Primordial non-Gaussianity -- the effects of relativistic and wide-angle corrections to the power spectrum

Roy Maartens; S\^ecloka L. Guedezounme; Sheean Jolicoeur

REVIEW 3 major objections 5 minor 5 cited by

Primordial non-Gaussianity -- the effects of relativistic and wide-angle corrections to the power spectrum

T0 review · 3 major / 5 minor · reviewed 2026-08-11 · deepseek-v4-flash

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Pith's one-line read This paper claims that adding the quadrupole of the galaxy power spectrum, together with leading-order wide-angle and relativistic corrections, improves forecasts of the local primordial non-Gaussianity parameter $f_{\mathrm{NL}}$ by…

desk verdict The quadrupole precision gain is the durable result; the SKAO2 'negligible shift' is a fragile near-cancellation the authors themselves only claim for their truncated model. read the letter →

arxiv 2412.06553 v2 pith:HS2JVESG submitted 2024-12-09 astro-ph.CO

Sêcloka L. Guedezounme , Sheean Jolicoeur , Roy Maartens This is my paper · ORCID

classification astro-ph.CO

keywords primordialnon-Gaussianityf_NLgalaxypowerspectrumwide-anglecorrectionsrelativisticlensingconvergenceparameterforecastSKAO2

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 sets out to show that next-generation galaxy surveys can measure the local primordial non-Gaussianity parameter $f_{\mathrm{NL}}$ far more precisely if the Fourier galaxy power spectrum is modelled with the quadrupole and with relativistic and wide-angle corrections to the standard flat-sky Newtonian spectrum. Using SKAO2 and MegaMapper survey specifications, the authors find that adding the quadrupole to the monopole improves the marginalised error on $f_{\mathrm{NL}}$ from $\sigma(f_{\mathrm{NL}})=5.21$ to $2.89$ (about 45%) for SKAO2 and from $1.49$ to $0.548$ (about 63%) for MegaMapper. They also quantify how much neglecting the corrections biases the estimated $f_{\mathrm{NL}}$: about $0.6\sigma$ for MegaMapper, while for SKAO2 the shift is negligible because non-integrated and integrated corrections nearly cancel. Because the corrections mimic the scale-dependent bias signature of local non-Gaussianity, the paper argues that future analyses should include them to avoid biased constraints.

What carries the argument

The central object is the leading-order corrected Fourier galaxy power spectrum $P_g = P^S_g + P^{\mathrm{NI}}_g + P^I_g$, expanded in the wide-angle parameter $1/(kr)$ and accurate to order $O(r^{-2}k^{-2},\, H^2k^{-2},\, r^{-1}Hk^{-2})$. $P^{\mathrm{NI}}$ contains the wide-angle, Doppler, and Sachs-Wolfe non-integrated corrections, while $P^I$ is built from the integrated kernel $K_{\mathrm{int}} = K_L + K_{\mathrm{TD}} + K_{\mathrm{ISW}}$, generated by lensing convergence, time-delay, and integrated Sachs-Wolfe effects. The machinery is completed by the monopole and quadrupole (the $\ell=0$ and $\ell=2$ angular moments) of this corrected spectrum, a Gaussian covariance between them, and the covariance-based shift formula $\delta f_{\mathrm{NL}} = -( {}^0F^{-1})_{f_{\mathrm{NL}}\alpha}\, {}^1F_{\alpha\varepsilon}\,\delta\varepsilon$ that quantifies the bias from using the standard instead of the corrected model.

What would settle it

Recompute the same two-survey forecasts with the full integrated correction including $L\times L$ and lensing-wide-angle terms and with cross-bin correlations (e.g., via a spherical Fourier-Bessel or angular power spectrum analysis); if the $f_{\mathrm{NL}}$ shift for SKAO2 becomes comparable to or larger than $0.1\sigma$, or the MegaMapper shift changes sign, then the leading-order cancellation is not robust.

Watch

Extended reading notes

Core claim

The discovery is that the quadrupole of the galaxy power spectrum is far more sensitive to wide-angle and relativistic corrections than the monopole, and that combining the correlated monopole and quadrupole dramatically tightens forecasts for local primordial non-Gaussianity. In the corrected model, $P_g = P^S_g + P^{\mathrm{NI}}_g + P^I_g$, where $P^{\mathrm{NI}}$ collects wide-angle, Doppler and Sachs-Wolfe terms and $P^I$ collects lensing convergence, time-delay and integrated Sachs-Wolfe terms; the paper finds that $P^{\mathrm{NI}}$ and $P^I$ have opposite signs on ultra-large scales and partially cancel. Using the monopole-quadrupole data vector with equal-volume redshift binning gives $\sigma(f_{\mathrm{NL}})=2.89$ for SKAO2 and $0.548$ for MegaMapper. Neglecting the corrections shifts $f_{\mathrm{NL}}$ by $0.614\sigma$ for MegaMapper but only $-0.001\sigma$ for SKAO2, with the authors warning that omitted higher-order integrated terms could make the SKAO2 cancellation partly artificial.

Load-bearing premise

The near-cancellation that makes the SKAO2 shift negligible depends on the assumption that the omitted higher-order integrated effects, such as lensing-lensing and lensing-wide-angle correlations and correlations between redshift bins, are small; if they are not, the cancellation could be an artifact.

Editorial extensions

If this is right

For SKAO2, the quadrupole-plus-monopole analysis improves $\sigma(f_{\mathrm{NL}})$ from 5.21 to 2.89, a 45% gain; for MegaMapper, from 1.49 to 0.548, a 63% gain.
Neglecting wide-angle and relativistic corrections biases the estimated $f_{\mathrm{NL}}$ by about $0.6\sigma$ for MegaMapper, so such surveys need the corrected model to avoid biased inference.
The non-integrated and integrated corrections partially cancel on ultra-large scales, and integrated Sachs-Wolfe plus time-delay effects are subdominant to lensing at $z\lesssim1$, making lensing the main integrated correction.
Equal-volume redshift binning, with 6 bins for SKAO2 and 3 for MegaMapper, gives the smallest $\sigma(f_{\mathrm{NL}})$ compared with other binning choices tested.

Reading between the lines

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

Editorial inference: The quoted precision gains likely overstate what a real analysis would achieve, because mode-coupling from wide-angle effects in the covariance is neglected; including it would widen errors but need not remove the relative gain from the quadrupole.
Editorial inference: Since the shift is sensitive to magnification bias $Q$ and evolution bias $E$, realistic uncertainties in these nuisance parameters could turn the predicted near-cancellation for SKAO2 into a non-negligible bias; the paper's fiducial amplitudes $Q_0=E_0=1$ are a sharp assumption.
Editorial inference: The omitted lensing-lensing correlation is not suppressed by powers of $H/k$, so on the ultra-large scales where local non-Gaussianity lives it might be as large as the leading integrated correction; a direct computation of $L\times L$ would be a decisive check.
Editorial inference: The same corrected-spectrum formalism could be applied to the bispectrum or to multi-tracer combinations, where relativistic corrections and the scale-dependent bias of non-Gaussianity enter differently and may break the degeneracy that causes the shift.

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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

Two things to know up front. The durable result is the precision gain: adding the quadrupole to the monopole improves σ(f_NL) by ~45% for SKAO2 and ~63% for MegaMapper, under the standard optimistic-Fisher caveats (no mode coupling, six parameters, no priors). The other headline — "negligible shift for SKAO2" — is a near-cancellation of two large opposite shifts (+0.51σ non-integrated, −0.50σ integrated). That is a statement about the truncated model, not a robustness result, and the authors say so in the abstract and in Section 5. Their honesty is the main reason I trust the paper.

What's new: the same group extends its own prior results — [35] gave the non-integrated monopole/dipole, [33] the integrated correction — to the quadrupole with both correction types, and turns it into concrete survey guidance: multipole choice, equal-volume binning, and the cost of ignoring corrections. Appendix B re-derives the integrated correction, survey inputs are tabulated, and the NI/I cancellation is a real observation. The math looks sound; the numerics are standard quadrature; the citations to [33,35] are the previous steps in the same derivation chain, not padding.

Soft spots, in order of importance:

1. The integrated correction keeps only I×S and S×I. The stress-test note says L×L is "not parametrically suppressed" because K_L has a piece with no positive power of k/H. I think that is the wrong metric: the lensing kernel is small in amplitude, so within-bin L×L is likely a few percent of L×S and will not move the cancellation much. The real gaps are cross-bin lensing correlations and lensing-wide-angle mixing, which a global-midpoint Fourier treatment cannot capture. The authors flag both, and note that the angular analyses [9,11] found larger shifts. The paper does not quantify how big the missing pieces might be, and that discrepancy is the strongest reason to treat the shift numbers as provisional.

2. The shifts are very sensitive to the magnification bias Q and evolution bias E, whose fiducial values carry O(1) uncertainty and which are free parameters in the forecast. The near-cancellation for SKAO2 looks fragile even within the model. The authors mention the sensitivity but do not show how δ(f_NL) moves with Q0, E0 — a referee should ask for that.

3. The absolute precision numbers are lower bounds by construction. I would quote the relative monopole-to-quadrupole gain, which is more robust, not σ(f_NL) = 0.55 for MegaMapper.

Minor: the optimal bin count (6 for SKAO2, 3 for MegaMapper) is chosen by minimizing σ(f_NL) on the same forecast. Mild selection effect, not a real flaw.

Bottom line: the paper deserves a serious referee. It is for anyone doing f_NL forecasts for SKAO2, MegaMapper, or similar, and for people working on relativistic power-spectrum corrections. For revision, I would want an order-of-magnitude estimate of the omitted terms, and the SKAO2 shift presented as "consistent with zero in our truncated model" rather than as a property of the real survey. Send it out — it is solid and it is honest.

Referee Report

3 major / 5 minor

Summary. This paper extends the leading-order Fourier-space galaxy power spectrum with wide-angle, Doppler/Sachs-Wolfe, and integrated lensing/time-delay/ISW corrections, following the framework of Refs. [33-35], and uses a Fisher forecast to assess the impact on local primordial non-Gaussianity constraints for SKAO2 and MegaMapper. The analysis keeps the monopole and quadrupole, uses equal-volume redshift bins selected by minimizing the forecast error, and computes the shift in f_NL when the corrections are neglected via a nested-model Fisher formula. The headline results are sigma(f_NL)=2.89 for SKAO2 and 0.548 for MegaMapper with the monopole+quadrupole combination, corresponding to improvements of about 45% and 63% over the monopole-only case, and shifts of -0.001 sigma (SKAO2) and 0.614 sigma (MegaMapper) when corrections are omitted. The paper explicitly warns that omitted terms, especially lensing-lensing correlations, may artificially suppress the shift.

Significance. If the quantitative claims hold, the paper makes a useful case that future spectroscopic surveys should include the quadrupole and the leading relativistic and wide-angle corrections when measuring f_NL. The integrated correction is re-derived in Appendix B rather than assumed, and the survey inputs (bias, magnification bias, evolution bias, number density) are specified in tables and fitting functions, which is a strength. The paper is also commendably explicit about its main approximations, including the truncation of the integrated correction and the neglect of mode coupling. However, the headline 'negligible shift for SKAO2' claim is sensitive to exactly those approximations, and the internal breakdown in Table 4 raises questions about the cancellation narrative.

major comments (3)

[Sec. 4, Table 4, Eq. (4.2)] Table 4 is internally inconsistent with an additive reading of the shift formula. For SKAO2, the NI and I entries are 0.513 and -0.498, whose sum is 0.015, but the NI+I entry is -0.001; for MegaMapper, the sum 0.410 + (-0.177) = 0.233 does not equal the quoted 0.614. Since Eq. (4.2) is linear in P_corr when the covariance is held fixed, either the shift calculation is nonlinear because the Fisher matrices or covariances are evaluated differently in the true and wrong models, in which case this must be stated explicitly, or the table entries are not the individual contributions of the two terms. In particular, the abstract and conclusion statement that MegaMapper shows 'partial cancellation' between integrated and non-integrated effects is not supported by the table, where the combined shift exceeds the NI-only shift. Please clarify the calculation and revise the interpretation accordingly.
[Sec. 1, Eq. (1.8); Sec. 2, Eq. (2.5); Sec. 5] The headline SKAO2 result that neglecting the corrections leaves f_NL unbiased is not established. The integrated correction in Eq. (1.8) is truncated to I x S + S x I, and the lensing-lensing (L x L) term is omitted. The lensing kernel in Eq. (2.5) contains a piece (the 1 - mu^2 term) with no positive power of k/H, so L x L is not suppressed by a positive power of k/H relative to the kept terms, as the authors themselves note in Sec. 5. Lensing-wide-angle and cross-bin lensing correlations are also omitted. Since the SKAO2 total shift is the small difference of two large opposite shifts (+0.513 and -0.498 in Table 4), a modest fractional change in P_I from the omitted terms could change the shift by O(0.1 sigma) or more. The paper's warning that the approximations 'may artificially suppress the shift' (abstract and Sec. 5) is appropriate, but the conclusion that the shift is negligible for SKAO2 should be presented as provisional within the truncated model unless bounds on the omitted terms are provided.
[Sec. 3, Eq. (3.1) and Fig. 9] The claimed precision improvements of about 45% and 63% rest on a Fisher forecast whose covariance ignores wide-angle mode coupling, which the paper acknowledges 'will lead to over-optimistic precision.' In addition, the number of equal-volume redshift bins is selected by minimizing sigma(f_NL) in the same Fisher forecast (Fig. 9), which introduces a selection effect that can bias the forecast low. The abstract and conclusion present the improvement percentages without these caveats. Please either soften the headline numbers or quantify how much of the improvement survives when mode coupling and bin-selection effects are incorporated.

minor comments (5)

[Sec. 5 vs Abstract] The Conclusion states improvements of about 40% and 60%, while the Abstract and Table 3 give about 45% and 63%; please harmonize these numbers.
[Sec. 4, Eq. (4.2)] The notation using superscripts 0 and 1 for the Fisher matrices is confusing; please define explicitly which matrix is evaluated at epsilon=0 and which at epsilon=1, and state whether the covariance is held fixed in the shift calculation.
[Appendix A, Fig. 12] Figure 12 is placed in Appendix A but is not referenced in the text near Eq. (A.4); please add an explicit reference there.
[Sec. 3, Fig. 9] The text says the optimal numbers of bins are 6 for SKAO2 and 3 for MegaMapper, but the figure axes do not mark these choices; adding markers or vertical lines would help the reader verify the claim.
[Sec. 3, Table 2] In Table 2, the first Delta z entry for SKAO2 (0.720) is much larger than the others; a brief note confirming that these are equal-volume comoving bins would avoid confusion.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity: the corrections are re-derived or explicitly reproduced, the f_NL forecasts and shifts follow from a standard Fisher pipeline with no fitted target, and the paper itself discloses the truncation caveat that limits its headline shift claim.

full rationale

The derivation chain is self-contained. The standard Newtonian flat-sky spectrum is defined in Eq. (1.4); the non-integrated wide-angle and relativistic corrections are reproduced explicitly in Appendix A (Eqs. A.2 and A.4) from [35], and the integrated correction is derived in Appendix B from the kernels in Eqs. (2.5)-(2.8), with the flat-sky and no-wide-angle-mixing assumptions stated ('we follow [33] and make the flat-sky approximation Equation 1.5'). The Fisher forecasts (Eqs. 3.6-3.7) and the f_NL shift computation (Eq. 4.2) are standard nested-model quantities evaluated from these spectra; no parameter is fitted to the reported sigma(f_NL) or delta(f_NL)/sigma values, and the survey inputs (bias, Q, E, n_g from [12,39]) are external. The self-citations [35] (and [34]) supply correction formulas that are printed in the current paper, so the argument does not reduce to those citations. The paper explicitly flags the principal limitation: the integrated correction is truncated to I x S plus S x I, omitting L x L, lensing-wide-angle, and cross-bin terms, which 'can have a larger than expected influence' and 'may artificially suppress the shift' (abstract and Sec. 5). This is a robustness caveat, not circularity, because the omitted terms are not used to construct the tabulated shifts and the near-cancellation for SKAO2 is a computed result of the retained terms rather than an imposed input. No circular step was found.

Assumptions & free parameters 4 free parameters · 7 assumptions · 0 invented entities

The forecast depends on survey bias functions fitted to simulations (b, Q, E) and on the choice of binning; no new physical constants are introduced. The shift result depends on the perturbative wide-angle expansion and the leading-order integrated kernel, which are assumptions from prior work, re-derived in Appendix B.

free parameters (4)

b0 = 1 (fiducial)
Amplitude of galaxy clustering bias; nuisance parameter in the Fisher forecast (Eq. 3.8).
E0 = 1 (fiducial)
Amplitude of evolution bias; nuisance parameter in the Fisher forecast (Eq. 3.8).
Q0 = 1 (fiducial)
Amplitude of magnification bias; nuisance parameter in the Fisher forecast (Eq. 3.8).
Number of equal-volume redshift bins = 6 (SKAO2), 3 (MegaMapper)
Selected by minimizing sigma(f_NL) on the same Fisher forecast (Figure 9), which optimizes the reported precision.

assumptions (7)

domain assumption Standard Lambda CDM background and linear perturbation theory
Used throughout for the matter power spectrum, growth factor, and Hubble rate; fiducial parameters from Planck [46].
domain assumption Poisson equation in comoving gauge (Eq. 1.6)
Connects metric potential to density contrast; required for the relativistic kernels.
domain assumption Universality relation for scale-dependent bias (Eq. 1.2)
Simple form of the f_NL bias correction; the paper notes serious issues with this assumption but uses it for model comparison.
domain assumption Wide-angle expansion valid for k > 1/r
Sets kmin in Eq. (3.5) and limits the validity of the correction terms.
domain assumption Integrated correction includes only I x S and S x I at leading order
Omits L x L, lensing-wide-angle, and cross-bin terms; the authors list these as limitations in Section 5.
domain assumption Survey bias functions from external fits
b, Q, E for SKAO2 from [12,38] and for MegaMapper from [13,39,54]; these are inputs from simulation-based fitting.
domain assumption No mode coupling in the covariance (Eq. 3.2)
The authors state this neglect leads to over-optimistic precision (Section 3).

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Cite this review

Pith. "Pith review of Primordial non-Gaussianity -- the effects of relativistic and wide-angle corrections to the power spectrum." pith.science (2026). https://pith.science/paper/HS2JVESG

@misc{pith2026241206553,
  author       = {Pith},
  title        = {Pith review of: Primordial non-Gaussianity -- the effects of relativistic and wide-angle corrections to the power spectrum},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/HS2JVESG}},
  note         = {Machine review of arXiv:2412.06553}
}

abstract

Wide-angle and relativistic corrections to the Newtonian and flat-sky approximations are important for accurate modeling of the galaxy power spectrum of next-generation galaxy surveys. In addition to Doppler and Sachs-Wolfe relativistic corrections, we include the effects of lensing convergence, time delay and integrated Sachs-Wolfe. We investigate the impact of these corrections on measurements of the local primordial non-Gaussianity parameter $f_{\mathrm{NL}}$, using two futuristic spectroscopic galaxy surveys, planned for SKAO2 and MegaMapper. In addition to the monopole, we include the quadrupole of the galaxy Fourier power spectrum. The quadrupole is much more sensitive to the corrections than the monopole. The combination with the quadrupole improves the precision on $f_{\mathrm{NL}}$ by $\sim {{45}}\%$ and $\sim {{63}}\%$ for SKAO2 and MegaMapper respectively. {Neglecting the wide-angle and relativistic corrections produces a shift in $f_{\mathrm{NL}}$ which is very sensitive to the magnification bias and the redshift evolution of the comoving number density. In the case of SKAO2, the shift in $f_{\mathrm{NL}}$ is negligible -- since the contributions to the shift from integrated and non-integrated effects nearly cancel. For MegaMapper, there is only partial cancellation of integrated and non-integrated effects and the shift is $\sim {0.6} \, \sigma$.} We point out that some of the approximations made in the wide-angle and relativistic corrections may artificially suppress the shift in $f_{\mathrm{NL}}$.

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Forward citations

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Reference graph

Works this paper leans on

54 extracted references · 7 canonical work pages · cited by 5 Pith papers

[35]

Jolicoeur, S

S. Jolicoeur, S. L. Guedezounme, R. Maartens, P. Paul, C. Clarkson, and S. Camera, Relativistic and wide-angle corrections to galaxy power spectra, JCAP 08 (2024) 027, [arXiv:2406.06274]

arXiv 2024
[33]

Noorikuhani and R

M. Noorikuhani and R. Scoccimarro,Wide-angle and relativistic effects in Fourier-space clustering statistics, Phys. Rev. D107 (2023), no. 8 083528, [arXiv:2207.12383]

arXiv 2023
[1]

Dalal, O

N. Dalal, O. Dore, D. Huterer, and A. Shirokov,The imprints of primordial non-gaussianities on large-scale structure: scale dependent bias and abundance of virialized objects, Phys. Rev. D77 (2008) 123514, [arXiv:0710.4560]

arXiv 2008
[2]

Komatsu,Hunting for Primordial Non-Gaussianity in the Cosmic Microwave Background, Class

E. Komatsu,Hunting for Primordial Non-Gaussianity in the Cosmic Microwave Background, Class. Quant. Grav.27 (2010) 124010, [arXiv:1003.6097]

arXiv 2010
[3]

Chen,Primordial Non-Gaussianities from Inflation Models, Adv

X. Chen,Primordial Non-Gaussianities from Inflation Models, Adv. Astron.2010 (2010) 638979, [arXiv:1002.1416]

arXiv 2010
[4]

Challinor and A

A. Challinor and A. Lewis,The linear power spectrum of observed source number counts, Phys. Rev. D84 (2011) 043516, [arXiv:1105.5292]

arXiv 2011
[5]

Raccanelli, F

A. Raccanelli, F. Montanari, D. Bertacca, O. Doré, and R. Durrer,Cosmological Measurements with General Relativistic Galaxy Correlations, JCAP 05 (2016) 009, [arXiv:1505.06179]

arXiv 2016
[6]

Alonso, P

D. Alonso, P. Bull, P. G. Ferreira, R. Maartens, and M. Santos,Ultra large-scale cosmology in next-generation experiments with single tracers, Astrophys. J. 814 (2015), no. 2 145, [arXiv:1505.07596]

arXiv 2015

Show all 54 references

[7]

Namikawa, T

T. Namikawa, T. Okamura, and A. Taruya,Magnification effect on the detection of primordial non-Gaussianity from photometric surveys, Phys. Rev. D83 (2011) 123514, [arXiv:1103.1118]

2011 arXiv
[8]

Bruni, R

M. Bruni, R. Crittenden, K. Koyama, R. Maartens, C. Pitrou, and D. Wands,Disentangling non-Gaussianity, bias and GR effects in the galaxy distribution, Phys. Rev. D85 (2012) 041301, [arXiv:1106.3999]

2012 arXiv
[9]

Camera, R

S. Camera, R. Maartens, and M. G. Santos,Einstein’s legacy in galaxy surveys, Mon. Not. Roy. Astron. Soc.451 (2015), no. 1 L80–L84, [arXiv:1412.4781]

2015 arXiv
[10]

C. S. Lorenz, D. Alonso, and P. G. Ferreira,Impact of relativistic effects on cosmological parameter estimation, Phys. Rev. D97 (2018), no. 2 023537, [arXiv:1710.02477]

2018 arXiv
[11]

Viljoen, J

J.-A. Viljoen, J. Fonseca, and R. Maartens,Multi-wavelength spectroscopic probes: biases from neglecting light-cone effects, JCAP 12 (2021), no. 12 004, [arXiv:2108.05746]

2021 arXiv
[12]

Maartens, J

R. Maartens, J. Fonseca, S. Camera, S. Jolicoeur, J.-A. Viljoen, and C. Clarkson, Magnification and evolution biases in large-scale structure surveys, JCAP 12 (2021), no. 12 009, [arXiv:2107.13401]

2021 arXiv
[13]

Sailer, E

N. Sailer, E. Castorina, S. Ferraro, and M. White,Cosmology at high redshift — a probe of fundamental physics, JCAP 12 (2021), no. 12 049, [arXiv:2106.09713]

2021 arXiv
[14]

Akrami et al.,Planck 2018 results

Planck Collaboration, Y. Akrami et al.,Planck 2018 results. IX. Constraints on primordial non-Gaussianity, Astron. Astrophys.641 (2020) A9, [arXiv:1905.05697]

2020 arXiv
[15]

Matarrese and L

S. Matarrese and L. Verde,The effect of primordial non-Gaussianity on halo bias, Astrophys. J. Lett. 677 (2008) L77–L80, [arXiv:0801.4826]

2008 arXiv
[16]

A. Barreira,Can we actually constrain fN Lusing the scale-dependent bias effect? An illustration of the impact of galaxy bias uncertainties using the BOSS DR12 galaxy power spectrum, JCAP 11 (2022) 013, [arXiv:2205.05673]

2022 arXiv
[17]

Barreira and E

A. Barreira and E. Krause,Towards optimal and robust f_nl constraints with multi-tracer analyses, JCAP 10 (2023) 044, [arXiv:2302.09066]

2023 arXiv
[18]

Fondi, L

E. Fondi, L. Verde, F. Villaescusa-Navarro, M. Baldi, W. R. Coulton, G. Jung, D. Karagiannis, M. Liguori, A. Ravenni, and B. D. Wandelt,Taming assembly bias for primordial non-Gaussianity, JCAP 02 (2024) 048, [arXiv:2311.10088]. – 27 –

2024 arXiv
[19]

A. G. Adame, S. Avila, V. Gonzalez-Perez, G. Yepes, M. Pellejero, M. S. Wang, C.-H. Chuang, Y. Feng, J. Garcia-Bellido, and A. Knebe,PNG-UNITsims: Halo clustering response to primordial non-Gaussianities as a function of mass, Astron. Astrophys.689 (2024) A69, [arXiv:2312.12405]

2024 arXiv
[20]

Matsubara,The Correlation function in redshift space: General formula with wide angle effects and cosmological distortions, Astrophys

T. Matsubara,The Correlation function in redshift space: General formula with wide angle effects and cosmological distortions, Astrophys. J. 535 (2000) 1, [astro-ph/9908056]

2000 arXiv
[21]

Matsubara,The gravitational lensing in redshift-space correlation functions of galaxies and quasars, Astrophys

T. Matsubara,The gravitational lensing in redshift-space correlation functions of galaxies and quasars, Astrophys. J. Lett.537 (2000) L77, [astro-ph/0004392]

2000 arXiv
[22]

Bertacca, R

D. Bertacca, R. Maartens, A. Raccanelli, and C. Clarkson,Beyond the plane-parallel and Newtonian approach: Wide-angle redshift distortions and convergence in general relativity, JCAP 1210 (2012) 025, [arXiv:1205.5221]

2012 arXiv
[23]

Tansella, C

V. Tansella, C. Bonvin, R. Durrer, B. Ghosh, and E. Sellentin,The full-sky relativistic correlation function and power spectrum of galaxy number counts. Part I: theoretical aspects, JCAP 03 (2018) 019, [arXiv:1708.00492]

2018 arXiv
[24]

Tansella, G

V. Tansella, G. Jelic-Cizmek, C. Bonvin, and R. Durrer,COFFE: a code for the full-sky relativistic galaxy correlation function, JCAP 10 (2018) 032, [arXiv:1806.11090]

2018 arXiv
[25]

Scaccabarozzi, J

F. Scaccabarozzi, J. Yoo, and S. G. Biern,Galaxy Two-Point Correlation Function in General Relativity, JCAP 10 (2018) 024, [arXiv:1807.09796]

2018 arXiv
[26]

Bonvin and R

C. Bonvin and R. Durrer,What galaxy surveys really measure, Phys. Rev. D84 (2011) 063505, [arXiv:1105.5280]

2011 arXiv
[27]

Camera, M

S. Camera, M. G. Santos, and R. Maartens,Probing primordial non-Gaussianity with SKA galaxy redshift surveys: a fully relativistic analysis, Mon. Not. Roy. Astron. Soc.448 (2015), no. 2 1035–1043, [arXiv:1409.8286]

2015 arXiv
[28]

Grimm, F

N. Grimm, F. Scaccabarozzi, J. Yoo, S. G. Biern, and J.-O. Gong,Galaxy Power Spectrum in General Relativity, JCAP 11 (2020) 064, [arXiv:2005.06484]

2020 arXiv
[29]

Castorina and E

E. Castorina and E. di Dio,The observed galaxy power spectrum in General Relativity, JCAP 01 (2022), no. 01 061, [arXiv:2106.08857]

2022 arXiv
[30]

Foglieni, M

M. Foglieni, M. Pantiri, E. Di Dio, and E. Castorina,Large Scale Limit of the Observed Galaxy Power Spectrum, Phys. Rev. Lett.131 (2023), no. 11 111201, [arXiv:2303.03142]

2023 arXiv
[31]

R. Y. Wen, H. S. Grasshorn Gebhardt, C. Heinrich, and O. Doré,Exact modeling of power spectrum multipole through spherical Fourier-Bessel basis, Phys. Rev. D110 (2024), no. 8 083525, [arXiv:2404.04812]

2024 arXiv
[32]

Semenzato, D

F. Semenzato, D. Bertacca, and A. Raccanelli,The full-sky Spherical Fourier-Bessel power spectrum in general relativity, arXiv:2406.09545

arXiv
[34]

P. Paul, C. Clarkson, and R. Maartens,Wide-angle effects in multi-tracer power spectra with Doppler corrections, JCAP 04 (2023) 067, [arXiv:2208.04819]

2023 arXiv
[36]

Bolejko, C

K. Bolejko, C. Clarkson, R. Maartens, D. Bacon, N. Meures, and E. Beynon,Antilensing: The Bright Side of Voids, Phys. Rev. Lett.110 (2013), no. 2 021302, [arXiv:1209.3142]

2013 arXiv
[37]

D. J. Bacon, S. Andrianomena, C. Clarkson, K. Bolejko, and R. Maartens,Cosmology with Doppler Lensing, Mon. Not. Roy. Astron. Soc.443 (2014), no. 3 1900–1915, [arXiv:1401.3694]. – 28 –

2014 arXiv
[38]

Yahya, P

S. Yahya, P. Bull, M. Santos, M. Silva, R. Maartens, P. Okouma, and B. Bassett,Cosmological performance of SKA HI galaxy surveys, Mon. Not. Roy. Astron. Soc.450 (2015), no. 3 2251–2260, [arXiv:1412.4700]

2015 arXiv
[39]

Kopana, S

M. Kopana, S. Jolicoeur, and R. Maartens,Multi-tracing the primordial Universe with future surveys, Eur. Phys. J. C84 (2024), no. 5 491, [arXiv:2312.12994]

2024 arXiv
[40]

Berti, M

M. Berti, M. Spinelli, and M. Viel,Multipole expansion for 21cm intensity mapping power spectrum: Forecasted cosmological parameters estimation for the SKA observatory, Mon. Not. Roy. Astron. Soc.521 (2023), no. 3 3221–3236, [arXiv:2209.07595]

2023 arXiv
[41]

Castorina and M

E. Castorina and M. White,Beyond the plane-parallel approximation for redshift surveys, Mon. Not. Roy. Astron. Soc.476 (2018), no. 4 4403–4417, [arXiv:1709.09730]

2018 arXiv
[42]

Blake, P

C. Blake, P. Carter, and J. Koda,Power spectrum multipoles on the curved sky: an application to the 6-degree Field Galaxy Survey, Mon. Not. Roy. Astron. Soc.479 (2018), no. 4 5168–5183, [arXiv:1801.04969]

2018 arXiv
[43]

Wadekar and R

D. Wadekar and R. Scoccimarro,Galaxy power spectrum multipoles covariance in perturbation theory, Phys. Rev. D102 (2020), no. 12 123517, [arXiv:1910.02914]

2020 arXiv
[44]

Wadekar, M

D. Wadekar, M. M. Ivanov, and R. Scoccimarro,Cosmological constraints from BOSS with analytic covariance matrices, Phys. Rev. D102 (2020) 123521, [arXiv:2009.00622]

2020 arXiv
[45]

VIRGO Consortium Collaboration, R. E. Smith, J. A. Peacock, A. Jenkins, S. D. M. White, C. S. Frenk, F. R. Pearce, P. A. Thomas, G. Efstathiou, and H. M. P. Couchmann,Stable clustering, the halo model and nonlinear cosmological power spectra, Mon. Not. Roy. Astron. Soc. 341 (2...

2003 arXiv
[46]

Aghanim et al.,Planck 2018 results

Planck Collaboration, N. Aghanim et al.,Planck 2018 results. VI. Cosmological parameters, Astron. Astrophys.641 (2020) A6, [arXiv:1807.06209]. [Erratum: Astron.Astrophys. 652, C4 (2021)]

2020 arXiv
[47]

d’Assignies, C

W. d’Assignies, C. Zhao, J. Yu, and J.-P. Kneib,Cosmological Fisher forecasts for next-generation spectroscopic surveys, Mon. Not. Roy. Astron. Soc.521 (2023), no. 3 3648–3662, [arXiv:2301.02289]

2023 arXiv
[48]

Camera, C

S. Camera, C. Carbone, C. Fedeli, and L. Moscardini,Neglecting Primordial non-Gaussianity Threatens Future Cosmological Experiment Accuracy, Phys. Rev. D91 (2015) 043533, [arXiv:1412.5172]

2015 arXiv
[49]

Fonseca, S

J. Fonseca, S. Camera, M. Santos, and R. Maartens,Hunting down horizon-scale effects with multi-wavelength surveys, Astrophys. J. 812 (2015), no. 2 L22, [arXiv:1507.04605]

2015 arXiv
[50]

Jelic-Cizmek, F

G. Jelic-Cizmek, F. Lepori, C. Bonvin, and R. Durrer,On the importance of lensing for galaxy clustering in photometric and spectroscopic surveys, JCAP 04 (2021) 055, [arXiv:2004.12981]

2021 arXiv
[51]

Bailoni, A

A. Bailoni, A. Spurio Mancini, and L. Amendola,Improving Fisher matrix forecasts for galaxy surveys: window function, bin cross-correlation, and bin redshift uncertainty, Mon. Not. Roy. Astron. Soc.470 (2017), no. 1 688–705, [arXiv:1608.00458]

2017 arXiv
[52]

P. H. F. Reimberg, F. Bernardeau, and C. Pitrou,Redshift-space distortions with wide angular separations, JCAP 1601 (2016), no. 01 048, [arXiv:1506.06596]

2016 arXiv
[53]

J. N. Benabou, I. Sands, H. S. Grasshorn Gebhardt, C. Heinrich, and O. Doré,Wide-angle effects in the power spectrum multipoles in next-generation redshift surveys, Phys. Rev. D110 (2024), no. 8 083526, [arXiv:2404.04811]

2024 arXiv
[54]

Rossiter, S

S. Rossiter, S. Camera, C. Clarkson, and R. Maartens,Decoupling Local Primordial non-Gaussianity from Relativistic Effects in the Galaxy Bispectrum, arXiv:2407.06301. – 29 –

arXiv

Pith tools

Reviewed August 11, 2026 · model on record in the stance chip above.

[1] [35]

Jolicoeur, S

S. Jolicoeur, S. L. Guedezounme, R. Maartens, P. Paul, C. Clarkson, and S. Camera, Relativistic and wide-angle corrections to galaxy power spectra, JCAP 08 (2024) 027, [arXiv:2406.06274]

arXiv 2024

[2] [33]

Noorikuhani and R

M. Noorikuhani and R. Scoccimarro,Wide-angle and relativistic effects in Fourier-space clustering statistics, Phys. Rev. D107 (2023), no. 8 083528, [arXiv:2207.12383]

arXiv 2023

[3] [1]

Dalal, O

N. Dalal, O. Dore, D. Huterer, and A. Shirokov,The imprints of primordial non-gaussianities on large-scale structure: scale dependent bias and abundance of virialized objects, Phys. Rev. D77 (2008) 123514, [arXiv:0710.4560]

arXiv 2008

[4] [2]

Komatsu,Hunting for Primordial Non-Gaussianity in the Cosmic Microwave Background, Class

E. Komatsu,Hunting for Primordial Non-Gaussianity in the Cosmic Microwave Background, Class. Quant. Grav.27 (2010) 124010, [arXiv:1003.6097]

arXiv 2010

[5] [3]

Chen,Primordial Non-Gaussianities from Inflation Models, Adv

X. Chen,Primordial Non-Gaussianities from Inflation Models, Adv. Astron.2010 (2010) 638979, [arXiv:1002.1416]

arXiv 2010

[6] [4]

Challinor and A

A. Challinor and A. Lewis,The linear power spectrum of observed source number counts, Phys. Rev. D84 (2011) 043516, [arXiv:1105.5292]

arXiv 2011

[7] [5]

Raccanelli, F

A. Raccanelli, F. Montanari, D. Bertacca, O. Doré, and R. Durrer,Cosmological Measurements with General Relativistic Galaxy Correlations, JCAP 05 (2016) 009, [arXiv:1505.06179]

arXiv 2016

[8] [6]

Alonso, P

D. Alonso, P. Bull, P. G. Ferreira, R. Maartens, and M. Santos,Ultra large-scale cosmology in next-generation experiments with single tracers, Astrophys. J. 814 (2015), no. 2 145, [arXiv:1505.07596]

arXiv 2015