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REVIEW 3 major objections 5 minor 76 references

Projecting Unequal Time Fields and Correlators of Large Scale Structure

T0 review · 3 major / 5 minor · reviewed 2026-08-07 · deepseek-v4-flash

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Pith's one-line read The paper claims that unequal-time field-level projection introduces three first-order correction terms to single-tracer power spectra, including within-bin and cross-bin terms with percent-level effects for typical survey bin widths.

desk verdict Genuine field-level extension of the correlator-level formalism, but the first-order single-tracer corrections may be artifacts of an asymmetric estimator rather than settled physics. read the letter →

arxiv 2502.09518 v1 pith:IIHKUEIW submitted 2025-02-13 astro-ph.CO

Theodore Steele , Alvise Raccanelli , Zvonimir Vlah This is my paper
classification astro-ph.CO
keywords unequaltimefieldlevelprojectionpowerspectrumlargescalestructureredshiftbinsequalapproximationfirstordercorrectionscross-bincorrelators
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

This paper tries to establish that the standard equal-time approximation—placing every tracer at the mean redshift of its bin—misses first-order corrections that a new field-level projection brings out. The method projects each density field onto the celestial sphere from its own displaced reference time and only then correlates the projected fields. Applied to a linearly biased, single-tracer power spectrum split into two redshift bins, it yields three new first-order terms: one for matter evolution between bins, one for bias evolution, and one for the displacement of fields from their bin means. If the claim holds, these corrections reach percent level for bins of order $100\,h^{-1}\mathrm{Mpc}$ width and for cross-bin pairs separated by about 10% in comoving distance, so upcoming surveys cannot automatically ignore them. The paper also shows the same terms can be rederived within an extended correlator-level projection, providing a consistency check.

What carries the argument

The load-bearing object is the field-level projection of Eq. (17), $\hat\delta(q,\bar\chi) = \int \frac{dk_{\hat n}}{2\pi} e^{-i\bar\chi k_{\hat n}} \int d\delta\chi\, e^{-i\delta\chi(k_{\hat n}+q_{\hat n})}\gamma(\chi)\delta(k_{\hat n},q_\perp,\chi)$, which projects each field individually while preserving its displacement from the bin mean. The workhorse identity is Eq. (19), $\int d\delta\chi\, e^{-i\delta\chi(k+q)}(\delta\chi)^j = 2\pi i^j \frac{d^j}{dq^j}\delta_D(k+q)$, which turns the Taylor expansion in time into derivatives acting on a delta function, the cross-bin phase $e^{-i(\bar\chi_1 q_{\hat n,1}+\bar\chi_2 q_{\hat n,2})}$, and the power spectrum. These derivatives generate the correction functions $R$ and $Y$ in Eqs. (31)–(32), and the final expression for the unequal-time power spectrum is Eq. (33).

What would settle it

Compute the field-level power spectrum with the two field momenta treated symmetrically—for example, averaging the result of integrating over $q_2$ with the result of integrating over $q_1$, or binning both fields with identical windows before correlating—and check whether the $R$ and $Y$ terms survive. If they cancel exactly, the claimed first-order corrections are artifacts of the integration order. Alternatively, measure the power spectrum from N-body or light-cone mock catalogues in bins of width $100\,h^{-1}\mathrm{Mpc}$: absence of the predicted percent-level correction would falsify the claim.

Watch

Extended reading notes

Core claim

The central discovery is that the order of the unequal-time correction to a single-tracer power spectrum depends on whether fields are projected before or after being correlated. In the field-level projection, each field is Fourier-transformed in its own displacement $\delta\chi_i$ from the bin mean; after integrating over one field's momentum the unequal-time power spectrum becomes Eq. (33): $P(q,\bar\chi_1,\bar\chi_2) = e^{i(\bar\chi_2-\bar\chi_1)q_{\hat n}}[1+R(\bar\chi_1,\bar\chi_2)+Y(q,\bar\chi_1,\bar\chi_2)]P(q,\bar\chi_1,\bar\chi_2)$, where $R$ carries the evolution of matter and bias between the two bins and $Y$ carries the displacement of the fields from the bin means. These are first-order terms, in contrast to the correlator-level projection where the two fields' displacements cancel because they are constrained to be equal and opposite around the correlator's mean.

Load-bearing premise

The paper's first-order corrections rest on treating the asymmetric object in Eq. (33)—obtained after integrating over only one field's momentum—as a physical power spectrum, even though $R$ and $Y$ are not symmetric under exchange of the two fields; if that asymmetry does not cancel under proper bin averaging or symmetrization, the corrections may be artifacts of the integration order.

Editorial extensions

If this is right

  • Single-tracer power spectra in redshift bins acquire corrections at first order in the time expansion, not only at second order as in the correlator-level projection.
  • Within a bin of width about $100\,h^{-1}\mathrm{Mpc}$ at $z=1$, the integrated $Y$ correction reaches percent level for modes with wavelengths around $10\,h^{-1}\mathrm{Mpc}$.
  • Cross-bin corrections from $R$ reach percent level when the bin mean comoving distances differ by roughly 10%, which is common for adjacent wide bins.
  • The within-bin corrections depend mainly on bin width and only weakly on the bin's mean redshift, so wide high-redshift bins are the most affected.
  • An extended correlator-level projection that includes a second Fourier transform reproduces the field-level single-bin results, confirming the two formalisms agree when both are fully extended.

Reading between the lines

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

  • If the asymmetric $R$ and $Y$ terms survive a symmetric treatment of the two field momenta, they will enter standard power-spectrum analyses; if they cancel under symmetrization, the claimed first-order corrections are an artifact of the chosen integration order. This is an arithmetic check not performed in the paper.
  • The same field-level projection should generate additional first-order terms in bispectra and higher-order correlators, since each extra field carries its own independent displacement; the paper does not compute these.
  • Correlating tracers near the boundary between two bins, instead of at the bin means, substantially reduces their radial separation, so the cross-bin corrections could effectively recover information that binning discards; the paper notes this direction but does not quantify it.
  • A relativistic extension, which the authors state is in preparation, could change the size of the cross-bin corrections by orders of magnitude because integrated relativistic effects dominate Newtonian cross-bin signals.
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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

3 major / 5 minor

Summary. The paper develops a 'field level projection' formalism for unequal-time large-scale structure correlators. Instead of projecting a pre-averaged unequal-time power spectrum (the earlier 'correlator-level' approach), the authors project each density field individually onto the celestial sphere, keeping a Fourier analogue of each field's displacement from its bin mean redshift. They derive expressions for the projected unequal-time field and its two-point correlator, and then claim that, unlike the correlator-level formalism, this new projection introduces first-order correction terms even for single-tracer power spectra. Three such terms are identified: one from matter evolution, one from bias evolution, and one from the finite width of redshift bins. The paper evaluates these corrections for a linearly biased power spectrum and reports percent-level effects for bins of order 100 Mpc/h and for cross-bin pairs separated by about 10% in distance. Appendices show that an extended correlator-level projection with an additional Fourier transform reproduces the single-bin results.

Significance. If the central claim is correct, the paper would provide a systematic first-order correction to the usual equal-time approximation, which is potentially relevant for wide-bin analyses in current and future surveys. The derivation in Secs. III-V is largely self-contained and does not depend on fitted parameters; the authors explicitly rederive the time-expansion formalism and they are transparent about the asymmetry of the objects defined in Eqs. (31)-(32). However, the significance is conditional: the headline 'first-order single-tracer corrections' rest on an object that is obtained by integrating over only one of the two field momenta, and the paper does not demonstrate that this object is what a survey power-spectrum estimator actually measures. The numerical percent-level claims also rely on a hard cutoff in the radial Fourier mode rather than on a survey-derived window function. If the asymmetry is an artifact of the integration order, the main physical conclusion would not survive.

major comments (3)
  1. [Sec. VI, Eqs. (30)-(33)] The object called the unequal-time power spectrum is constructed by integrating Eq. (28) over q2 only, and the authors explicitly note that R and Y are not invariant under exchange of the two fields. This is not a harmless convention: the full correlator in Eq. (28) is symmetric, and a physical estimator must specify how the delta function and its derivatives are sampled. In particular, an evaluation that treats q1 and q2 symmetrically (for example, extracting the coefficient of delta^3(q1+q2) with both derivative operators acting, or averaging the two one-sided marginalizations) does not in general reproduce Eqs. (31)-(32). For C1=C2, the first-order corrections from the two orderings cancel, leaving corrections at most of order C1-C2. The authors need to show that a concrete survey estimator, including its bin windows and symmetrization, reduces to Eq. (33); otherwise the central claim of new first-order single-tracer corrections is not established.
  2. [Sec. VI, Eq. (34) and Fig. 4] The numerical percent-level corrections are obtained by integrating q_hat over hard-cutoff intervals whose limits are described as the 'longest and shortest modes viable within a given redshift bin.' Since the projection in Eq. (16) sets W(chi,chi')=delta_D, no survey window connects the chi-bin width to these q_hat limits. For a single bin, the Y contribution to the integral in Eq. (35) is a boundary term proportional to P(b)-P(a), so its magnitude is controlled by the arbitrarily chosen cutoffs. The authors should derive the integration measure and limits from a concrete redshift-bin window and demonstrate that the claimed percent-level corrections are stable under changes in the window shape.
  3. [Sec. VI, Eq. (37)] The cross-bin correction R is interpreted as accounting for the evolution of matter and bias between the two reference times. However, the underlying unequal-time power spectrum evaluated at the bin means has no first-order dependence on chi_bar1-chi_bar2: expanding D(chi_bar1)D(chi_bar2)b1(chi_bar1)b2(chi_bar2) around the mean redshift of the two bins gives a correction of order (chi_bar1-chi_bar2)^2. The R term instead arises from the derivative of the projection phase and delta function in Eq. (28). The authors should clarify whether R is a genuinely new projection effect or an artifact of their phase convention, and how it relates to the standard first-order-in-Delta-chi expansion of unequal-time correlators.
minor comments (5)
  1. [Sec. V] The text says 'the correlator-level projection studied in Sec. VA1'; this should be Sec. IVA or Sec. IV A.
  2. [Sec. IV A] There is a typo: 'We do his by defining' should be 'We do this by defining'.
  3. [Sec. VI, Eq. (34)] The symbol P is used both for the full unequal-time power spectrum and for the q_hat-integrated spectrum; please introduce a distinct notation for the integrated object to avoid confusion.
  4. [Fig. 4] The top-left panel label contains a stray 'x' and the notation 'chi(1)' is unclear; it should read '-iY(q_hat, chi_bar_1)' or similar.
  5. [App. B] In the paragraph before Eq. (B2), the text says 'Introducing our Taylor expansion to Eq.(B2)' but the equation being expanded is Eq. (B1).

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the time expansion and field-level projection are derived in-paper with no fitted inputs; self-citations are contextual and not load-bearing.

full rationale

The paper's central derivation is self-contained. Section III rederives the time-displacement expansion for linear and biased density fields directly from the definition of the growth rate, rather than importing it as an unexamined black box (Eqs. 4-9). Section V constructs the field-level projection from the Fourier transform definition and derives the unequal-time two-point expression (Eqs. 15-29), and Section VI evaluates the power spectrum by direct manipulation of derivatives of the delta function and phase terms (Eqs. 30-33). No parameter is fitted to data and then renamed as a prediction; the correction functions R and Y are defined algebraically from the expansion coefficients and the power spectrum itself. Self-citations [54-57] are used to contrast the new field-level projection with the earlier correlator-level projection and to frame the known result that first-order terms cancel in single-tracer correlator-level analyses; the new first-order single-tracer result is derived here, not assumed from those citations. The appendix consistency checks (Apps. A and B) show that an extended correlator-level projection reproduces the field-level results, which is an internal equivalence check rather than a circular dependence. The asymmetry of R and Y under exchange of the two fields, noted after Eq. (33), is a mathematical property of the chosen momentum integration order and not an input-output circularity; whether the physical estimator should be symmetrized is a correctness or modeling question, not a circularity of the derivation chain. Therefore no step reduces by construction to its own inputs, and the appropriate circularity score is 0.

Assumptions & free parameters 2 free parameters · 7 assumptions · 0 invented entities

No new particles, forces, or conserved quantities are introduced. 'Hyperuranion space' is a label for the usual time-evolving 3D real-space grid, not a new entity. The parameter-free analytic derivation rests on standard linear growth, a linear bias model, a delta-function window, and a first-order Taylor truncation, with illustrative numerical choices for the toy-model estimates.

free parameters (2)
  • Redshift-bin width / q_n integration range = O(100 Mpc/h), q_max ~ 0.1 h/Mpc in Fig. 4
    The percent-level single-bin correction claim is computed for a chosen bin width and mode range; the paper notes the correction vanishes when the q_n integral limits diverge. The choice is illustrative, not fitted to data.
  • Bias parametrization b(chi) = sqrt(1 + z(chi)) = not fitted, illustrative
    Used for the R panel of Fig. 4; the size of the cross-bin bias-evolution correction depends on this model.
assumptions (7)
  • domain assumption Linear growth relation d delta / d chi = -f a H delta (Eq. 5 in Sec. III)
    Standard linear perturbation theory; used to Taylor expand time-displaced fields. Neglects nonlinear evolution.
  • domain assumption First-order Taylor truncation in delta chi, dropping O(delta chi^2) terms
    Used throughout Secs. III-VI; the numerical claims for O(100 Mpc/h) bins sit near the boundary of this truncation.
  • ad hoc to paper Window function W(chi, chi') = delta_D(chi' - chi) in Eq. (16)
    Removes the radial selection function of real surveys; the paper does not quantify the impact of realistic windows on R and Y.
  • domain assumption Subleading terms O(1/chi-bar^n) in the gamma, epsilon, and upsilon expansions are set to zero
    Standard flat-sky approximation, stated after Eq. (20); not derived with error bounds.
  • domain assumption The momentum integrals commute, so the integrated single-bin Y correction vanishes at divergent limits
    Asserted after Eq. (35) and in the Fig. 4 caption; used to interpret the finite-bin imaginary correction.
  • domain assumption Linear bias model delta_g = b(chi) delta with redshift-dependent b(chi)
    Used in Eqs. (8)-(9), (22), (36)-(37); higher-order and nonlocal bias are dropped.
  • standard math Natural units c = 1
    Harmless unit choice stated at the end of Sec. I.

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Pith. "Pith review of Projecting Unequal Time Fields and Correlators of Large Scale Structure." pith.science (2026). https://pith.science/paper/IIHKUEIW

@misc{pith2026250209518,
  author       = {Pith},
  title        = {Pith review of: Projecting Unequal Time Fields and Correlators of Large Scale Structure},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/IIHKUEIW}},
  note         = {Machine review of arXiv:2502.09518}
}
read the original abstract

Many large scale structure surveys sort their observations into redshift bins and treat every tracer as being located at the mean redshift of its bin, a treatment which we refer to as the equal time approximation. Recently, a new method was developed which allows for the estimation and correction of errors introduced by this approximation, which we refer to as the unequal time correlator-level projection. For single tracer power spectra, corrections arise at second order and above in a series expansion, with first order terms surviving only in multi-tracer analyses. In this paper we develop a new method which we refer to as the unequal time field level projection. This formalism projects the fields individually onto the celestial sphere, displaced from individual reference times, before defining their correlators. This method introduces new, first order correction terms even in the case of single tracer power spectra. Specifically, new first order terms are introduced which apply to both cross-bin and single bin correlators. All of these new corrections originate with derivatives over combinations of a delta function, a cross-bin phase term, and the power spectrum itself and stem from the introduction of two unequal time Fourier transforms into the analysis. We analyse these corrections in the context of a linearly biased power spectrum divided between two redshift bins and find that they can lead to non-trivial corrections, particularly to cross-bin correlators. We also show that these terms can be replicated by appropriately extending the correlator-level analysis to include a second Fourier transform which allows for a full redshift bin integration.

Figures

Figures reproduced from arXiv: 2502.09518 by the authors.

Figure 1
Figure 1. An illustration of a light cone through the celestial sphere showing the sorting of observables, represented by black [PITH_FULL_IMAGE:figures/full_fig_p005_1.png] view at source ↗
Figure 2
Figure 2. An illustration of the correlator-level projection of a power spectrum from Hyperuranion space onto a light cone [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗
Figure 3
Figure 3. An illustration of the field level projection of a pair of fields from Hyperuranion space onto a light cone through the [PITH_FULL_IMAGE:figures/full_fig_p009_3.png] view at source ↗
Figures from the paper (1 more)
Figure 4
Figure 4. Figure 4: Top left panel: The magnitude of the within-bin correction factor Y as given by applying Eq. (32) to a toy model power spectrum using the BBKS function. As can be seen, the corrections become percent level when deviations from the bin mean exceed qnˆ ≈ 10−2h Mpc−1 . We…

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Works this paper leans on

76 extracted references · 23 canonical work pages

  1. [1]

    Displaced Correlators Transforming a power spectrum with two instances of the operation given in Eq. (17) gives us ⟨ ˆδ (q1, ¯χ1) ˆδ (q2, ¯χ2) ⟩ = (2π)3 ∫dkˆn,1 2π ∫dkˆn,2 2π e−i(¯χ1k ˆn,1+¯χ2k ˆn,2) ∫ dδχ1 ∫ dδχ2e−i(δχ1(k ˆn,1+q ˆn,1)+δχ2(k ˆn,2+q ˆn,2)) ×γ(χ1)γ(χ2)δ3D(k1 + k2)P(k1, k2,χ 1,χ 2). (23) Implementing Eq. (18) into Eq. (23), we obtain ⟨ ˆδ (q...

    work page

  2. [2]

    (12) In Fig

    , (11) where ˜ℓ = ℓ/χ′, in the second step we have integrated over our momentum delta function, and on the last line we introduced the angular power spectrum C(ℓ,χ 1,χ 2)≡ 1 χ1χ2 ∫dkˆn 2π eik ˆn(χ1−χ2)P(kˆn, ℓ,χ 1,χ 2) . (12) In Fig. 1 we illustrate the celestial sphere as divided into three redshift bins and the notion of projected power spectra within i...

    work page

  3. [3]

    We do this by taking the expectation value of the product of two individually projected fields, each as described in Eq

    Displaced Fields We will now rederive the above equations from the point of view of projecting the fields individually onto the celestial sphere and only then correlating them. We do this by taking the expectation value of the product of two individually projected fields, each as described in Eq. (18). Up to first order in the time expansion, this gives u...

    work page

  4. [4]

    Taking these derivatives yields correction terms which were not present in the correlator-level analysis as previously defined

    Summary Having defined the two point unequal time ensemble average in momentum space and shown that, using the field level projection formalism shown in Eq.(18), the operations of correlation and projection commute, we may now note that the field level projection formalism places the phase terms and the delta function within the domain of the derivative o...

    work page

  5. [5]

    Dipartimenti di eccellenza

    Biased Tracers Generalising Eq. (30) by repeating the derivation in the context of biased tracers, we see that ∫ dq2 ⟨ ˆδ(q1, ¯χ1)ˆδ(q2, ¯χ2) ⟩ =(2π)3ei(¯χ2−¯χ1)q ˆn,1b2(¯χ2) [b1(¯χ1) + (Fa(¯χ1)b1(¯χ1) +∂zb1(¯χ1))H(¯χ1) (¯χ1− ¯χ2) +ib1(¯χ1)Fa(¯χ1)H(¯χ1)∂q ˆn,1 ] P(q1, ¯χ1, ¯χ2) =(2π)3ei(¯χ2−¯χ1)q ˆn,1b1(¯χ1)b2(¯χ2) [1 +R(¯χ1, ¯χ2) +Y (q1, ¯χ1, ¯χ2)]P(q1, ...

    work page

  6. [6]

    Laureijs, ,et al., Euclid Definition Study Report, arXiv e-prints , arXiv:1110.3193 (2011), arXiv:1110.3193 [astro-ph.CO]

    R. Laureijs, ,et al., Euclid Definition Study Report, arXiv e-prints , arXiv:1110.3193 (2011), arXiv:1110.3193 [astro-ph.CO]

    arXiv 2011

  7. [7]

    Doré et al., Cosmology with the SPHEREX All-Sky Spectral Survey, (2014), arXiv:1412.4872 [astro-ph.CO]

    O. Doré et al., Cosmology with the SPHEREX All-Sky Spectral Survey, (2014), arXiv:1412.4872 [astro-ph.CO]

    arXiv 2014

  8. [8]

    Ivezić et al., LSST: From Science Drivers to Reference Design and Anticipated Data Products, Astrophys

    Ž. Ivezić et al., LSST: From Science Drivers to Reference Design and Anticipated Data Products, Astrophys. J.873, 111 (2019), arXiv:0805.2366 [astro-ph]

    arXiv 2019

Show all 76 references
  1. [9]

    Hamana et al., Cosmological constraints from cosmic shear two-point correlation functions with HSC survey first-year data, Publ

    T. Hamana et al., Cosmological constraints from cosmic shear two-point correlation functions with HSC survey first-year data, Publ. Astron. Soc. Jap.72, Publications of the Astronomical Society of Japan, Volume 72, Issue 1, February 2020, 16, https://doi.org/10.1093/pasj/psz13...

    2020 arXiv

  2. [10]

    S. Yahyaet al., Cosmological performance of SKA Hi galaxy surveys, Monthly Notices of the Royal Astronomical Society 450, 2251 (2015), https://academic.oup.com/mnras/article-pdf/450/3/2251/18504481/stv695.pdf

    2015

  3. [11]

    Wanget al., The clustering of galaxies in the DESI imaging legacy surveys DR8: I

    Z. Wanget al., The clustering of galaxies in the DESI imaging legacy surveys DR8: I. The luminosity and color dependent intrinsic clustering, Sci. China Phys. Mech. Astron.64, 289811 (2021), arXiv:2106.14159 [astro-ph.GA]

    2021 arXiv

  4. [12]

    Pullen, C

    A. Pullen, C. Hirata, O. Doré, and A. Raccanelli, Interloper bias in future large-scale structure surveys, Publications of the Astronomical Society of Japan68 (2015)

    2015

  5. [13]

    Richardet al., 4most consortium survey 8: Cosmology redshift survey (crs) (2019)

    J. Richardet al., 4most consortium survey 8: Cosmology redshift survey (crs) (2019)

    2019

  6. [14]

    M. Takadaet al., Extragalactic science, cosmology, and Galactic archaeology with the Subaru Prime Focus Spectrograph, PublicationsoftheAstronomicalSocietyofJapan 66,10.1093/pasj/pst019(2014),r1,https://academic.oup.com/pasj/article- pdf/66/1/R1/4425324/pst019.pdf

    2014 doi

  7. [15]

    Hildebrandt et al., KiDS-1000 catalogue: Redshift distributions and their calibration, Astron

    H. Hildebrandt et al., KiDS-1000 catalogue: Redshift distributions and their calibration, Astron. Astrophys.647, A124 (2021), arXiv:2007.15635 [astro-ph.CO]

    2021 arXiv

  8. [16]

    K. S. Dawsonet al., The Baryon Oscillation Spectroscopic Survey of SDSS-III, The Astronomical Journal145, 10.1088/0004- 6256/145/1/10, arXiv:1208.0022 [astro-ph.CO]

    arXiv

  9. [17]

    M. Icaza-Lizaola et al., The clustering of the SDSS-IV extended Baryon Oscillation Spectroscopic Survey DR14 LRG sample: structure growth rate measurement from the anisotropic LRG correlation function in the redshift range 0.6<z< 1.0, Monthly Notices of the Royal Astronomical ...

    2019

  10. [18]

    D. H. Weinberg et al., Observational probes of cosmic acceleration, Physics Report530, 87 (2013), arXiv:1201.2434 [astro-ph.CO]

    2013 arXiv

  11. [19]

    Martinelli et al

    M. Martinelli et al. (Euclid), Euclid: Constraining dark energy coupled to electromagnetism using astrophysical and laboratory data, Astron. Astrophys.654, A148 (2021), arXiv:2105.09746 [astro-ph.CO]

    2021 arXiv

  12. [20]

    L. Piga, M. Marinucci, G. D’Amico, M. Pietroni, F. Vernizzi, and B. S. Wright, Constraints on modified gravity from the BOSS galaxy survey, JCAP04, 038, arXiv:2211.12523 [astro-ph.CO]. 15

    arXiv

  13. [21]

    Holsclaw et al., Nonparametric reconstruction of the dark energy equation of state from diverse data sets, Phys

    T. Holsclaw et al., Nonparametric reconstruction of the dark energy equation of state from diverse data sets, Phys. Rev. D 84, 083501 (2011), arXiv:1104.2041 [astro-ph.CO]

    2011 arXiv

  14. [22]

    Giannantonio et al., Constraining primordial non-Gaussianity with future galaxy surveys, Mon

    T. Giannantonio et al., Constraining primordial non-Gaussianity with future galaxy surveys, Mon. Not. Roy. Astron. Soc. 422, 2854 (2012), arXiv:1109.0958 [astro-ph.CO]

    2012 arXiv

  15. [23]

    Karagiannis et al., Constraining primordial non-Gaussianity with bispectrum and power spectrum from upcoming optical and radio surveys, Mon

    D. Karagiannis et al., Constraining primordial non-Gaussianity with bispectrum and power spectrum from upcoming optical and radio surveys, Mon. Not. Roy. Astron. Soc.478, 1341 (2018), arXiv:1801.09280 [astro-ph.CO]

    2018 arXiv

  16. [24]

    Yamauchi, K

    D. Yamauchi, K. Takahashi, and M. Oguri, Constraining primordial non-Gaussianity via a multitracer technique with surveys by Euclid and the Square Kilometre Array, Phys. Rev. D90, 083520 (2014), arXiv:1407.5453 [astro-ph.CO]

    2014 arXiv

  17. [25]

    Brownet al., Constraining primordial non-Gaussianity from the large scale structure two-point and three-point correlation functions, (2024), arXiv:2403.18789 [astro-ph.CO]

    Z. Brownet al., Constraining primordial non-Gaussianity from the large scale structure two-point and three-point correlation functions, (2024), arXiv:2403.18789 [astro-ph.CO]

    2024

  18. [26]

    C. Hahn, F. Villaescusa-Navarro, E. Castorina, and R. Scoccimarro, ConstrainingMν with the bispectrum. Part I. Breaking parameter degeneracies, JCAP03, 040, arXiv:1909.11107 [astro-ph.CO]

    1909 arXiv

  19. [27]

    M. C. A. Cerbolini et al. , Constraining neutrino properties with a Euclid-like galaxy cluster survey, JCAP06, 020, arXiv:1303.4550 [astro-ph.CO]

    arXiv

  20. [28]

    Adamek et al

    J. Adamek et al. (Euclid), Euclid: Modelling massive neutrinos in cosmology – a code comparison, JCAP 06, 035, arXiv:2211.12457 [astro-ph.CO]

    arXiv

  21. [29]

    Dvorkin et al., Neutrino Mass from Cosmology: Probing Physics Beyond the Standard Model, (2019), arXiv:1903.03689 [astro-ph.CO]

    C. Dvorkin et al., Neutrino Mass from Cosmology: Probing Physics Beyond the Standard Model, (2019), arXiv:1903.03689 [astro-ph.CO]

    2019 arXiv

  22. [30]

    Nesseris et al

    S. Nesseris et al. (Euclid), Euclid: Forecast constraints on consistency tests of theΛCDM model, Astron. Astrophys.660, A67 (2022), arXiv:2110.11421 [astro-ph.CO]

    2022 arXiv

  23. [31]

    Camarena et al., Euclid: Testing the Copernican principle with next-generation surveys, Astronomy and Astrophysics 671, A68 (2023), arXiv:2207.09995 [astro-ph.CO]

    D. Camarena et al., Euclid: Testing the Copernican principle with next-generation surveys, Astronomy and Astrophysics 671, A68 (2023), arXiv:2207.09995 [astro-ph.CO]

    2023 arXiv

  24. [32]

    Pandey and S

    B. Pandey and S. Sarkar, Testing homogeneity of the galaxy distribution in the SDSS using Renyi entropy 10.1088/1475- 7516/2021/07/019 (2021), arXiv:2103.11954 [astro-ph.CO]

    2021 arXiv

  25. [33]

    Zunckel, D

    C. Zunckel, D. Huterer, and G. D. Starkman, Testing the statistical isotropy of large scale structure with multipole vectors, Phys. Rev. D84, 043005 (2011), arXiv:1009.4701 [astro-ph.CO]

    2011 arXiv

  26. [34]

    Bernardeau, S

    F. Bernardeau, S. Colombi, E. Gaztanaga, and R. Scoccimarro, Large scale structure of the universe and cosmological perturbation theory, Phys. Rept.367, 1 (2002), arXiv:astro-ph/0112551

    2002 arXiv

  27. [35]

    D. Blas, M. Garny, M. M. Ivanov, and S. Sibiryakov, Time-Sliced Perturbation Theory for Large Scale Structure I: General Formalism, JCAP07, 052, arXiv:1512.05807 [astro-ph.CO]

    arXiv

  28. [36]

    D. Blas, M. Garny, M. M. Ivanov, and S. Sibiryakov, Time-Sliced Perturbation Theory II: Baryon Acoustic Oscillations and Infrared Resummation, JCAP07, 028, arXiv:1605.02149 [astro-ph.CO]

    arXiv

  29. [37]

    Blas et al., Large scale structure from viscous dark matter, JCAP11, 049, arXiv:1507.06665 [astro-ph.CO]

    D. Blas et al., Large scale structure from viscous dark matter, JCAP11, 049, arXiv:1507.06665 [astro-ph.CO]

    arXiv

  30. [38]

    Baumann, A

    D. Baumann, A. Nicolis, L. Senatore, and M. Zaldarriaga, Cosmological Non-Linearities as an Effective Fluid, JCAP07, 051, arXiv:1004.2488 [astro-ph.CO]

    arXiv

  31. [39]

    J. J. M. Carrasco, M. P. Hertzberg, and L. Senatore, The Effective Field Theory of Cosmological Large Scale Structures, JHEP 09, 082, arXiv:1206.2926 [astro-ph.CO]

    arXiv

  32. [40]

    Aricò, R

    G. Aricò, R. E. Angulo, and M. Zennaro, Accelerating Large-Scale-Structure data analyses by emulating Boltzmann solvers and Lagrangian Perturbation Theory 10.12688/openreseurope.14310.2 (2021), arXiv:2104.14568 [astro-ph.CO]

    2021 arXiv

  33. [41]

    Cusin, M

    G. Cusin, M. Lewandowski, and F. Vernizzi, Dark Energy and Modified Gravity in the Effective Field Theory of Large-Scale Structure, JCAP 04, 005, arXiv:1712.02783 [astro-ph.CO]

    arXiv

  34. [42]

    Assassi et al., Effective theory of large-scale structure with primordial non-Gaussianity, JCAP11, 024, arXiv:1505.06668 [astro-ph.CO]

    V. Assassi et al., Effective theory of large-scale structure with primordial non-Gaussianity, JCAP11, 024, arXiv:1505.06668 [astro-ph.CO]

    arXiv

  35. [43]

    Senatore and M

    L. Senatore and M. Zaldarriaga, The Effective Field Theory of Large-Scale Structure in the presence of Massive Neutrinos, (2017), arXiv:1707.04698 [astro-ph.CO]

    2017 arXiv

  36. [44]

    Chudaykin and M

    A. Chudaykin and M. M. Ivanov, Measuring neutrino masses with large-scale structure: Euclid forecast with controlled theoretical error, JCAP11, 034, arXiv:1907.06666 [astro-ph.CO]

    1907 arXiv

  37. [45]

    Vasudevan, M

    A. Vasudevan, M. M. Ivanov, S. Sibiryakov, and J. Lesgourgues, Time-sliced perturbation theory with primordial non- Gaussianity and effects of large bulk flows on inflationary oscillating features, JCAP09, 037, arXiv:1906.08697 [astro-ph.CO]

    1906 arXiv

  38. [46]

    Zhang and Y

    P. Zhang and Y. Cai, BOSS full-shape analysis from the EFTofLSS with exact time dependence, JCAP01 (01), 031, arXiv:2111.05739 [astro-ph.CO]

    arXiv

  39. [47]

    M. M. Ivanov, M. Simonović, and M. Zaldarriaga, Cosmological Parameters from the BOSS Galaxy Power Spectrum, JCAP 05, 042, arXiv:1909.05277 [astro-ph.CO]

    1909 arXiv

  40. [48]

    Carrilho, C

    P. Carrilho, C. Moretti, and A. Pourtsidou, Cosmology with the EFTofLSS and BOSS: dark energy constraints and a note on priors, JCAP01, 028, arXiv:2207.14784 [astro-ph.CO]

    arXiv

  41. [49]

    A. G. Adameet al. (DESI), DESI 2024 VI: Cosmological Constraints from the Measurements of Baryon Acoustic Oscillations, (2024), arXiv:2404.03002 [astro-ph.CO]

    2024 arXiv

  42. [50]

    Chenet al., Suppression without Thawing: Constraining Structure Formation and Dark Energy with Galaxy Clustering, (2024), arXiv:2406.13388 [astro-ph.CO]

    S.-F. Chenet al., Suppression without Thawing: Constraining Structure Formation and Dark Energy with Galaxy Clustering, (2024), arXiv:2406.13388 [astro-ph.CO]

    2024 arXiv

  43. [51]

    Cabass et al., BOSS Constraints on Massive Particles during Inflation: The Cosmological Collider in Action, (2024), arXiv:2404.01894 [astro-ph.CO]

    G. Cabass et al., BOSS Constraints on Massive Particles during Inflation: The Cosmological Collider in Action, (2024), arXiv:2404.01894 [astro-ph.CO]

    2024 arXiv

  44. [52]

    N. S. Sugiyamaet al., New constraints on cosmological modified gravity theories from anisotropic three-point correlation functions of BOSS DR12 galaxies 10.1093/mnras/stad1505 (2023), arXiv:2302.06808 [astro-ph.CO]

    2023 arXiv

  45. [53]

    Hoyle et al

    B. Hoyle et al. (DES), Dark Energy Survey Year 1 Results: Redshift distributions of the weak lensing source galaxies, Mon. 16 Not. Roy. Astron. Soc.478, 592 (2018), arXiv:1708.01532 [astro-ph.CO]

    2018 arXiv

  46. [54]

    Ilbert et al

    O. Ilbert et al. (Euclid), Euclid preparation. XI. Mean redshift determination from galaxy redshift probabilities for cosmic shear tomography, Astron. Astrophys.647, A117 (2021), arXiv:2101.02228 [astro-ph.CO]

    2021 arXiv

  47. [55]

    A. S. Boltonet al., Spectral Classification and Redshift Measurement for the SDSS-III Baryon Oscillation Spectroscopic Survey, The Astronomical Journal144, 144 (2012), arXiv:1207.7326 [astro-ph.CO]

    2012 arXiv

  48. [56]

    Scoccimarro, S

    R. Scoccimarro, S. Colombi, J. N. Fry, J. A. Frieman, E. Hivon, and A. Melott, Nonlinear evolution of the bispectrum of cosmological perturbations, Astrophys. J.496, 586 (1998), arXiv:astro-ph/9704075

    1998 arXiv

  49. [57]

    Pryer, R

    D. Pryer, R. E. Smith, R. Booth, C. Blake, A. Eggemeier, and J. Loveday, The galaxy power spectrum on the lightcone: deep, wide-angle redshift surveys and the turnover scale, JCAP08 (08), 019, arXiv:2111.01811 [astro-ph.CO]

    arXiv

  50. [58]

    Semenzato, D

    F. Semenzato, D. Bertacca, and A. Raccanelli, The full-sky Spherical Fourier-Bessel power spectrum in general relativity, (2024), arXiv:2406.09545 [astro-ph.CO]

    2024 arXiv

  51. [59]

    Raccanelli and Z

    A. Raccanelli and Z. Vlah, Power spectrum in the cave, (2023), arXiv:2305.16278 [astro-ph.CO]

    2023 arXiv

  52. [60]

    Raccanelli and Z

    A. Raccanelli and Z. Vlah, Observed power spectrum and frequency-angular power spectrum, Phys. Rev. D108, 043537 (2023), arXiv:2306.00808 [astro-ph.CO]

    2023 arXiv

  53. [61]

    Z. Gao, A. Raccanelli, and Z. Vlah, Asymptotic connection between full- and flat-sky angular correlators, Phys. Rev. D 108, 043503 (2023), arXiv:2306.02993 [astro-ph.CO]

    2023 arXiv

  54. [62]

    Z. Gao, Z. Vlah, and A. Challinor, Flat-sky angular power spectra revisited, JCAP02, 003, arXiv:2307.13768 [astro-ph.CO]

    arXiv

  55. [63]

    Desjacques, D

    V. Desjacques, D. Jeong, and F. Schmidt, Large-Scale Galaxy Bias, Phys. Rept.733, 1 (2018), arXiv:1611.09787 [astro- ph.CO]

    2018 arXiv

  56. [64]

    D. L. Tuckeret al., The Las Campanas Redshift Survey galaxy—galaxy autocorrelation function, Monthly Notices of the Royal Astronomical Society285, L5 (1997), https://academic.oup.com/mnras/article-pdf/285/1/L5/3158615/285-1-L5.pdf

    1997

  57. [65]

    Krause and C

    E. Krause and C. M. Hirata, Weak lensing power spectra for precision cosmology. Multiple-deflection, reduced shear, and lensing bias corrections, Astronomy and Astrophysics

  58. [66]

    A. C. Deshpandeet al., Euclid preparation. XXXVI. Modelling the weak lensing angular power spectrum, Astronomy and Astrophysics 684, A138 (2024), arXiv:2302.04507 [astro-ph.CO]

    2024 arXiv

  59. [67]

    Hayashi and S

    E. Hayashi and S. D. M. White, Understanding the halo-mass and galaxy-mass cross-correlation functions, Monthly Notices of the Royal Astronomical Society388, 2 (2008), https://academic.oup.com/mnras/article-pdf/388/1/2/18718120/mnras0388- 0002.pdf

    2008

  60. [68]

    T. S. Fraser, E. Paillas, W. J. Percival, S. Nadathur, S. Radinović, and H. A. Winther, Modelling the BOSS void-galaxy cross-correlation function using a neural-network emulator, (2024), arXiv:2407.03221 [astro-ph.CO]

    2024 arXiv

  61. [69]

    Kirk et al., Cross correlation surveys with the Square Kilometre Array, (2015), arXiv:1501.03848 [astro-ph.CO]

    D. Kirk et al., Cross correlation surveys with the Square Kilometre Array, (2015), arXiv:1501.03848 [astro-ph.CO]

    2015 arXiv

  62. [70]

    L. Dam, K. Bolejko, and G. F. Lewis, Exploring the redshift-space peculiar velocity field and its power spectrum, JCAP09, 018, arXiv:2105.12933 [astro-ph.CO]

    arXiv

  63. [71]

    Howlett et al., 2MTF – VI

    C. Howlett et al., 2MTF – VI. Measuring the velocity power spectrum, Mon. Not. Roy. Astron. Soc.471, 3135 (2017), arXiv:1706.05130 [astro-ph.CO]

    2017 arXiv

  64. [72]

    Tonegawaet al., The effects of non-linearity on the growth rate constraint from velocity correlation functions, Mon

    M. Tonegawaet al., The effects of non-linearity on the growth rate constraint from velocity correlation functions, Mon. Not. Roy. Astron. Soc.529, 4787 (2024), arXiv:2309.14457 [astro-ph.CO]

    2024 arXiv

  65. [73]

    Kacprzak and J

    T. Kacprzak and J. Fluri, DeepLSS: Breaking Parameter Degeneracies in Large-Scale Structure with Deep-Learning Analysis of Combined Probes, Phys. Rev. X12, 031029 (2022), arXiv:2203.09616 [astro-ph.CO]

    2022 arXiv

  66. [74]

    Singh et al., Cosmological constraints from galaxy lensing cross-correlations using BOSS galaxies with SDSS and CMB lensing, Mon

    S. Singh et al., Cosmological constraints from galaxy lensing cross-correlations using BOSS galaxies with SDSS and CMB lensing, Mon. Not. Roy. Astron. Soc.491, 51 (2020), arXiv:1811.06499 [astro-ph.CO]

    2020 arXiv

  67. [75]

    Schmittfull and U

    M. Schmittfull and U. Seljak, Parameter constraints from cross-correlation of CMB lensing with galaxy clustering, Phys. Rev. D 97, 123540 (2018), arXiv:1710.09465 [astro-ph.CO]

    2018 arXiv

  68. [76]

    Scoccimarro, Fast Estimators for Redshift-Space Clustering, Phys

    R. Scoccimarro, Fast Estimators for Redshift-Space Clustering, Phys. Rev. D92, 083532 (2015), arXiv:1506.02729 [astro- ph.CO]

    2015 arXiv

Pith tools

Reviewed August 7, 2026 · model on record in the stance chip above.