. These gaps are fixable with additional robustness tests and careful rephrasing, so the paper is a strong candidate for major revision rather than rejection.

major comments (4)
  1. [Sec. V C / Fig. 7] The abstract's claim 3 ('the value of its amplitude with an uncertainty') is not supported as stated: the quadratic-estimator demonstration marginalizes only g itself, while bias, growth rate, and the power-spectrum shape are held fixed. The paper explicitly notes (Sec. V C) that uncertainties in bias and cosmological parameters are neglected and that the absolute errorbars should not be interpreted at face value. Because the LBG field's μ-dependence is assumed to be perfectly known as b^(1)+f μ^2, any error in b^(1) or f enters the conditional mean in Eq. (14) and the QE weighting in Eq. (36) and can masquerade as an RT signal. A few-percent bias error is typical for LBGs at z∼3, so this is a load-bearing limitation. I request either a demonstration of robustness to bias/growth-rate offsets (e.g., a Fisher or Monte Carlo run with b^(1) and f marginalized) or a revision of the abstract and conclusions to make the conditional nature of the uncertainty explicit.
  2. [Sec. III, Fig. 5] The model-misspecification test is demonstrated only for g=5f, which is far larger than the RT amplitudes suggested by the simulation literature cited in the Introduction (where the effect is described as numerically small). The paper states that for g very close to f and noisy data one might jump directly to Sec. IV, but no calculation or figure shows the detection significance of the Sec. III test as a function of g/f for the pilot or S5 configurations. Without such a sensitivity curve, the 'rapidly identify' claim is not quantitatively supported. Please add a figure or table presenting, for a few realistic g/f values (e.g., 1.1, 1.3, 2), the significance of the residual power in the high-μ bins as a function of survey volume or number density.
  3. [Sec. IV, Eq. (24)] The optimal-filter step is restricted to a Legendre basis with ℓmax=2, and Fig. 6 shows that the true angular dependence in the linear Kaiser model is not quadratic; the reconstruction does not saturate the shot-noise floor. The claim that the method determines 'the functional form itself' is therefore only meaningful within the assumed basis. The paper does not provide a model-selection rule for choosing ℓmax (or for comparing non-polynomial forms), and the subsequent quadratic estimator in Sec. V assumes the selected model is correct. The error on the amplitude in Sec. V therefore does not include functional-form uncertainty. I recommend adding a discussion of model selection and, if possible, a demonstration with an RT form outside the fitted basis (e.g., a non-polynomial μ-dependence).
  4. [Sec. II A vs Sec. V C] There is a tension between the Fisher forecasts of Sec. II A, which marginalize over linear bias, σ8, and higher g_n, and the QE demonstration of Sec. V C, which marginalizes only g. Since the abstract's claims are made without distinguishing these settings, the reader may infer that the large multi-tracer gains shown in Figs. 1–3 apply to the final amplitude estimate. Please clarify that the large multi-tracer gains apply to the marginalized forecasts, while the QE demonstration shows a more modest gain (approximately 20% in Fig. 7) under conditional assumptions.
minor comments (5)
  1. [Sec. III, Eq. (15)] In the sentence preceding Eq. (15), 'the factor K^(1) carries the g dependence' appears to be a typo: the g dependence enters through K^(2), the LAE effective bias, not K^(1).
  2. [References] Refs. [10] and [11] are identical entries (same authors, title, journal, year, and arXiv number); one should be removed or replaced with the correct reference.
  3. [Sec. V C] The section heading 'Optimmally recovering R T amplitude' contains a typo ('Optimmally'); it should be 'Optimally recovering RT amplitude'.
  4. [Abstract] The phrase 'with an uncertainty' in claim 3 is vague; consider specifying that the uncertainty is conditional on the assumed clean-tracer model and the chosen functional form.
  5. [Fig. 6] The right panel's legend is difficult to read because the line styles for different μ bins are not clearly distinguished; consider adding explicit μ-bin labels or a table of values.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the paper's estimators are derived from the stated linear-Gaussian model, and the relevant self-citation supplies external simulation evidence for a nuisance amplitude.

full rationale

The central derivation chain is self-contained. Section III constructs the conditional density from the Gaussian conditional mean, Eq. (14), P(δ_g^(2)|δ_g^(1)) = N(P12/P11 δ_g^(1), P22 - P12^2/P11), and uses it as a misspecification diagnostic; the test compares data to the model, so the model is not defined in terms of the outcome. Section IV derives the optimal filter by minimizing the weighted residual (Eqs. 16-21); the recovered Legendre coefficients are the least-squares fit to the relative transfer function, and the paper labels them as an estimate, not as an independent prediction. Section V derives the quadratic estimator from the Gaussian likelihood and corrects its bias and variance (Eqs. 26-35); the demonstration on Gaussian mocks with a known input g tests internal consistency of the estimator, which is a standard validation rather than circularity. The relevant self-citation, Ref. [29], is used in Appendix A to argue that LAE-LBG cross-stochasticity is small; it is an external, falsifiable simulation/EFT study of a nuisance parameter, not the target of the paper's claims, and the text notes results are insensitive once cross-noise is 2-3 times below shot noise. Section V C explicitly states that 'we neglect realistic observational effects ... and uncertainties in the bias and cosmological parameters, so the absolute errorbars should be considered optimistic and are not to be interpreted at face value.' That is a stated limitation on the error budget, but it does not make any derived quantity equivalent to an input by construction. No fitted parameter is renamed as a prediction, no uniqueness theorem from prior work is imported, and no known result is merely relabeled. The method's restriction to the linear-Gaussian model and its reliance on a clean second tracer are assumptions of the hypothetical scenario, not circular reductions.

Assumptions & free parameters 0 free parameters · 5 assumptions · 0 invented entities

The paper fits no free parameters and introduces no new physical entities. Its central claim depends on the Gaussian approximation, the existence of a clean second tracer, and negligible cross-stochasticity, all stated as modeling assumptions rather than derived results.

assumptions (5)
  • domain assumption The overdensity fields are zero-mean Gaussian random fields on large scales.
    Used throughout Sections II, III, and V to derive the conditional distribution, Fisher matrix, and quadratic estimator. The paper states 'we assume the stochastic field can be approximated as Gaussian' in Section III.
  • domain assumption The clean tracer (LBG) has known angular dependence (b + f μ^2) and is immune to the RT effect.
    Entered in Section II: 'the presence of a second tracer, assumed to be immune to the effects under consideration'. If false, the diagnostics misattribute the angular dependence.
  • domain assumption Cross-stochasticity between LAEs and LBGs is negligible.
    Justified in Appendix A using Ref 29's Astrid/EFT fits, showing an order-of-magnitude suppression. The forecasts in Section II A set nbar12 = -10 nbarLAE.
  • domain assumption The linear bias expansion δg = b δm + bθ θ with bθ = g for LAEs and f for LBGs.
    Assumed in Section II, Eq (1) and throughout the model.
  • domain assumption Cosmology is held fixed at Planck 2015.
    The forecasts use a fiducial Planck 2015 cosmology, stated in Section II A.

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Cite this review

Pith. "Pith review of Sample Variance Cancellation for Future Spectroscopic Surveys." pith.science (2026). https://pith.science/paper/7NHGKJVM

@misc{pith2026260807339,
  author       = {Pith},
  title        = {Pith review of: Sample Variance Cancellation for Future Spectroscopic Surveys},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/7NHGKJVM}},
  note         = {Machine review of arXiv:2608.07339}
}
abstract

High-redshift spectroscopic galaxy surveys will be the scientific engines of the next generation of large-scale structure cosmology. The clustering signal of high redshift, star-forming Lyman-$\alpha$ emitters (LAEs) will be of key importance for obtaining high-redshift constraints on the growth of structure and redshift-space distortions. The complex radiative transfer (RT) of Lyman-$\alpha$ photons alters the symmetry group respected by the overdensity field constructed from these galaxies, and so the observed large-scale clustering of LAEs may have an angular dependence that differs significantly from that of linear theory, possibly biasing inference of cosmological parameters. While such an effect has been seen in simulations, its amplitude in nature and its detailed form remains unclear. In the restricted context of a linear, Gaussian model, we outline a procedure for pinning down the type and amplitude of such changes in angular dependence on large scales due to unknown RT or a more general unmodeled angular effect in the hypothetical scenario in which an observer is presented with LAE data containing such an effect. We show that if a second tracer without the modified angular dependence is available for cross correlation with the LAEs at the same redshifts (e.g., Lyman-break galaxies), then, with a high redshift survey of modest size, it is possible to rapidly identify: 1) the presence of a nontrivial angular functional form of radiative transfer (by a conditional field-level realization), 2) the functional form itself (with an optimal filter that we derive), and 3) the value of its amplitude with an uncertainty (via an adaptation of the standard quadratic estimator). Such sample-variance-cancellation strategies therefore provide a statistical solution to unknown astrophysical or systematic angular clustering dependence, including from RT.

Figures

Figures reproduced from arXiv: 2608.07339 by the authors.

Figure 2
Figure 2. FIG. 2. Similar to Fig. 1, but as a function of angular sky [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3. Similar to Fig. 1, but as a function of minimum [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗
Figure 4
Figure 4. shows the conditional density procedure in ac￾tion. Working in a 250 h −1Mpc periodic box, we adopt 80% of the S5 survey number densities and linear bias model described in Section II with b (1) = 3.5, b (2) = 2.0 at z = 3 for the purposes of this demonstration. For illus￾tration, we have dramatically increased g such that verti￾cal (up-and-down) streaking due to line-of-sight cluster￾ing enhancement is readily visi… view at source ↗
Figures from the paper (4 more)
Figure 5
Figure 5. Figure 5: makes this comparison slightly more quanti￾tative, showing that the error power spectrum (the power of the residual field between the conditional density re￾construction and the true LAE field) exhibits strong µ dependence at higher µ values. Specifically, these are th…
Figure 6
Figure 6. Figure 6: shows the optimal filter for the linear LAE￾LBG mock configuration described in Section III, but 11 The assumption of a theoretical model will introduce an error in cℓ, which can be mitigated by adding more data. However, this error should be small for RT models that a…
Figure 7
Figure 7. Figure 7: shows the recovery of the value of δg for an ar￾ray of initial guesses for g (as we might anticipate from particularly noisy data). We show both the single-tracer estimates and multi-tracer estimates before and after ap￾plying the corrections above. To assess unbiasedn…
Figure 8
Figure 8. Figure 8: shows the error power spectrum Perr in real space for simulated LBGs and LAEs in the Astrid simu￾lation at z = 3. Specifically, these are error power spec￾tra computed from the EFT model fits of Ref. [29] for the ODIN and CARS LAE and LBG samples, respec￾tively. Notabl…

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Reference graph

Works this paper leans on

45 extracted references · 6 canonical work pages

  1. [1]

    Collaboration, A

    D. Collaboration, A. Aghamousa, J. Aguilar, S. Ahlen, S. Alam, L. E. Allen et al.,The desi experiment part i: Science,targeting, and survey design, 2016

    work page 2016

  2. [2]

    Collaboration, A

    D. Collaboration, A. Aghamousa, J. Aguilar, S. Ahlen, S. Alam, L. E. Allen et al.,The desi experiment part ii: Instrument design, 2016

    work page 2016

  3. [3]

    Laureijs, J

    R. Laureijs, J. Amiaux, S. Arduini, J. L. Augu` eres, J. Brinchmann, R. Cole et al.,Euclid definition study report, 2011

    work page 2011

  4. [4]

    Amendola, S

    L. Amendola, S. Appleby, A. Avgoustidis, D. Bacon, T. Baker, M. Baldi et al.,Cosmology and fundamental physics with the euclid satellite,Living Reviews in Relativity21(2018)

    2018

  5. [5]

    Takada, R

    M. Takada, R. S. Ellis, M. Chiba, J. E. Greene, H. Aihara, N. Arimoto et al.,Extragalactic science, cosmology, and Galactic archaeology with the Subaru Prime Focus Spectrograph, PASJ66(2014) R1 [1206.0737]

    arXiv 2014

  6. [6]

    Bacon, V

    R. Bacon, V. Maineiri, S. Randich, A. Cimatti, J.-P. Kneib, J. Brinchmann et al.,WST – Widefield Spectroscopic Telescope: Motivation, science drivers and top-level requirements for a new dedicated facility,arXiv e-prints(2024) arXiv:2405.12518 [2405.12518]

    arXiv 2024

  7. [7]

    Besuner, A

    R. Besuner, A. Dey, A. Drlica-Wagner, H. Ebina, G. Fernandez Moroni, S. Ferraro et al.,The Spectroscopic Stage-5 Experiment,arXiv e-prints(2025) arXiv:2503.07923 [2503.07923]

    arXiv 2025

  8. [8]

    Kaiser,Clustering in real space and in redshift space, MNRAS227(1987) 1

    N. Kaiser,Clustering in real space and in redshift space, MNRAS227(1987) 1

    1987

Show all 45 references
  1. [9]

    Zheng, R

    Z. Zheng, R. Cen, H. Trac and J. Miralda-Escud´ e, Radiative Transfer Modeling of LyαEmitters. II. New Effects on Galaxy Clustering, ApJ726(2011) 38 [1003.4990]

    2011 arXiv

  2. [11]

    Behrens, C

    C. Behrens, C. Byrohl, S. Saito and J. C. Niemeyer, The impact of Lyman-αradiative transfer on large-scale clustering in the Illustris simulation, A&A614(2018) A31 [1710.06171]

    2018 arXiv

  3. [12]

    Gurung-L´ opez,´A

    S. Gurung-L´ opez,´A. A. Orsi, S. Bonoli, C. M. Baugh and C. G. Lacey,Lyαemitters in a cosmological volume - I. The impact of radiative transfer, MNRAS486 (2019) 1882 [1807.00006]

    2019 arXiv

  4. [13]

    Momose, K

    R. Momose, K. Shimasaku, K. Nagamine, I. Shimizu, N. Kashikawa, M. Ando et al.,Catch Me if You Can: Biased Distribution of Lyα-emitting Galaxies according to the Viewing Direction, ApJ912(2021) L24 [2104.10580]

    2021 arXiv

  5. [14]

    Khoraminezhad, S

    H. Khoraminezhad, S. Saito, M. Gronke and C. Byrohl, Simulating realistic Lyman-αemitting galaxies including the effect of radiative transfer,arXiv e-prints(2025) arXiv:2507.16707 [2507.16707]

    2025

  6. [15]

    Gurung-L´ opez,´A

    S. Gurung-L´ opez,´A. A. Orsi, S. Bonoli, N. Padilla, C. G. Lacey and C. M. Baugh,Lyαemitters in a cosmological volume II: the impact of the intergalactic medium, MNRAS491(2020) 3266 [1904.04274]

    2020 arXiv

  7. [16]

    Seljak,Extracting Primordial Non-Gaussianity without Cosmic Variance, Phys

    U. Seljak,Extracting Primordial Non-Gaussianity without Cosmic Variance, Phys. Rev. Lett.102(2009) 021302 [0807.1770]

    2009 arXiv

  8. [17]

    McDonald and U

    P. McDonald and U. Seljak,How to evade the sample variance limit on measurements of redshift-space distortions, J. Cosmology Astropart. Phys.2009(2009) 007 [0810.0323]

    2009 arXiv

  9. [18]

    L. R. Abramo, L. F. Secco and A. Loureiro,Fourier analysis of multitracer cosmological surveys, MNRAS 455(2016) 3871 [1505.04106]

    2016 arXiv

  10. [19]

    Rubiola, S

    A. Rubiola, S. Camera and N. Fornengo,Wiener filtering and multi-tracer techniques for dark matter cross-correlations between gamma-ray emission and galaxy catalogs,arXiv e-prints(2025) arXiv:2508.02160 [2508.02160]

    2025

  11. [20]

    Mergulh˜ ao, H

    T. Mergulh˜ ao, H. Rubira, R. Voivodic and L. R. Abramo,The effective field theory of large-scale structure and multi-tracer, J. Cosmology Astropart. Phys.2022(2022) 021 [2108.11363]

    2022 arXiv

  12. [21]

    Rubira and F

    H. Rubira and F. Conteddu,Multi-tracer beyond linear theory, J. Cosmology Astropart. Phys.2025(2025) 111 [2504.18245]

    2025

  13. [22]

    J. M. Sullivan, T. Prijon and U. Seljak,Learning to concentrate: multi-tracer forecasts on local primordial non-Gaussianity with machine-learned bias, J. Cosmology Astropart. Phys.2023(2023) 004 [2303.08901]

    2023 arXiv

  14. [23]

    Barreira and E

    A. Barreira and E. Krause,Towards optimal and robust f NL constraints with multi-tracer analyses, J. Cosmology Astropart. Phys.2023(2023) 044 [2302.09066]

    2023 arXiv

  15. [24]

    Fondi, L

    E. Fondi, L. Verde, F. Villaescusa-Navarro, M. Baldi, W. R. Coulton, G. Jung et al.,Taming assembly bias for primordial non-Gaussianity, J. Cosmology Astropart. Phys.2024(2024) 048 [2311.10088]

    2024 arXiv

  16. [25]

    Kokron, S.-F

    N. Kokron, S.-F. Chen, M. White, J. DeRose and M. Maus,Accurate predictions from small boxes: variance suppression via the Zel’dovich approximation, J. Cosmology Astropart. Phys.2022(2022) 059 [2205.15327]

    2022 arXiv

  17. [26]

    Desjacques, D

    V. Desjacques, D. Jeong and F. Schmidt,The galaxy power spectrum and bispectrum in redshift space, J. Cosmology Astropart. Phys.2018(2018) 035 [1806.04015]

    2018 arXiv

  18. [27]

    White, A

    M. White, A. Raichoor, A. Dey, L. H. Garrison, E. Gawiser, D. Lang et al.,The clustering of Lyman Alpha Emitting galaxies at z=2–3, J. Cosmology Astropart. Phys.2024(2024) 020 [2406.01803]. 14

    2024 arXiv

  19. [28]

    Ruhlmann-Kleider, C

    V. Ruhlmann-Kleider, C. Y` eche, C. Magneville, H. Coquinot, E. Armengaud, N. Palanque-Delabrouille et al.,High redshift LBGs from deep broadband imaging for future spectroscopic surveys, J. Cosmology Astropart. Phys.2024(2024) 059 [2404.03569]

    2024 arXiv

  20. [29]

    J. M. Sullivan, C. Cuesta-Lazaro, M. M. Ivanov, Y. Ni, S. Bose, B. Hadzhiyska et al.,High-redshift Millennium and Astrid galaxies in effective field theory at the field level,arXiv e-prints(2025) arXiv:2505.03626 [2505.03626]

    2025 arXiv

  21. [30]

    Planck Collaboration, P. A. R. Ade, N. Aghanim, M. Arnaud, M. Ashdown, J. Aumont et al.,Planck 2015 results. XIII. Cosmological parameters, A&A594 (2016) A13 [1502.01589]

    2016 arXiv

  22. [31]

    Tegmark, A

    M. Tegmark, A. J. S. Hamilton, M. A. Strauss, M. S. Vogeley and A. S. Szalay,Measuring the Galaxy Power Spectrum with Future Redshift Surveys, ApJ499(1998) 555 [astro-ph/9708020]

    1998 arXiv

  23. [32]

    A. J. S. Hamilton,Towards optimal measurement of power spectra - I. Minimum variance pair weighting and the Fisher matrix, MNRAS289(1997) 285 [astro-ph/9701008]

    1997 arXiv

  24. [33]

    Tegmark, A

    M. Tegmark, A. N. Taylor and A. F. Heavens, Karhunen-Lo` eve Eigenvalue Problems in Cosmology: How Should We Tackle Large Data Sets?, ApJ480 (1997) 22 [astro-ph/9603021]

    1997 arXiv

  25. [34]

    J. R. Bond, A. H. Jaffe and L. Knox,Estimating the power spectrum of the cosmic microwave background, Phys. Rev. D57(1998) 2117 [astro-ph/9708203]

    1998 arXiv

  26. [35]

    O. H. E. Philcox,Cosmology without window functions: Quadratic estimators for the galaxy power spectrum, Phys. Rev. D103(2021) 103504 [2012.09389]

    2021 arXiv

  27. [36]

    Seljak, G

    U. Seljak, G. Aslanyan, Y. Feng and C. Modi,Towards optimal extraction of cosmological information from nonlinear data, J. Cosmology Astropart. Phys.2017 (2017) 009 [1706.06645]

    2017 arXiv

  28. [37]

    Ebina, M

    H. Ebina, M. J. White, R. Zhou, A. Dey, D. Schlegel, J. N. Aguilar et al.,The 3D clustering of Lyman Alpha Emitters measured with DESI,arXiv e-prints(2026) arXiv:2606.24852 [2606.24852]

    2026 arXiv

  29. [38]

    Ebina and M

    H. Ebina and M. White,Cosmology before noon with multiple galaxy populations, J. Cosmology Astropart. Phys.2024(2024) 052 [2401.13166]

    2024 arXiv

  30. [39]

    de Belsunce, J

    R. de Belsunce, J. M. Sullivan and P. McDonald, Compressed 3D Lyman-αforest bispectrum, Phys. Rev. D113(2026) 063550 [2510.23597]

    2026 arXiv

  31. [40]

    de Belsunce, M

    R. de Belsunce, M. M. Ivanov, J. M. Sullivan, K. Akitsu and S.-F. Chen,Modeling the Cosmological Lyman-α Forest at the Field Level, Phys. Rev. Lett.136(2026) 101001 [2507.00284]

    2026 arXiv

  32. [41]

    M. M. Ivanov,Lyman alpha forest power spectrum in effective field theory, Phys. Rev. D109(2024) 023507 [2309.10133]

    2024 arXiv

  33. [42]

    Chudaykin and M

    A. Chudaykin and M. M. Ivanov,Lyman alpha forest-halo cross-correlations in effective field theory, Phys. Rev. D111(2025) 083515 [2501.04770]

    2025 arXiv

  34. [43]

    S.-F. Chen, Z. Vlah and M. White,The Lyαforest flux correlation function: a perturbation theory perspective, J. Cosmology Astropart. Phys.2021(2021) 053 [2103.13498]

    2021 arXiv

  35. [44]

    P. McDonald,Toward a Measurement of the Cosmological Geometry at z ˜2: Predicting LyαForest Correlation in Three Dimensions and the Potential of Future Data Sets, ApJ585(2003) 34 [astro-ph/0108064]

    2003 arXiv

  36. [45]

    Seljak,Bias, redshift space distortions and primordial nongaussianity of nonlinear transformations: application to Ly-αforest, J

    U. Seljak,Bias, redshift space distortions and primordial nongaussianity of nonlinear transformations: application to Ly-αforest, J. Cosmology Astropart. Phys.2012(2012) 004 [1201.0594]

    2012 arXiv

  37. [46]

    Baldauf, U

    T. Baldauf, U. Seljak, R. E. Smith, N. Hamaus and V. Desjacques,Halo stochasticity from exclusion and nonlinear clustering, Phys. Rev. D88(2013) 083507 [1305.2917]

    2013 arXiv

Pith tools

Reviewed August 10, 2026 · model on record in the stance chip above.