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Imprints of Large-Scale Structures in the Anisotropies of the Cosmological Gravitational Wave Background

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

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Pith's one-line read Cosmological gravitational-wave background anisotropies are predicted to correlate with galaxy density through the late ISW effect, a signature that could separate cosmological from astrophysical signals.

desk verdict New CGWB-LSS cross-correlation probe with a plausible ISW-dominance claim; main risk is an unverified low-ell approximation and an idealized forecast. read the letter →

arxiv 2505.15084 v1 pith:NBA2SBCP submitted 2025-05-21 astro-ph.CO gr-qchep-th

Rafael Bravo , Walter Riquelme This is my paper · ORCID
classification astro-ph.COgr-qchep-th
keywords cosmologicalgravitationalwavebackgroundintegratedSachs-WolfeeffectGW-LSScross-correlationscalar-inducedwavesprimordialnon-GaussianitygalaxybiasangularpowerspectrumFisherforecast
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

The paper predicts that anisotropies in a cosmological gravitational-wave background (CGWB) are correlated with the galaxy density contrast, and that the correlation is dominated by the late integrated Sachs-Wolfe (ISW) effect, the same potential-decay imprint seen in CMB and large-scale structure studies. If this is right, the correlation supplies a nearly source-independent baseline: all cosmological GW sources should show roughly $\sim 1/\sqrt{(\ell+1)^3}$ scaling on large scales, plus a $\propto f_{\rm NL}/(\ell\sqrt{(\ell+1)^3})$ term, while astrophysical backgrounds scale as $1/(\ell+1/2)$. The paper also shows that for scalar-induced gravitational waves with local primordial non-Gaussianity, the cross-correlation carries $f_{\rm NL}$ information, with a forecast uncertainty of order $\sigma(f_{\rm NL})\sim 10$ under cosmic variance alone and a modest improvement when combined with galaxy clustering. A reader would care because a measurable CGWB$\times$LSS signal would be a new cosmological probe and a way to identify the origin of the stochastic background.

What carries the argument

The machinery is the line-of-sight solution of the linearized kinetic equation for gravitons, decomposed into initial-condition, early-time line-of-sight, and ISW contributions. The load-bearing element is the late-ISW kernel $I^{\rm ISW}_\ell$ built from the growth rate $\mathrm{d}g/\mathrm{d}\eta\simeq -(4/5)(\eta/\eta_0)^3$ during dark-energy domination, together with the Bessel-integral estimate of Eq. (52) that removes the early-time terms from the galaxy cross-correlation. A second ingredient is the $f_{\rm NL}$ bridge for scalar-induced GWs, which couples long-wavelength curvature modes to the short-scale GW source and generates the initial anisotropy, and the corresponding scale-dependent galaxy bias that lets $f_{\rm NL}$ enter the galaxy side of the correlation. These pieces together produce the characteristic large-scale slope and the forecast signal-to-noise behavior.

What would settle it

A decisive numerical check is to compute $C^{\rm CGWB-gal}_\ell$ at $\ell=2$-$5$ with and without the initial-condition and early-time line-of-sight terms; if the difference is comparable to the cosmic-variance error from the variance formula of Eq. (60), the claimed ISW-only dominance and source-independent universality fail. A decisive observational check is to measure the large-scale angular slope of the GW-galaxy correlation in future survey data: the predicted $\sim 1/\sqrt{(\ell+1)^3}$ shape is the fingerprint that would separate a cosmological from an astrophysical background.

Watch

Extended reading notes

Core claim

The central claim is that $C^{\rm CGWB-gal}_\ell$ is nonzero and essentially equal to the late-ISW piece $C^{\rm ISW-gal}_\ell$. The initial-condition and early-time line-of-sight terms are suppressed by a Bessel factor $((\eta_0-\eta_z)/(\eta_0-\eta_{\rm in}))^{\ell\pm 1/2}$, whose magnitude at the lowest multipoles is only $\sim 0.1$-$0.3$, and the paper argues from full numerical integration that those terms are subdominant. The resulting large-scale estimate is $C^{\rm ISW-gal}_\ell \sim 1/\sqrt{(\ell+1)^3} + A f_{\rm NL}/(\ell\sqrt{(\ell+1)^3})$, which differs from the astrophysical scaling $C^{\rm AGW-gal}_\ell \sim 1/(\ell+1/2)$. For scalar-induced GWs with local non-Gaussianity, $f_{\rm NL}$ enters both the GW background amplitude and the galaxy scale-dependent bias, and the paper forecasts $\sigma(f_{\rm NL})\sim 10$ with cosmic variance only, $\sigma(f_{\rm NL})\sim 11.75$ with interferometer noise included, and a joint analysis that improves galaxy-only constraints by about 4%.

Load-bearing premise

The claim that the cross-correlation is completely driven by the late ISW effect rests on the assumption that the early-time initial-condition and line-of-sight terms are strongly suppressed at low multipoles by the Bessel factor $((\eta_0-\eta_z)/(\eta_0-\eta_{\rm in}))^{\ell\pm 1/2}$; at $\ell=2$-$5$ that factor is only $\sim 0.1$-$0.3$, so the assertion must be validated by the full numerical integration against the ISW-only curve.

Editorial extensions

If this is right

  • If the prediction holds, a detection of CGWB$\times$LSS at low multipoles would distinguish cosmological from astrophysical GW backgrounds by their angular slope: roughly $1/\sqrt{(\ell+1)^3}$ rather than $1/(\ell+1/2)$.
  • Because the late ISW effect dominates, the cross-correlation becomes a nearly source-independent cosmological probe, robust to how the CGWB was generated.
  • For scalar-induced GWs with local non-Gaussianity, the same cross-correlation carries $f_{\rm NL}$ information, with forecast $\sigma(f_{\rm NL})\sim 10$ under cosmic variance alone and a joint analysis improving galaxy-only constraints by about 4%.
  • Signal-to-noise estimates indicate the cross-correlation could be distinguishable from noise for favorable $f_{\rm NL}$ values, with the SNR peaking near $f_{\rm NL}=-0.1$.

Reading between the lines

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

  • Beyond the paper's claims, the implied frequency independence of the late-ISW contribution suggests the angular slope of the CGWB$\times$LSS correlation should be stable across GW frequency bands after rescaling by the monopole, so a measured slope that changes with frequency would flag astrophysical contamination.
  • Beyond the paper's claims, because the late ISW is shared with the CMB, a joint analysis of CGWB$\times$LSS and CMB$\times$LSS could isolate the gravitational-wave transfer function and provide a dark-energy consistency test without CMB temperature foregrounds.
  • Beyond the paper's forecast, the quoted 4% improvement assumes full sky, no mask, and no shot noise; realistic survey masks and parameter degeneracies will dilute it, but the multi-tracer strategy can still be combined with other forthcoming probes.
  • A testable extension is to look for the same $1/\sqrt{(\ell+1)^3}$ shape in the cross-correlation of the stochastic background with galaxy surveys before GW anisotropy maps reach detection threshold, using the ISW-galaxy correlation as a template.
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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 computes the angular cross-correlation between anisotropes of the cosmological gravitational wave background (CGWB) and the galaxy density contrast, using a Boltzmann treatment of tensor modes and specializing the CGWB to scalar-induced gravitational waves (SIGWs) with local primordial non-Gaussianity. It argues that at large angular scales this cross-correlation is dominated by the late integrated Sachs-Wolfe (ISW) effect, with the scaling C_ℓ^CGWB−gal ≈ C_ℓ^ISW−gal ∝ 1/√(ℓ+1)^3 plus a term ∝ f_NL/(ℓ√(ℓ+1)^3), in contrast to the astrophysical gravitational wave background (AGWB)−galaxy correlation scaling ∼1/(ℓ+1/2). Using an LSST-like galaxy survey and ET+CE noise, the paper performs an SNR analysis and Fisher forecasts, reporting σ(f_NL) ≈ 10 from the cross-correlation alone and a roughly 4% improvement when the cross-correlation is combined with galaxy clustering.

Significance. If the ISW-dominance result is robust, the paper provides a potentially useful, source-universal baseline for separating cosmological from astrophysical gravitational wave backgrounds, and it identifies a new multi-tracer route to constraining f_NL. The analytic estimates are instructive, the relevant equations are presented transparently, and the numerical pipeline builds on public codes. The two main caveats are that the central low-multipole numerical check behind the universality claim is not yet reproducible because the modified GW CLASS code is not public, and that the detectability and forecast numbers rest on several explicitly optimistic assumptions. With those caveats addressed, the work would be a solid contribution to the CGWB×LSS literature.

major comments (3)
  1. [Sec. IV, Eq. (52), Fig. 4] The universality claim that the cross-correlation is "completely driven by the ISW effect" and therefore "general for all possible sources of CGWB anisotropies" rests on the suppression of the initial-condition term (32) and Schwarschild/Sachs-Wolfe term (33 evaluated at η_in) in the Bessel integral (51), as estimated in Eq. (52). For the adopted LSST-like bins (z≈0.3–1.1), the suppression is not overwhelming at the lowest multipoles: at ℓ=2–5 the factor in Eq. (52) is of order 0.1–0.3, exactly where the ISW signal is largest. The analytic estimate therefore does not by itself establish that the early-time contributions are negligible. The paper states that the total and late-ISW-only curves coincide in the middle panel of Fig. 4, but the modified GW CLASS code is not public, so this decisive numerical check cannot be independently verified. I request a quantitative breakdown of [C_total^(CGWB−gal) − C_ISW^(CGWB−gal)]/C_total^(CGWB−gal) for ℓ=2–20, or release of the code, so the low-ℓ residual is quantified. If the residual is not small, the universality statement and the clean shape distinction from the AGWB scaling (ℓ+1/2)^{-1} need to be qualified. Also, even in the ISW-dominated limit the observed cross-correlation (58) retains a source-dependent prefactor Ω_GW(q)(4−n_GW(q)), so the universality applies to the shape, not to the amplitude; this should be stated explicitly.
  2. [Sec. V.B, Eq. (60), Table I] The detectability statements in Section V rely on a chain of optimistic choices: a detection threshold SNR>1, full-sky coverage f_sky=1, no integral constraint, no shot noise in the galaxy sample, and a CGWB monopole amplitude fixed five orders of magnitude above the ET+CE sensitivity at f_pivot=63 Hz. The text labels these as optimistic, but the SNR values in Table I and Fig. 5 are nonetheless presented as the paper's detection prospects. For the "general CGWB" model, the CV-only SNR is only about 2.7–3.0, so a realistic sky fraction, a mask, or the integral constraint could move the claimed detection below threshold. I recommend adding at least a simple robustness test (e.g., f_sky<1 or a non-ideal noise case) or, failing that, rewording the abstract and conclusions so that the "could be distinguishable from noise" claim is explicitly tied to the idealized assumptions.
  3. [Sec. V.C, Table II] The Fisher forecast varies only f_NL while holding all cosmological and nuisance parameters fixed, ignores cross-covariance between galaxy bins, and drops the galaxy−cross covariance because the galaxy autocorrelation amplitude is about nine orders of magnitude larger. The authors acknowledge that realistic scenarios will worsen the constraint, but the 4% and 3.5% improvement numbers are therefore upper limits rather than expected constraints. I would ask that this be stated explicitly in the abstract or conclusions, so the quantitative claim is not over-read.
minor comments (5)
  1. [Sec. III, Eq. (42)] The Gaussian selection function appears to have a typo: the exponent should be −(z−z_bin)^2/(2σ_z^2), not −(z−z_bin)^2/(2πσ_z^2).
  2. [Sec. IV, Eq. (52)] The display of Eq. (52) is hard to parse: the placement of parentheses and exponents should be made explicit, and the dimensional consistency of the expression should be checked.
  3. [Sec. IV and Sec. V.C] There are small typos: "fromm" in Section IV and "CGBW" in Section V.C should be corrected.
  4. [Fig. 4 caption] The color references in the caption and text are inconsistent ("red and green dashed" vs. the text saying "green line"); please unify them.
  5. [Sec. II.A, around Eq. (28)] The notation for the expansion order of the background in powers of f_NL is described as "(f_NL^{2n})"; this should be written unambiguously, e.g., as proportional to (f_NL^2)^n.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity: the CGWB×LSS cross-correlation is derived from Boltzmann transport with no fitted inputs; the ISW-dominance claim is an approximation to be validated numerically, not a definitional reduction.

full rationale

The paper's derivation chain is self-contained against standard Boltzmann transport. The CGWB anisotropies in Eq. (5) come from solving the linear Boltzmann equation with initial-condition, Sachs-Wolfe and ISW terms; the galaxy density contrast in Eq. (43) uses standard bias and selection functions. The central claim that C^{CGW-gal}_ℓ ≃ C^{ISW-gal}_ℓ is supported by the analytic Bessel-integral suppression estimate (Eqs. 51–52) and by a full numerical comparison (Fig. 4, middle panel); it is an approximation to be checked at low ℓ, not a definitional identity and not a fitted parameter. The f_NL forecast in Sec. V treats f_NL as an input and computes σ(f_NL) from Fisher information; no prediction reduces to a fitted value. The SIGW background and anisotropy expressions cite external public literature and public codes (GW CLASS, Multi CLASS, and the public ngsigw-results repository); the only in-house self-citations ([39] on single-field soft theorems and [41] on angular-correlation integral constraints) are contextual or a caveat and carry no load in the computation. The possible low-ℓ failure of the ISW-dominance approximation is a correctness and validation risk, not a circularity.

Assumptions & free parameters 3 free parameters · 6 assumptions · 0 invented entities

The central cross-correlation result needs only standard LambdaCDM inputs and the Boltzmann framework, so the ledger is light. The parameters that matter for detection and forecast numbers are the chosen SIGW amplitude A_s, the fiducial f_NL values, and the optimistic monopole normalization relative to ET+CE sensitivity. The main domain assumptions concern the growth-factor approximation, the monochromatic peak model for SIGW, and the galaxy bias model. No new particles or forces are introduced.

free parameters (3)
  • Short-scale curvature power amplitude A_s = 3e-3
    Set by hand to define the SIGW peak (Eq. 29 and Fig. 2). It controls the overall GW background amplitude and therefore the SNR in the ET+CE scenario, but not the existence of the cross-correlation.
  • Fiducial f_NL^loc values = -0.1, 0.4, 1.2
    Chosen as fiducial values for the Fisher forecast based on the SNR analysis (Table II). They are model inputs, not fitted to data.
  • CGWB monopole normalization = 5 orders of magnitude above ET+CE sensitivity at fpivot=63 Hz
    Optimistic assumption adopted in Section V to estimate detector noise via schNell; strongly affects the detectability forecast but not the theoretical cross-correlation.
assumptions (6)
  • standard math Boltzmann equation for collisionless massless gravitons in a linearly perturbed FLRW metric (Eqs. 2-5).
    Underpins the computation of all CGWB anisotropies; standard in the field.
  • domain assumption SIGW source is described by a monochromatic peak in the curvature power spectrum with A_s = 3e-3 and local-type non-Gaussianity (Eqs. 1, 23, 29).
    Used to build the background and anisotropies; not derived from data.
  • domain assumption Long-wavelength modes relevant for the cross-correlation re-entered during matter domination, with T(k << 1) = 1 and growth rate dg/deta = -(4/5)(eta/eta0)^3 (Eqs. 33, 35-36).
    Required for the late-ISW kernel and the analytic estimates; deviations in the growth history would alter the signal.
  • domain assumption Galaxy bias is the sum of a linear Gaussian bias and the scale-dependent non-Gaussian correction with p = 1 and delta_c = 1.686 (Eqs. 40, 48).
    Standard local-PNG bias model used for all LSS calculations and forecasts.
  • ad hoc to paper Detection forecasts assume full-sky coverage (fsky = 1), no integral constraint, no shot noise, and an optimistic SNR threshold of 1 (Section V).
    Explicitly optimistic; the authors state that realistic masks and noise will worsen the results.
  • ad hoc to paper The CGWB monopole amplitude is taken to be five orders of magnitude above ET+CE sensitivity at fpivot = 63 Hz.
    Adopted to make the detectability forecasts concrete; not an output of the model.

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Cite this review

Pith. "Pith review of Imprints of Large-Scale Structures in the Anisotropies of the Cosmological Gravitational Wave Background." pith.science (2026). https://pith.science/paper/NBA2SBCP

@misc{pith2026250515084,
  author       = {Pith},
  title        = {Pith review of: Imprints of Large-Scale Structures in the Anisotropies of the Cosmological Gravitational Wave Background},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/NBA2SBCP}},
  note         = {Machine review of arXiv:2505.15084}
}
abstract

We compute the cross-correlation between the anisotropies of the cosmological gravitational wave background (CGWB) and the galaxy density contrast. We show that the cross-correlation is non-zero due to the {\it late} integrated Sachs-Wolfe (ISW) effect experienced by tensor modes. We study the detection prospects of the cross-correlation signal against cosmic variance (CV), and in the light of incoming LSS and GW surveys, where we found that the signal under certain conditions could be distinguishable from noise. In addition, by considering a CGWB sourced by scalar-induced gravitational waves, and the inclusion of a scale-dependent galaxy bias, we use the cross-correlation to forecast local primordial non-Gaussianity, where we find $\sigma(f_\text{NL}^\text{loc})\sim10$ for CV only and a LSST-like survey. Moreover, by combining the Fisher information of CGWB$\times$LSS with LSS, we are able to improve the constraints by 4\% compared to an LSS-only analysis. Our results imply that a cross-correlation between GW anisotropies and LSS can indeed come from a stochastic background of cosmological origin and could be used to distinguish it from an astrophysical one.

Figures

Figures reproduced from arXiv: 2505.15084 by the authors.

Figure 1
Figure 1. FIG. 1. Diagrammatic representation of [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
Figure 3
Figure 3. FIG. 3. Diagrammatic representation of [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗
Figure 4
Figure 4. FIG. 4. Comparison between the multiple correlations [PITH_FULL_IMAGE:figures/full_fig_p007_4.png] view at source ↗
Figures from the paper (1 more)
Figure 5
Figure 5. Figure 5: FIG. 5. SNR for the cross-correlation as a function of [PITH_FULL_IMAGE:figures/full_fig_p010_5.png]

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Forward citations

Cited by 1 Pith paper

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Reference graph

Works this paper leans on

72 extracted references · 13 canonical work pages · cited by 1 Pith paper

  1. [1]

    Background Once the solution (19) is known, we can compute the background GW energy density spectrum as the monopole term ¯ΩGW(q) = q5 48π2a2H 2 X +,× ⟨hλ(η, q)hλ′(η, q′)⟩, (21) where the over-bar denotes a time average over the os- cillations of the tensor modes. Explicitly the graviton two-point function is given by ⟨hλ1 (η, q1)hλ2 (η, q2)⟩ = 16 Z d3p1 ...

    work page

  2. [2]

    The for- mer contribution, for the case of SIGWs, appears only when there is a coupling between the short scale q−1 ∗ at which the GW was produced and a cosmological scale k−1

    Anisotropies As we mentioned at the beginning of this section, anisotropies in the GW energy spectrum can arise from both initial conditions and propagation effects. The for- mer contribution, for the case of SIGWs, appears only when there is a coupling between the short scale q−1 ∗ at which the GW was produced and a cosmological scale k−1. Primordial loc...

    work page

  3. [3]

    Caprini and D

    C. Caprini and D. G. Figueroa, Cosmological Backgrounds of Gravitational Waves, Class. Quant. Grav. 35 (2018) 163001 [1801.04268]

    arXiv 2018

  4. [4]

    Next, we compute the SNR of the cross-correlation for a LSST-like survey

    We begin by estimating the maximum SNR that could come from the ISW effect. Next, we compute the SNR of the cross-correlation for a LSST-like survey. Lastly, after studying the detectability of the CGWB-LSS cross- correlation signal, we use it in a Fisher-matrix forecast of the constraints on f loc NL.5 Our main focus is the detectability of the CGWB- LSS...

    work page

  5. [5]

    LIGO Scientific, Virgocollaboration, Observation of Gravitational Waves from a Binary Black Hole Merger , Phys. Rev. Lett. 116 (2016) 061102 [ 1602.03837]

    arXiv 2016

  6. [6]

    Maggiore, Gravitational wave experiments and early universe cosmology, Phys

    M. Maggiore, Gravitational wave experiments and early universe cosmology, Phys. Rept. 331 (2000) 283 [gr-qc/9909001]

    arXiv 2000

  7. [7]

    D. J. Reardon et al., Search for an Isotropic Gravitational-wave Background with the Parkes Pulsar Timing Array, Astrophys. J. Lett. 951 (2023) L6 [2306.16215]

    arXiv 2023

  8. [8]

    NANOGrav collaboration, The NANOGrav 15 yr Data Set: Evidence for a Gravitational-wave Background , Astrophys. J. Lett. 951 (2023) L8 [ 2306.16213]

    arXiv 2023

Show all 72 references
  1. [9]

    Xu et al., Searching for the Nano-Hertz Stochastic Gravitational Wave Background with the Chinese Pulsar Timing Array Data Release I , Res

    H. Xu et al., Searching for the Nano-Hertz Stochastic Gravitational Wave Background with the Chinese Pulsar Timing Array Data Release I , Res. Astron. Astrophys. 23 (2023) 075024 [ 2306.16216]

    2023 arXiv

  2. [10]

    Search for gravitational wave signals , Astron

    EPTA, InPTA:collaboration, The second data release from the European Pulsar Timing Array - III. Search for gravitational wave signals , Astron. Astrophys. 678 (2023) A50 [2306.16214]

    2023 arXiv

  3. [11]

    NANOGrav collaboration, The NANOGrav 15 yr Data Set: Search for Signals from New Physics , Astrophys. J. Lett. 951 (2023) L11 [ 2306.16219]

    2023 arXiv

  4. [12]

    KAGRA, Virgo, LIGO Scientificcollaboration, Upper limits on the isotropic gravitational-wave background from Advanced LIGO and Advanced Virgo’s third observing run , Phys. Rev. D 104 (2021) 022004 [ 2101.12130]

    2021

  5. [13]

    D. G. Figueroa, M. Pieroni, A. Ricciardone and P. Simakachorn, Cosmological Background Interpretation of Pulsar Timing Array Data , Phys. Rev. Lett. 132 (2024) 171002 [2307.02399]

    2024 arXiv

  6. [14]

    Ellis, M

    J. Ellis, M. Fairbairn, G. Franciolini, G. H¨ utsi, A. Iovino, M. Lewicki et al., What is the source of the PTA GW signal?, Phys. Rev. D 109 (2024) 023522 [ 2308.08546]

    2024 arXiv

  7. [15]

    Ricciardone, L

    A. Ricciardone, L. V. Dall’Armi, N. Bartolo, D. Bertacca, M. Liguori and S. Matarrese, Cross-Correlating Astrophysical and Cosmological Gravitational Wave Backgrounds with the Cosmic Microwave Background , Phys. Rev. Lett. 127 (2021) 271301 [2106.02591]

    2021 arXiv

  8. [16]

    C. R. Contaldi, Anisotropies of Gravitational Wave Backgrounds: A Line Of Sight Approach , Phys. Lett. B 771 (2017) 9 [ 1609.08168]

    2017 arXiv

  9. [17]

    J.-P. Li, S. Wang, Z.-C. Zhao and K. Kohri, Primordial non-Gaussianity f N Land anisotropies in scalar-induced gravitational waves, JCAP 10 (2023) 056 [ 2305.19950]

    2023 arXiv

  10. [18]

    LISA Cosmology Working Groupcollaboration, Probing anisotropies of the Stochastic Gravitational Wave Background with LISA , JCAP 11 (2022) 009 [ 2201.08782]

    2022 arXiv

  11. [19]

    Scelfo, N

    G. Scelfo, N. Bellomo, A. Raccanelli, S. Matarrese and L. Verde, GW×LSS: chasing the progenitors of merging binary black holes , JCAP 09 (2018) 039 [ 1809.03528]

    2018 arXiv

  12. [20]

    Braglia and S

    M. Braglia and S. Kuroyanagi, Probing prerecombination physics by the cross-correlation of stochastic gravitational waves and CMB anisotropies , Phys. Rev. D 104 (2021) 123547 [2106.03786]

    2021 arXiv

  13. [21]

    Perna, A

    G. Perna, A. Ricciardone, D. Bertacca and S. Matarrese, Non-Gaussianity from the cross-correlation of the 13 astrophysical Gravitational Wave Background and the Cosmic Microwave Background , JCAP 10 (2023) 014 [2302.08429]

    2023 arXiv

  14. [22]

    Z.-C. Zhao, S. Wang, J.-P. Li and K. Kohri, Study of primordial non-Gaussianity fNL and gNL with the cross-correlations between the scalar-induced gravitational waves and the cosmic microwave background , [2412.02500]

  15. [23]

    Cusin, C

    G. Cusin, C. Pitrou, M. Pijnenburg and A. Sesana, Measuring anisotropies in the PTA band with cross-correlations, [2502.17401]

    arXiv

  16. [24]

    M. Bosi, N. Bellomo and A. Raccanelli, Constraining extended cosmologies with GW ×LSS cross-correlations, JCAP 11 (2023) 086 [ 2306.03031]

    2023 arXiv

  17. [25]

    Semenzato, J

    F. Semenzato, J. A. Casey-Clyde, C. M. F. Mingarelli, A. Raccanelli, N. Bellomo, N. Bartolo et al., Cross-Correlating the Universe: The Gravitational Wave Background and Large-Scale Structure, [2411.00532]

    arXiv

  18. [26]

    Pedrotti, M

    A. Pedrotti, M. Mancarella, J. Bel and D. Gerosa, Cosmology with the angular cross-correlation of gravitational-wave and galaxy catalogs: forecasts for next-generation interferometers and the Euclid survey , [2504.10482]

    arXiv

  19. [27]

    Giannantonio, R

    T. Giannantonio, R. Scranton, R. G. Crittenden, R. C. Nichol, S. P. Boughn, A. D. Myers et al., Combined analysis of the integrated Sachs-Wolfe effect and cosmological implications, Phys. Rev. D 77 (2008) 123520 [ 0801.4380]

    2008 arXiv

  20. [28]

    Libanore, M

    S. Libanore, M. C. Artale, D. Karagiannis, M. Liguori, N. Bartolo, Y. Bouffanais et al., Gravitational Wave mergers as tracers of Large Scale Structures , JCAP 02 (2021) 035 [2007.06905]

    2021 arXiv

  21. [29]

    R. K. Sachs and A. M. Wolfe, Perturbations of a cosmological model and angular variations of the microwave background, Astrophys. J. 147 (1967) 73

    1967

  22. [30]

    R. G. Crittenden and N. Turok, Looking for Lambda with the Rees-Sciama effect, Phys. Rev. Lett. 76 (1996) 575 [astro-ph/9510072]

    1996 arXiv

  23. [31]

    Dom` enech,Scalar Induced Gravitational Waves Review , Universe 7 (2021) 398 [ 2109.01398]

    G. Dom` enech,Scalar Induced Gravitational Waves Review , Universe 7 (2021) 398 [ 2109.01398]

    2021 arXiv

  24. [32]

    Cooray, Integrated sachs-Wolfe effect: Large scale structure correlation, Phys

    A. Cooray, Integrated sachs-Wolfe effect: Large scale structure correlation, Phys. Rev. D 65 (2002) 103510 [astro-ph/0112408]

    2002 arXiv

  25. [33]

    S. Ho, C. Hirata, N. Padmanabhan, U. Seljak and N. Bahcall, Correlation of CMB with large-scale structure: I. ISW Tomography and Cosmological Implications , Phys. Rev. D 78 (2008) 043519 [ 0801.0642]

    2008 arXiv

  26. [34]

    Giannantonio, A

    T. Giannantonio, A. J. Ross, W. J. Percival, R. Crittenden, D. Bacher, M. Kilbinger et al., Improved Primordial Non-Gaussianity Constraints from Measurements of Galaxy Clustering and the Integrated Sachs-Wolfe Effect , Phys. Rev. D 89 (2014) 023511 [ 1303.1349]

    2014 arXiv

  27. [35]

    Wang, Z.-C

    S. Wang, Z.-C. Zhao, J.-P. Li and Q.-H. Zhu, Implications of pulsar timing array data for scalar-induced gravitational waves and primordial black holes: Primordial non-Gaussianity fNL considered, Phys. Rev. Res. 6 (2024) L012060 [2307.00572]

    2024 arXiv

  28. [36]

    Sasaki, T

    M. Sasaki, T. Suyama, T. Tanaka and S. Yokoyama, Primordial black holes—perspectives in gravitational wave astronomy, Class. Quant. Grav. 35 (2018) 063001 [1801.05235]

    2018 arXiv

  29. [37]

    B. Carr, S. Clesse, J. Garcia-Bellido, M. Hawkins and F. Kuhnel, Observational evidence for primordial black holes: A positivist perspective, Phys. Rept. 1054 (2024) 1 [2306.03903]

    2024 arXiv

  30. [38]

    R.-g. Cai, S. Pi and M. Sasaki, Gravitational Waves Induced by non-Gaussian Scalar Perturbations , Phys. Rev. Lett. 122 (2019) 201101 [ 1810.11000]

    2019 arXiv

  31. [39]

    Bravo and G

    R. Bravo and G. A. Palma, Unifying attractor and nonattractor models of inflation under a single soft theorem , Phys. Rev. D 107 (2023) 043524 [ 2009.03369]

    2023 arXiv

  32. [40]

    Tanaka and Y

    T. Tanaka and Y. Urakawa, Dominance of gauge artifact in the consistency relation for the primordial bispectrum , JCAP 05 (2011) 014 [ 1103.1251]

    2011 arXiv

  33. [41]

    Pajer, F

    E. Pajer, F. Schmidt and M. Zaldarriaga, The Observed Squeezed Limit of Cosmological Three-Point Functions , Phys. Rev. D 88 (2013) 083502 [ 1305.0824]

    2013 arXiv

  34. [42]

    G. L. Pimentel, Inflationary Consistency Conditions from a Wavefunctional Perspective, JHEP 02 (2014) 124 [1309.1793]

    2014 arXiv

  35. [43]

    R. A. Isaacson, Gravitational Radiation in the Limit of High Frequency. I. The Linear Approximation and Geometrical Optics, Phys. Rev. 166 (1968) 1263

    1968

  36. [44]

    Chaussidon et al., Constraining primordial non-Gaussianity with DESI 2024 LRG and QSO samples , [2411.17623]

    E. Chaussidon et al., Constraining primordial non-Gaussianity with DESI 2024 LRG and QSO samples , [2411.17623]

    2024 arXiv

  37. [45]

    5 10-3 10-2 10-1 10010-10 10-9 10-8 10-7 10-6 10-5 10-4 FIG

    publicly available at https://github.com/zachjweiner/ ngsigw-results. 5 10-3 10-2 10-1 10010-10 10-9 10-8 10-7 10-6 10-5 10-4 FIG. 2. Background induced GW spectrum Ω GW(q) for a monochromatic source with As = 3 × 10−3 for various values of f loc NL. By showing the spectrum as...

  38. [46]

    Riquelme et al., Primordial non-Gaussianity with angular correlation function: integral constraint and validation for DES , Mon

    W. Riquelme et al., Primordial non-Gaussianity with angular correlation function: integral constraint and validation for DES , Mon. Not. Roy. Astron. Soc. 523 (2023) 603 [2209.07187]

    2023 arXiv

  39. [47]

    L. R. Abramo and K. E. Leonard, Why multi-tracer surveys beat cosmic variance, Mon. Not. Roy. Astron. Soc. 432 (2013) 318 [ 1302.5444]

    2013 arXiv

  40. [48]

    Unal, Imprints of Primordial Non-Gaussianity on Gravitational Wave Spectrum, Phys

    C. Unal, Imprints of Primordial Non-Gaussianity on Gravitational Wave Spectrum, Phys. Rev. D 99 (2019) 041301 [1811.09151]

    2019 arXiv

  41. [49]

    Adshead, K

    P. Adshead, K. D. Lozanov and Z. J. Weiner, Non-Gaussianity and the induced gravitational wave background, JCAP 10 (2021) 080 [ 2105.01659]

    2021 arXiv

  42. [50]

    Escriv` a, F

    A. Escriv` a, F. Kuhnel and Y. Tada,Primordial Black Holes , [2211.05767]

    arXiv

  43. [51]

    Bartolo, D

    N. Bartolo, D. Bertacca, V. De Luca, G. Franciolini, S. Matarrese, M. Peloso et al., Gravitational wave anisotropies from primordial black holes , JCAP 02 (2020) 028 [1909.12619]

    2020 arXiv

  44. [52]

    Tada and S

    Y. Tada and S. Yokoyama, Primordial black holes as biased tracers, Phys. Rev. D 91 (2015) 123534 [ 1502.01124]

    2015 arXiv

  45. [53]

    J.-P. Li, S. Wang, Z.-C. Zhao and K. Kohri, Complete analysis of the background and anisotropies of scalar-induced gravitational waves: primordial non-Gaussianity f N Land g N Lconsidered, JCAP 06 (2024) 039 [ 2309.07792]

    2024 arXiv

  46. [54]

    Maggiore, Gravitational Waves

    M. Maggiore, Gravitational Waves. Vol. 2: Astrophysics and Cosmology. Oxford University Press, 3, 2018

    2018

  47. [55]

    Dodelson and F

    S. Dodelson and F. Schmidt, Modern Cosmology. Academic Press, 2020, 10.1016/C2017-0-01943-2

    2020 doi

  48. [56]

    D. H. Lyth and A. R. Liddle, The Primordial Density Perturbation. 6, 2009, 10.1017/cbo9780511819209

    2009 doi

  49. [57]

    Schulze, L

    F. Schulze, L. Valbusa Dall’Armi, J. Lesgourgues, A. Ricciardone, N. Bartolo, D. Bertacca et al., GW CLASS: Cosmological Gravitational Wave Background in the cosmic linear anisotropy solving system , JCAP 10 (2023) 025 [2305.01602]

    2023 arXiv

  50. [58]

    Bellomo, J

    N. Bellomo, J. L. Bernal, G. Scelfo, A. Raccanelli and L. Verde, Beware of commonly used approximations. Part I. Errors in forecasts, JCAP 10 (2020) 016 [ 2005.10384]

    2020 arXiv

  51. [59]

    J. L. Bernal, N. Bellomo, A. Raccanelli and L. Verde, Beware of commonly used approximations. Part II. Estimating systematic biases in the best-fit parameters , JCAP 10 (2020) 017 [2005.09666]

    2020 arXiv

  52. [60]

    D. Blas, J. Lesgourgues and T. Tram, The cosmic linear anisotropy solving system (class). part ii: Approximation schemes, Journal of Cosmology and Astroparticle Physics 2011 (2011) 034034

    2011

  53. [61]

    LSST Dark Energy Sciencecollaboration, The LSST Dark Energy Science Collaboration (DESC) Science Requirements Document, [1809.01669]

    arXiv

  54. [62]

    De Vicente, E

    J. De Vicente, E. S´ anchez and I. Sevilla-Noarbe, DNF – Galaxy photometric redshift by Directional Neighbourhood Fitting, Mon. Not. Roy. Astron. Soc. 459 (2016) 3078 [1511.07623]. 14

    2016 arXiv

  55. [63]

    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. D 77 (2008) 123514 [ 0710.4560]

    2008 arXiv

  56. [64]

    Slosar, C

    A. Slosar, C. Hirata, U. Seljak, S. Ho and N. Padmanabhan, Constraints on local primordial non-Gaussianity from large scale structure, JCAP 08 (2008) 031 [ 0805.3580]

    2008 arXiv

  57. [65]

    Alonso, C

    D. Alonso, C. R. Contaldi, G. Cusin, P. G. Ferreira and A. I. Renzini, Noise angular power spectrum of gravitational wave background experiments, Phys. Rev. D 101 (2020) 124048 [2005.03001]

    2020 arXiv

  58. [66]

    Alonso, G

    D. Alonso, G. Cusin, P. G. Ferreira and C. Pitrou, Detecting the anisotropic astrophysical gravitational wave background in the presence of shot noise through cross-correlations , Phys. Rev. D 102 (2020) 023002 [ 2002.02888]

    2020 arXiv

  59. [67]

    Terasawa, Y

    R. Terasawa, Y. Nan and M. Takada, On the equivalence between galaxy angular correlation function and power spectrum in constraining primordial non-Gaussianity , [2501.12661]

    arXiv

  60. [68]

    G. Jung, M. Citran, B. van Tent, L. Dumilly and N. Aghanim, Constraints on primordial non-Gaussianity from Planck PR4 data , [2504.00884]

  61. [69]

    Euclid collaboration, Euclid. I. Overview of the Euclid mission, Astron. Astrophys. 697 (2025) A1 [ 2405.13491]

    2025

  62. [70]

    DESI collaboration, The Dark Energy Spectroscopic Instrument (DESI) , [1907.10688]

    1907 arXiv

  63. [71]

    Corbin and N

    V. Corbin and N. J. Cornish, Detecting the cosmic gravitational wave background with the big bang observer , Class. Quant. Grav. 23 (2006) 2435 [ gr-qc/0512039]

    2006 arXiv

  64. [72]

    Kawamura et al., Current status of space gravitational wave antenna DECIGO and B-DECIGO , PTEP 2021 (2021) 05A105 [ 2006.13545]

    S. Kawamura et al., Current status of space gravitational wave antenna DECIGO and B-DECIGO , PTEP 2021 (2021) 05A105 [ 2006.13545]

    2021 arXiv

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