Acoustic Signatures in the Primary Microwave Background Bispectrum

David N. Spergel (Princeton University); Eiichiro Komatsu

REVIEW

Acoustic Signatures in the Primary Microwave Background Bispectrum

Eiichiro Komatsu, David N. Spergel (Princeton University)

Astrophysics · Submitted 2 May 2000 · 48 references

Pith's verdict: The paper that gave the field its local f_NL bispectrum template with full transfer functions, plus the matched-filter argument; the physics holds up, the soft spots are the toy cosmology and the order-of-magnitude foreground numbers.

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arXiv IDastro-ph/0005036 (version 2)

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CitationDavid N. Spergel (Princeton University), Eiichiro Komatsu. "Acoustic Signatures in the Primary Microwave Background Bispectrum." arXiv:astro-ph/0005036 (2000). https://pith.science/paper/ZUNEAW4C

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Editor's note

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This is the paper that turned the CMB bispectrum from a Sachs-Wolfe curiosity into a working template. The core of it is Eqs. (16)-(19): the reduced bispectrum computed with the full CMBFAST transfer function rather than the large-scale limit. The result in Figure 2, that the primary bispectrum oscillates and changes sign with twice the period of the power spectrum, is the thing everyone since has built on. The matched-filter argument in Sec. III.C is the other keeper: once you know the shape, the bispectrum beats the skewness by roughly an order of magnitude, and Table V makes that concrete. The Fisher-matrix machinery in Sec. V, including the degradation parameters and correlation coefficients in Table IV, is clean and reusable. The derivation is straightforward and I don't see a step that's wrong. The numerical work uses the public transfer code with stated parameters, so it's reproducible in principle. Credit where due: this is careful, honest formalism work, and the authors flag their own weak spots in the body even though the abstract doesn't carry them. The classifier record says no limitations are stated; that's wrong. Sec. III.B says SCDM is nearly excluded, and Sec. V.C says the SZ amplitudes are order-of-magnitude only. Soft spots, in order of how much they matter. The background is SCDM with Omega_m = 1, which was already in trouble in 2000; the shape result is robust to that but the S/N numbers aren't. The foreground amplitudes are estimates, and the Fisher separation neglects sky coverage, so the 1% separation claim for MAP and Planck is optimistic. The dust skewness of 51 in Sec. VI is a single number with no sky cut and no error bar; I'd drop it or do it properly. On the stress-test note: it lands, but it's minor. The abstract's 'problematic for simple slow-roll' leans on f_NL ~ 0.01, while Sec. III.A and Sec. VI both say Pyne-Carroll second-order terms give f_NL ~ 1 and dominate for generic slow-roll. With f_NL ~ 1 the conclusion still holds, but Planck's threshold of 5 is only a factor of a few away, not hundreds. One clause in the abstract would fix it. Who should read it: anyone doing CMB non-Gaussianity, and anyone who wants the reference template. Send it to referees; the revision is light.

Referee report

Significance

This is a substantial and, if the results hold, high-impact contribution. The reduced-bispectrum formalism of Sec. II is a genuine conceptual contribution that has become the standard language for CMB bispectrum work, and the observation that the primary bispectrum oscillates and changes sign while secondaries do not is a physically well-motivated route to foreground separation. The paper is commendably explicit about its machinery: it uses the publicly available CMBFAST transfer function, states its cosmological parameters, and quotes all forecasts per unit f_NL, so the numbers in Table V are falsifiable predictions rather than fits to data. The matched-filter argument of Sec. III.C — that a computable bispectrum template is strictly more sensitive than the coarse-grained skewness — is supported quantitatively by Fig. 5 and Table V, with the ratio of required f_NL growing from 1.3 (COBE) to 20 (ideal) as resolution improves, which is exactly what the cancellation argument predicts. The internal arithmetic of the order-of-magnitude scalings in Eqs. (55)–(58) checks out against the numerical results of Tables I–III, which is a good sign for the robustness of the forecast pipeline.

Major objections (3)

[Abstract [s7]; Sec. III.A, final paragraph; Sec. VI, first paragraph] The headline claim of the abstract — that detection 'should be problematic for the simple slow-roll inflationary scenarios' — is stated without specifying which value of f_NL it rests on, and the body supplies two values that differ by two orders of magnitude. Sec. III.A states that Gangui et al. find f_NL ~ 10^{-2} for quadratic and quartic potentials, but then states that Pyne and Carroll's second-order general-relativistic terms give f_NL ~ O(1) and that 'for generic slow-roll models, these terms dominate the primary non-Gaussianity'; Sec. VI repeats both numbers. The conclusion survives either way, but the margin does not: against the Planck threshold of f_NL > 5 and the ideal-experiment threshold of f_NL > 3 (Table V), an operative value of f_NL ~ 1 leaves only a factor of a few, not the factor of 10^2–10^3 that the abstract's framing suggests. The abstract should state explicitly which value is being used for the 'problematic' claim, and should note that with the O(1) second-order contribution the Planck and ideal-experiment forecasts are marginal rather than hopeless. The same sentence in the abstract [s2] that MAP and Planck 'should be able to detect weak non-Gaussianity' is in mild tension with the paper's own conclusion and would read better if it were qualified in the same way.
[Sec. III.B and Table V] All numerical thresholds quoted in Table V and in the abstract's discussion are computed for a scale-invariant SCDM model with Omega_m = 1, Omega_Lambda = 0, Omega_b = 0.05, h = 0.5, which the authors themselves describe as 'almost excluded by current observations.' The sign-alternating acoustic peak structure of Fig. 2 is robust to this choice, but the specific f_NL thresholds are not obviously so: the peak positions and the damping-tail behaviour that set the l at which d(S/N)/d ln l saturates both shift with the acoustic scale and with the epoch of matter-radiation equality. Since the numbers in Table V are the paper's most quotable output, the manuscript should either repeat the forecast for a currently viable flat-LambdaCDM model or state explicitly, with an argument, why the thresholds are expected to be insensitive to the background cosmology at the factor-of-two level. A single sentence quantifying the expected shift would be sufficient; silence on this point leaves the headline numbers less transferable than they appear.
[Sec. IV.A, Eqs. (33)–(35); Sec. V.C and Table IV] The secondary-bispectrum budget of Sec. IV includes only the SZ-times-lensing coupling and Poisson point sources. The lensing of the primary CMB by the same large-scale structure also generates a bispectrum through the correlation between the lensing potential and the integrated Sachs–Wolfe effect, which is not estimated anywhere in the paper. This matters specifically for the separability claim in Table IV: the Planck forecast is quoted for the 217 GHz channel, where the authors themselves note that j_nu ~ 0 and the SZ-lensing term therefore vanishes, so at that channel the ISW-lensing bispectrum may be the dominant residual secondary rather than a negligible one. Because the ISW-lensing shape is smooth and non-oscillatory, it would be partially degenerate with the SZ-lensing template and could raise the degradation parameter d_primary above the quoted 1.00. The authors should either add an order-of-magnitude estimate of the ISW-lensing bispectrum in the same style as Eq. (35), or state explicitly why it is expected to be smaller than the SZ-lensing term at the relevant scales and frequencies.

Minor objections (7)

[Abstract and Sec. V.B] The statement in Sec. V.B that 'MAP and Planck experiments will separate the primary bispectrum from others at 1% or better accuracies' conflates two different quantities. The 1% figure is the degradation parameter d_primary = 1.01 from Table IV, which measures the loss in signal-to-noise, whereas the quantity that actually measures separation is the correlation coefficient r_primary,sz-lens = -0.12 for MAP and -0.059 for Planck. The qualitative claim of the abstract [s9] is supported by the r values, but the '1% accuracy' phrasing overstates the degree of separation and should be reworded to refer to the correlation coefficients.
[Sec. VI, final paragraph] The dust result — a dimensionless skewness of 51 measured from the 100 micron HEALPix map with 12,582,912 pixels and mean intensity 14.8 MJy/sr — is introduced without a beam or pixel-scale specification, and the skewness of a smoothed map is resolution-dependent. Since this number is offered as motivation for a future dust-bispectrum study, the authors should state the angular resolution at which it was computed and note explicitly that it is an upper bound that will fall substantially once the Galactic plane is masked.
[Eqs. (49) and (51)] The variance in Eq. (49) carries the multiplicity factor Delta_{l1l2l3} = 1, 2, 6, while the Fisher sum in Eq. (51) runs over the ordered set 2 <= l1 <= l2 <= l3. The two conventions are consistent, but the reader has to reconstruct that the Delta factor is what converts between them. A short sentence after Eq. (51) stating this explicitly would remove the ambiguity.
[Tables I and II] The Fisher matrix entries in Tables I and II are quoted as pure numbers with no indication of their dimensions or of the normalization convention used for the reduced bispectrum b_{l1l2l3}. Since b has dimensions that depend on the convention adopted in Eq. (5), the tables should state the units, or state that the entries are dimensionless under the stated normalization.
[Fig. 2 and its caption] The caption does not state the integration limits or step size used for the line-of-sight integral, although the text does (c(tau_0 - 2 tau_*) <= r <= c(tau_0 - 0.1 tau_*) with step 0.1 c tau_*). Repeating these in the caption would make the figure self-contained, and would also make clear that the plotted quantity is b^primary_{l1l2l3} f_NL^{-1} rather than the full bispectrum.
[Sec. IV.A, Eq. (34)] Eq. (34) uses the linear power spectrum P_Phi(k), while the discussion in Sec. V.C notes that Cooray and Hu find the non-linear power spectrum enhances the effect by a factor of several at l ~ 3000. A forward reference from Eq. (34) to that caveat would prevent a reader from taking the SZ-lensing estimate as a firm amplitude prediction.
[Throughout] Several typographical and grammatical points should be corrected: the title reads 'Bi spectrum'; the abstract has 'On smaller scales; however,' where a comma is required; 'change a sign' should read 'change sign'; 'separatability' should read 'separability'; 'signal-to-noises' should read 'signal-to-noise ratios'; and 'the ideal noise-free and infinitesimal thin-beam experiment' should read 'infinitesimally thin beam'.

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The paper

The paper claims

The paper computes the three-point statistics of the microwave background with the full radiation transfer function, shows that it oscillates through a series of acoustic peaks that alternate in sign, and uses that shape to forecast how far

The reading

The cosmic microwave background is expected to be almost perfectly Gaussian, so almost all of its information sits in the two-point function, the angular power spectrum. This paper asks what the *next* statistic would look like if the primordial fluctuations carried a small non-Gaussian component, and answers it by pushing the calculation beyond the large-angle Sachs–Wolfe regime where earlier work stopped: it evaluates the angular bispectrum $b_{l_1 l_2 l_3}$ with the full radiation transfer function, so the prediction holds down to arcminute scales where MAP and Planck operate. The result is a template with a distinctive signature — a sequence of acoustic peaks that change sign, oscillating with twice the period of the power spectrum — whose overall amplitude is set by a single coupling constant $f_{NL}$. That template then does double duty: it yields concrete detection thresholds for COBE, MAP, Planck and an ideal experiment, and it acts as a matched filter that separates the primordial signal from the bispectra produced by lensing, the Sunyaev–Zel'dovich effect, and unresolved point sources. The payoff is a sharp statement about inflation: for the simplest slow-roll models, which predict $f_{NL} = O(10^{-2})$, no experiment can see this signal, so a positive detection would be evidence that the simplest picture is wrong.

What carries the argument

The load-bearing object is the *reduced* bispectrum $b_{l_1 l_2 l_3}$, defined by factoring the angle-averaged bispectrum into a Gaunt integral times a symmetric function of the three multipoles, $B^{m_1 m_2 m_3}_{l_1 l_2 l_3} = G^{m_1 m_2 m_3}_{l_1 l_2 l_3} b_{l_1 l_2 l_3}$. The Gaunt integral carries only the triangle conditions and selection rules, so $b_{l_1 l_2 l_3}$ holds all the physics and is the quantity plotted, fitted, and compared across models. For the local coupling ansatz $b^{primary}_{l_1 l_2 l_3} = 2f_{NL} b^L_{l_1} b^L_{l_2} b^L_{l_3} + (2f_{NL} b^L_{l_1} b^L_{l_2} b^L_{l_3}) + (2f_{NL} b^L_{l_1} b^L_{l_2} b^L_{l_3})$ — written in the paper as a radial integral over products of $b^L_l(r)$ and $b^{NL}_l(r)$, the line-of-sight projections of the linear power spectrum and of the coupling term against the transfer function. The second piece of machinery is a Fisher matrix over the reduced bispectrum, $F_{ij} = 2f_{NL} b^L_{l_1} b^L_{l_2} b^L_{l_3}$, which simultaneously gives the signal-to-noise for each component, the correlation coefficients between components, and a degradation parameter measuring how much the presence of the others weakens the measurement. That matrix is what turns a template into a separability claim.

Extended reading notes

Core claim

The central claim is that the primary CMB bispectrum, computed with the full transfer function rather than the large-scale Sachs–Wolfe approximation, is not a slowly varying function but an oscillating one: it has a series of acoustic peaks that alternate in sign, and the period of those oscillations is twice as long as the period of the angular power spectrum. Because the sign changes are a direct imprint of the transfer function, they are absent from the secondary bispectra — the lensing–Sunyaev–Zel'dovich coupling falls off as $l^{-3}$ and the Poisson bispectrum from extragalactic sources is flat — which is what makes the primary signal separable on shape alone. Parameterising the amplitude by a single non-linear coupling $f_{NL}$, the paper finds that a signal-to-noise of one requires $f_{NL} > 600$ for COBE, $> 20$ for MAP, $> 5$ for Planck, and $> 3$ for an ideal noise-free, infinitesimally thin-beam experiment. Since slow-roll inflation gives $f_{NL} = O(10^{-2})$, and second-order general relativity gives $f_{NL} = O(1)$, the primary bispectrum should be out of reach — which is itself the useful result, because it converts a non-detection into a constraint on departures from the simplest inflationary scenario.

Load-bearing premise

Everything numerical rests on the assumption that the primordial three-point function has the local, factorisable form with one scale-independent constant $f_{NL}$; the paper itself notes that if slow roll fails then $f_{NL}$ becomes a function of $k_1$, $k_2$, $k_3$, and the sign-changing peaks and all the quoted thresholds change with it.

Editorial extensions

If this is right

Planck would need $f_{NL} > 5$, MAP $> 20$, COBE $> 600$, and an ideal experiment $> 3$ to reach signal-to-noise one on the primary bispectrum, so the simplest slow-roll prediction of $f_{NL} \sim 10^{-2}$ is undetectable by any of them.
The bispectrum is a better non-Gaussianity detector than the skewness: the skewness requires $f_{NL} > 800$, $80$, $70$, and $60$ for COBE, MAP, Planck, and the ideal experiment, because integrating the sign-changing oscillations cancels signal, and the skewness saturates at MAP resolution around $\ell \sim 500$.
MAP and Planck can separate the primary bispectrum from the lensing–Sunyaev–Zel'dovich and point-source bispectra at the 1% level or better, with degradation parameters of $1.01$ and $1.00$, precisely because only the primary template oscillates.
Planck should detect the lensing–Sunyaev–Zel'dovich bispectrum and the point-source bispectrum, while MAP should detect only the point-source one; COBE cannot discriminate among the three.
A significant detection of the primary bispectrum or the skewness by any experiment would mean the simplest inflationary scenario needs modification, for example through features in the inflaton potential.

Reading between the lines

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

Because the peak pattern depends on how the three-point function depends on momentum, measuring the alternation itself is a shape measurement, not merely an amplitude measurement — a non-local or equilateral-type primordial shape would produce a different peak structure and would not be captured by this single-parameter template.
The ideal-experiment threshold of $f_{NL} > 3$ sits just above the $f_{NL} \sim 1$ floor that second-order general relativity guarantees, so the minimum non-Gaussianity that must exist is only a factor of a few below what a perfect all-sky experiment could reach; the guaranteed signal is marginally inaccessible by design, not merely by current technology.
The Fisher machinery is written to fit several templates at once, so the same construction could be run in reverse as a null test: projecting foreground-cleaned maps at several frequencies onto the sign-flipping template while marginalising over the smooth secondary shapes.
If the skewness genuinely saturates at $\ell \sim 500$, then skewness-based non-Gaussianity claims from higher-resolution data add no independent information beyond that scale, which is a testable statement about published analyses.

Original abstract

If the primordial fluctuations are non-Gaussian, then this non-Gaussianity will be apparent in the cosmic microwave background (CMB) sky. With their sensitive all-sky observation, MAP and Planck satellites should be able to detect weak non-Gaussianity in the CMB sky. On large angular scale, there is a simple relationship between the CMB temperature and the primordial curvature perturbation. On smaller scales; however, the radiation transfer function becomes more complex. In this paper, we present the angular bispectrum of the primary CMB anisotropy that uses the full transfer function. We find that the bispectrum has a series of acoustic peaks that change a sign, and a period of acoustic oscillations is twice as long as that of the angular power spectrum. Using a single non-linear coupling parameter to characterize the amplitude of the bispectrum, we estimate the expected signal-to-noise ratio for COBE, MAP, and Planck experiments. We find that the detection of the primary bispectrum by any kind of experiments should be problematic for the simple slow-roll inflationary scenarios. We compare the sensitivity of the primary bispectrum to the primary skewness and conclude that when we can compute the predicted form of the bispectrum, it becomes a ``matched filter'' for detecting the non-Gaussianity in the data, and much more powerful tool than the skewness. We also show that MAP and Planck can separate the primary bispectrum from various secondary bispectra on the basis of the shape difference. The primary CMB bispectrum is a test of the inflationary scenario, and also a probe of the non-linear physics in the very early universe.

The compiled record

The paper's own sentences, arranged, kept beside the review and separate from it. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.

Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 8,295 input tokens.

What the abstract itself states, as probabilities: claims first 0.05 · states limitation 0.58 · human participants 0.01 · controlled comparison 0.11 · randomized assignment 0.01 · states quantitative result 0.72 · compares with prior results 0.90 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v2. Results and the main claim are underlined; show every role.

If the primordial fluctuations are non-Gaussian, then this non-Gaussianity will be apparent in the cosmic microwave background (CMB) sky. With their sensitive all-sky observation, MAP and Planck satellites should be able to detect weak non-Gaussianity in the CMB sky. On large angular scale, there is a simple relationship between the CMB temperature and the primordial curvature perturbation. On smaller scales; however, the radiation transfer function becomes more complex. In this paper, we present the angular bispectrum of the primary CMB anisotropy that uses the full transfer function. We find that the bispectrum has a series of acoustic peaks that change a sign, and a period of acoustic oscillations is twice as long as that of the angular power spectrum. Using a single non-linear coupling parameter to characterize the amplitude of the bispectrum, we estimate the expected signal-to-noise ratio for COBE, MAP, and Planck experiments. We find that the detection of the primary bispectrum by any kind of experiments should be problematic for the simple slow-roll inflationary scenarios. We compare the sensitivity of the primary bispectrum to the primary skewness and conclude that when we can compute the predicted form of the bispectrum, it becomes a ``matched filter'' for detecting the non-Gaussianity in the data, and much more powerful tool than the skewness. We also show that MAP and Planck can separate the primary bispectrum from various secondary bispectra on the basis of the shape difference. The primary CMB bispectrum is a test of the inflationary scenario, and also a probe of the non-linear physics in the very early universe.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#	sentence	role	the authors' own work	states the main conclusion	strength
s0	If the primordial fluctuations are non-Gaussian, then this non-Gaussianity will be apparent in the cosmic microwave background (CMB) sky.	background 1.00	0.06	0.04	asserted 0.57
s1	With their sensitive all-sky observation, MAP and Planck satellites should be able to detect weak non-Gaussianity in the CMB sky.	background 0.98	0.07	0.04	hedged possibility 0.98
s2	On large angular scale, there is a simple relationship between the CMB temperature and the primordial curvature perturbation.	background 1.00	0.07	0.02	asserted 1.00
s3	On smaller scales; however, the radiation transfer function becomes more complex.	background 0.97	0.07	0.02	asserted 1.00
s4	In this paper, we present the angular bispectrum of the primary CMB anisotropy that uses the full transfer function.	contribution 0.97	0.92	0.05	asserted 0.99
s5	We find that the bispectrum has a series of acoustic peaks that change a sign, and a period of acoustic oscillations is twice as long as that of the angular power spectrum.	result 1.00	0.96	0.21	asserted 1.00
s6	Using a single non-linear coupling parameter to characterize the amplitude of the bispectrum, we estimate the expected signal-to-noise ratio for COBE, MAP, and Planck experiments.	method 0.78	0.94	0.06	asserted 1.00
s7	We find that the detection of the primary bispectrum by any kind of experiments should be problematic for the simple slow-roll inflationary scenarios.	interpretation 0.82	0.89	0.43	asserted 0.91
s8	We compare the sensitivity of the primary bispectrum to the primary skewness and conclude that when we can compute the predicted form of the bispectrum, it becomes a ``matched filter'' for detecting the non-Gaussianity in the data, and much more powerful tool than the skewness.	result 0.58	0.90	0.26	asserted 0.99
s9	We also show that MAP and Planck can separate the primary bispectrum from various secondary bispectra on the basis of the shape difference.	result 0.95	0.89	0.11	asserted 1.00
s10	The primary CMB bispectrum is a test of the inflationary scenario, and also a probe of the non-linear physics in the very early universe.	interpretation 1.00	0.22	0.24	asserted 1.00

What kind of paper the classifier reports this is: theoretical result 0.87 · evidence from simulation or computation 0.61.

What was examined, and what was not

sources read

arXiv listing abstract v2

not examined

full text
figures and tables
references and citing sentences
relations to other papers

levels run

P abstract

not run

S sections
T body sentences
C citations
R cross-paper relations

Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

Figures

**Figure 2.** FIG. 2. The primary CMB angular bispectrum (Eq.(16)) divide

**Figure 3.** FIG. 3. The upper panel shows the primary CMB skewness (Eq.(2

**Figure 4.** FIG. 4. The predictions of the signal-to-noise ratio,

**Figure 5.** FIG. 5. The comparison of the signal-to-noise ratio summed u

Figures reproduced from arXiv:astro-ph/0005036 by the authors.

References

Works cited (48)

[1]

L. Verde, L. Wang, A. F. Heavens and M. Kamionkowski, Mon. Not. R. Astron. Soc. 313, 141 (2000)

View on Pith 2000
[2]

K. Sato, Mon. Not. R. Astron. Soc. 195, 467 (1981); Phys. Lett. 99B, 66 (1981)

View on Pith 1981
[3]

A. Guth, Phys. Rev. D 23, 347 (1981)

View on Pith 1981
[4]

A. Albrecht and P. J. Steinhardt, Phys. Rev. Lett. 48, 1220 (1982)

View on Pith 1982
[5]

A. D. Linde, Phys. Lett. 108B, 389 (1982)

View on Pith 1982
[6]

A. Guth and S. Y. Pi, Phys. Rev. Lett. 49, 1110 (1982)

View on Pith 1982
[7]

S. Hawking, Phys. Lett. 115B, 295 (1982)

View on Pith 1982
[8]

J. M. Bardeen, P. J. Steinhardt and M. S. Turner, Phys. Rev . D 28, 679 (1983)

View on Pith 1983
[9]

A. A. Starobinsky, Phys. Lett. 117B, 175 (1982)

View on Pith 1982
[10]

A. A. Starobinsky, in Field Theory, Quantum Gravity, and Strings , edited by H. T. de Vega and N. Sanchez, Lecture Notes in Physics, Vol. 246 (Springer-Verlag, Berlin, 1986), p.10 7

View on Pith 1986
[11]

D. S. Salopek and J. R. Bond, Phys. Rev. D 42, 3936 (1990); ibid. 43, 1005 (1991)

View on Pith 1990
[12]

A. Gangui, F. Lucchin, S. Matarrese and S. Mollerach, As trophys. J. 430, 447 (1994). 14

View on Pith 1994
[13]

E. Calzetta and B. L. Hu, Phys. Rev. D 52, 6770 (1995)

View on Pith 1995
[14]

A. Matacz, Phys. Rev. D 55, 1860 (1997); ibid. 56, R1836 (1997)

View on Pith 1997
[15]

L. Kofman, G. R. Blumenthal, H. Hodges and J. R. Primack, in Large-Scale Structures and Peculiar Motions in the Universe, edited by D. W. Latham and L. N. daCosta, ASP Conference Seri es, Vol. 15, 1991, p.339

View on Pith 1991
[16]

A. Kogut, A. J. Banday, C. L. Bennett, K. M. Gorski, G. Hin shaw, G. F. Smoot and E. L. Wright, Astrophys. J. Lett. 464, L29 (1996)

View on Pith 1996
[17]

P. G. Ferreira, J. Magueijo and K. M. G´ orski, Astrophys . J. Lett. 503, L1 (1998)

View on Pith 1998
[18]

J. Magueijo, Astrophys. J. Lett. 528, L57 (2000)

View on Pith 2000
[19]

A. J. Banday, S. Zaroubi and K. M. G´ orski, Astrophys. J. 533, 575 (2000)

View on Pith 2000
[20]

D. N. Spergel and D. M. Goldberg, Phys. Rev. D 59, 103001 (1999)

View on Pith 1999
[21]

D. M. Goldberg and D. N. Spergel, Phys. Rev. D 59, 103002 (1999)

View on Pith 1999
[22]

A. Cooray and W. Hu, Astrophys. J. 534, 533 (2000)

View on Pith 2000
[23]

W. Hu, Phys. Rev. D 62, 043007 (2000)

View on Pith 2000
[24]

J. R. Bond, G. Efstathiou and M. Tegmark, Mon. Not. R. Ast ron. Soc. 291, L33 (1997)

View on Pith 1997
[25]

L. Wang and M. Kamionkowski, Phys. Rev. D 61, 063504 (2000)

View on Pith 2000
[26]

T. Pyne and S. M. Carroll, Phys. Rev. D 53, 2920 (1996)

View on Pith 1996
[27]

U. Seljak and M. Zaldarriaga, Astrophys. J. 469, 437 (1996)

View on Pith 1996
[28]

E. F. Bunn and M. White, Astrophys. J. 480, 6 (1997)

View on Pith 1997
[29]

Ya. B. Zel’dovich and R. A. Sunyaev, Astrophys. Space. S ci. 4, 301 (1969)

View on Pith 1969
[30]

F. M. Persi, D. N. Spergel, R. Cen and J. P. Ostriker, Astr ophys. J. 442, 1 (1995)

View on Pith 1995
[31]

R. Cen and J. Ostriker, Astrophys. J. 514, 1 (1999)

View on Pith 1999
[32]

A. Refregier, E. Komatsu, D. N. Spergel and U. Pen, Phys. Rev. D 61, 123001 (2000)

View on Pith 2000
[33]

V. Springel, M. White and L. Hernquist, preprint, astro -ph/0008133

View on Pith
[34]

P. Zhang and U. Pen, preprint, astro-ph/0007462

View on Pith Pith review arXiv
[35]

L. Toﬀolatti, F. Arg¨ ueso G´ omez, G. De Zotti, P. Mazzei , A. Franceschini, L. Danese and C. Burigana, Mon. Not. R. Astron. Soc., 297, 117 (1998)

View on Pith 1998
[36]

A. Refregier, D. N. Spergel and T. Herbig, Astrophys. J. 531, 31 (2000)

View on Pith 2000
[37]

X. Luo, Astrophys. J. Lett. 427, L71 (1994)

View on Pith 1994
[38]

A. F. Heavens, Mon. Not. R. Astron. Soc., 299, 805 (1998)

View on Pith 1998
[39]

A. Gangui and J. Martin, Mon. Not. R. Astron. Soc., 313, 323 (2000); Phys. Rev. D 62, 103004 (2000)

View on Pith 2000
[40]

L. Knox, Phys. Rev. D 48, 3502 (1995)

View on Pith 1995
[41]

C. L. Bennett, et al., Astrophys. J. Lett. 464, L1 (1996)

View on Pith 1996
[42]

U. Seljak, Astrophys. J. 463, 1 (1996)

View on Pith 1996
[43]

T. Kitayama and Y. Suto, Astrophys. J. 490, 557 (1997)

View on Pith 1997
[44]

M. Srednicki, Astrophys. J. Lett. 416, L1 (1993)

View on Pith 1993
[45]

M. Tegmark and G. Efstathiou, Mon. Not. R. Astron. Soc. 281, 1297 (1996)

View on Pith 1996
[46]

A. Cooray, W. Hu and M. Tegmark, Astrophys. J. 540, 1 (2000)

View on Pith 2000
[47]

D. J. Schlegel, D. P. Finkbeiner and M. Davis, Astrophys . J. 500, 525 (1998)

View on Pith 1998
[48]

K. M. G´ orski, F. Hivon and B. D. Wandelt, in Proceedings of the MPA/ESO Conference on Evolution of Large -Scale Structure: from Recombination to Garching , edited by A. J. Banday, R. K. Sheth and L. N. daCosta, (1998). 15 TABLE I. The Fisher matrix Fij (Eq.(51)). i and j denote components listed in the ﬁrst row and the ﬁrst column, respectively. T ρ0 is...

View on Pith 1998

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Showing 60 of 132 Pith papers that cite this

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. See all 132 Pith citations

Non-Gaussian features of primordial fluctuations in single field inflationary models
astro-ph 2002-10 accept novelty 9.0 of 10

Single-field slow-roll inflation produces a calculable, small, and specific non-Gaussian three-point function whose squeezed limit is fixed by the scalar tilt, not by an independent parameter.
Non-Gaussianities in Single Field Inflation and their Optimal Limits from the WMAP 5-year Data
astro-ph.CO 2009-05 accept novelty 8.0 of 10

Single-field inflation generically produces two independent non-Gaussian shapes, equilateral and a new orthogonal one, and WMAP 5-year data constrain both to be consistent with zero.
The imprints of primordial non-gaussianities on large-scale structure: scale dependent bias and abundance of virialized objects
astro-ph 2007-10 accept novelty 8.0 of 10

Local primordial non-Gaussianity imprints a 1/k^2 scale-dependent halo bias that upcoming large-scale structure surveys can use to constrain fNL to roughly 10, competitive with the cosmic microwave background.
Detection of Gravitational Lensing in the Cosmic Microwave Background
astro-ph 2007-05 conditional novelty 8.0 of 10

A 3.4-sigma cross-correlation of WMAP CMB maps with NVSS radio galaxy counts is reported as the first detection of gravitational lensing of the cosmic microwave background.
The shape of non-Gaussianities
astro-ph 2004-05 accept novelty 8.0 of 10

Primordial non-Gaussianity comes in two nearly orthogonal momentum-space shapes, equilateral and squeezed, so constraints on one model do not transfer to another by simple equilateral normalization.

Show 55 more citing papers

Boosted Odds: Lower-Point Probes of Parity Violation with Momentum Fields
astro-ph.CO 2026-10 conditional novelty 7.0 of 10

A density-density-momentum bispectrum carries a clean, isolatable parity-violating signal from inflation, with a Fisher forecast reaching sigma(pNL) ~ 10^4.
Tide-and-Seek: Anisotropic scale-dependent bias in the Lyman-alpha forest and designer samples
astro-ph.CO 2026-09 conditional novelty 7.0 of 10

Anisotropic primordial non-Gaussianity can imprint a unique large-scale 1/k-squared clustering signal in Lyman-alpha forest and shape-selected galaxy samples, with BOSS DR12 data finding no detection.
Dissecting the Scalar Cosmological Collider with the Cosmic Microwave Background
astro-ph.CO 2026-07 accept novelty 7.0 of 10

A joint Bayesian fit of the multi-field inflationary Lagrangian to Planck bispectrum data finds no cosmological collider signal (max Δχ²=5.3) and shows weak-mixing template searches are invalid except at the smallest masses.
Pushing the Primordial Frontier: Cosmological Collider Signatures at Strong Mixing
astro-ph.CO 2026-07 conditional novelty 7.0 of 10

Exact analytic squeezed-limit bispectra for strongly mixed two-field inflation, nonperturbative in the curvature-isocurvature mixing λ.
On-Shell Bootstrap of Loop Inflation Correlators with Spectral Dispersion
hep-th 2026-06 unverdicted novelty 7.0 of 10

Introduces spectral dispersion bootstrap combining dS spectral decomposition and dispersion relations to compute 3- and 4-point loop correlators with massive scalar and vector exchanges.
Non-Gaussianity in SMICA
astro-ph.CO 2025-11 unverdicted novelty 7.0 of 10

New SMICA formalism and binned bispectrum estimator jointly recover power spectra, spectral parameters, foreground 3-point correlators, and primordial non-Gaussianity constraints from multi-frequency polarization maps...
Scalar-induced gravitational waves with non-Gaussianity up to all orders
astro-ph.CO 2025-08 unverdicted novelty 7.0 of 10

Lattice simulations directly calculate SIGW spectra with non-Gaussianity to all orders and show that modest non-Gaussianity alters ultraviolet spectral behavior.
Searching for Inflationary Physics with the CMB Trispectrum: 1. Primordial Theory & Optimal Estimators
astro-ph.CO 2025-02 conditional novelty 7.0 of 10

A set of quasi-optimal CMB trispectrum estimators is derived for local, EFT, direction-dependent, spinning-particle, point-source, and lensing templates, enabling first collider searches.
Primordial gravitational waves from excited states
astro-ph.CO 2021-11 accept novelty 7.0 of 10

Excited scalar states during inflation source a gravitational-wave background peaking near 3.5 times the feature scale with order-one oscillations, which can exceed the post-inflationary scalar-induced signal.
Bootstrapping Large Graviton non-Gaussianities
hep-th 2021-09 conditional novelty 7.0 of 10

Unitarity plus locality plus scale invariance allow only three parity-odd graviton three-point shapes at tree level, to all orders in derivatives, while parity-even shapes form an infinite family.
From Locality and Unitarity to Cosmological Correlators
hep-th 2021-03 conditional novelty 7.0 of 10

A locality derivative test plus a partial-energy recursion relation let the authors derive inflationary bispectra to all derivative orders and exchange trispectra up to contact terms, reproducing bulk calculations in ...
Holography for Cosmology
hep-th 2009-07 conditional novelty 7.0 of 10

Cosmological power spectra from inflation are shown to equal analytic continuations of two-point functions in a dual three-dimensional quantum field theory, opening a holographic route to early-universe observables.
Algorithms for bispectra: forecasting, optimal analysis, and simulation
astro-ph 2006-12 accept novelty 7.0 of 10

A factorizability ansatz turns otherwise intractable CMB bispectrum forecasts, estimators, and simulations into fast, general algorithms.
Primordial non-gaussianities in single field inflation
astro-ph 2005-03 accept novelty 7.0 of 10

For single-field inflation with a general first-derivative Lagrangian, the tree-level scalar three-point function is computed explicitly in slow roll, yielding new momentum-dependent terms whenever the sound speed dif...
Non-Gaussian timing residual skewness in pulsar timing arrays
gr-qc 2026-10 conditional novelty 6.0 of 10

A quadratic non-Gaussian ansatz in GW helicity amplitudes fails polarization-frame covariance in PTA bispectra, while a detector-projected construction yields a timing residual skewness of order 10^-15 in Gaussian-rms units.
Constraining Inflation with Little Red Dots
astro-ph.CO 2026-09 conditional novelty 6.0 of 10

A forecast predicts a JWST Little Red Dot survey could measure local primordial non-Gaussianity to sigma(f_NL)=0.32, crossing the threshold that separates single- and multi-field inflation.
It's All About the Environment: Local $f_{\rm NL}$ from a Dark Matter Conditioned Multitracer Analysis
astro-ph.CO 2026-09 conditional novelty 6.0 of 10

Splitting tracers into two equal bins of the large-scale dark matter environment keeps the f_NL response b_phi fixed while changing the linear bias, enabling cosmic-variance-cancelling multitracer f_NL constraints.
Probing Parity Violation with Weak Lensing Trispectrum
astro-ph.CO 2026-07 conditional novelty 6.0 of 10

A parity-odd weak lensing convergence trispectrum is derived and forecast to be detectable with DES Y3/LSST Y10-like surveys under optimistic template amplitudes.
Impact and measurability of linear relativistic effects in galaxy surveys
astro-ph.CO 2026-07 accept novelty 6.0 of 10

Neglecting linear GR effects biases f_NL at 1–3σ for Euclid/SPHEREx in SFB forecasts; multi-tracer improves Doppler detection and weakly breaks b_ϕ f_NL degeneracy.
Anisotropic Gravitational Waves from Anisotropic Axion Rotation
hep-ph 2025-08 conditional novelty 6.0 of 10

A transiently dominant rotating axion sources an induced gravitational wave background whose amplitude and large-scale anisotropy trace the axion's isocurvature fluctuations, with detection prospects for BBO and DECIGO.
Velocity Reconstruction from KSZ: Measuring $f_{NL}$ with ACT and DESILS
astro-ph.CO 2025-06 conditional novelty 6.0 of 10

The first 3D velocity reconstruction from a photometric galaxy survey detects the galaxy-velocity power spectrum at 11.7 sigma and constrains fNL = -39 +40/-33.
Separating Angular and Radial Modes with Spherical-Fourier Bessel Power Spectrum on All Scales and Implications for Systematics Mitigation
astro-ph.CO 2025-06 conditional novelty 6.0 of 10

A spherical Fourier-Bessel analysis of galaxy clustering lets survey analysts cut only the angular and radial modes contaminated by systematics, preserving large-scale modes that standard multipole analyses would discard.
Isotropy, anisotropies and non-Gaussianity in the scalar-induced gravitational-wave background: diagrammatic approach for primordial non-Gaussianity up to arbitrary order
astro-ph.CO 2025-05 unverdicted novelty 6.0 of 10

Extends diagrammatic approach for scalar-induced gravitational waves to arbitrary-order local PNG, deriving semi-analytic spectra for energy density, anisotropies, bispectrum and trispectrum up to quartic terms.
CMB Lensing Trispectrum as a Probe of Parity Violation in LSS
astro-ph.CO 2025-05 conditional novelty 6.0 of 10

The CMB lensing trispectrum is sensitive to parity violation in large-scale structure, and a parity-odd toy model predicts a detectable signal in idealized noiseless forecasts.
Curvature Perturbations from First-Order Phase Transitions: Implications to Black Holes and Gravitational Waves
hep-ph 2025-03 unverdicted novelty 6.0 of 10

Covariant analysis of curvature perturbations from first-order phase transitions reveals gauge-dependent overestimation of primordial black holes and gravitational waves in prior non-covariant calculations, leading to...
The Irrelevance of Primordial Black Hole Clustering in the LVK mass range
astro-ph.CO 2025-02 accept novelty 6.0 of 10

Initial spatial clustering of primordial black holes is irrelevant for binary mergers in the LVK mass range because FIRAS spectral-distortion constraints limit the clustering scale to below the merger-relevant separat...
How Well Do We Know the Scalar-Induced Gravitational Waves?
astro-ph.CO 2024-12 conditional novelty 6.0 of 10

Non-Gaussian curvature perturbations, related to Gaussian ones by a logarithmic mapping, can make the scalar-induced gravitational wave background much larger or smaller than the standard quadratic calculation predicts.
Constraints on local primordial non-Gaussianity with 3d Velocity Reconstruction from the Kinetic Sunyaev-Zeldovich Effect
astro-ph.CO 2024-11 conditional novelty 6.0 of 10

The first 3D kSZ velocity reconstruction yields a 7.2-sigma galaxy-velocity cross-correlation and a constraint fNL = -90 +210 -350, still consistent with zero.
Implications for the non-Gaussianity of curvature perturbation from pulsar timing arrays
astro-ph.CO 2023-07 conditional novelty 6.0 of 10

Joint NANOGrav, PPTA, and EPTA data, assuming scalar-induced gravitational waves, bound the local non-Gaussianity parameter to |F_NL| ≲ 13.9, narrowing to -13.9 ≲ F_NL ≲ -0.1 once primordial black hole overproduction ...
Primordial Non-Gaussianity $f_{\mathrm{NL}}$ and Anisotropies in Scalar-Induced Gravitational Waves
astro-ph.CO 2023-05 conditional novelty 6.0 of 10

The angular power spectrum of scalar-induced gravitational waves is derived including all local-type non-Gaussian contributions, showing a 1/[ell(ell+1)] multipole dependence and a frequency-dependent term that breaks...
Bootstrapping Multi-Field Inflation: non-Gaussianities from light scalars revisited
astro-ph.CO 2022-12 accept novelty 6.0 of 10

Massless scalar exchange during inflation is bootstrapped with an explicit late-time cutoff, yielding corrected seed functions, a full classification of bispectrum shapes, and a new multi-speed template whose peak loc...
Lattice Simulations of Axion-U(1) Inflation
astro-ph.CO 2022-04 conditional novelty 6.0 of 10

A lattice simulation of axion-U(1) inflation shows that strong backreaction drives the curvature perturbation toward Gaussian, weakening primordial-black-hole constraints on the gauge coupling.
Building a Boostless Bootstrap for the Bispectrum
hep-th 2020-10 conditional novelty 6.0 of 10

A boundary-based bootstrap, built without de Sitter boosts, reproduces known inflationary bispectra and yields the scalar bispectrum in the Effective Field Theory of inflation to arbitrary derivative order.
PBHs and secondary GWs from ultra slow roll and punctuated inflation
astro-ph.CO 2020-08 conditional novelty 6.0 of 10

Inflection-point single-field inflation splits into punctuated and ultra slow roll classes, and only the ultra-slow-roll-like cases survive CMB constraints while still producing primordial black holes and detectable s...
Galaxy bias and primordial non-Gaussianity: insights from galaxy formation simulations with IllustrisTNG
astro-ph.CO 2020-06 conditional novelty 6.0 of 10

For stellar-mass-selected galaxies, the standard universality relation b_phi = 2 delta_c (b_1 - 1) understates the PNG bias; the IllustrisTNG separate-universe simulations prefer b_phi = 2 delta_c (b_1 - p) with p bet...
Characterizing the Cosmological Gravitational Wave Background Anisotropies and non-Gaussianity
astro-ph.CO 2019-12 accept novelty 6.0 of 10

The authors derive the angular power spectrum and bispectrum of the stochastic gravitational wave background energy density, including a squeezed-limit consistency relation analogous to the CMB case.
Anisotropies and non-Gaussianity of the Cosmological Gravitational Wave Background
astro-ph.CO 2019-08 conditional novelty 6.0 of 10

The angular anisotropy and bispectrum of the cosmological gravitational wave background can encode primordial perturbations, including order-one frequency dependence and primordial non-Gaussianity.
Probing non-Gaussian Stochastic Gravitational Wave Backgrounds with LISA
astro-ph.CO 2018-06 conditional novelty 6.0 of 10

The authors derive LISA's response functions to a general stochastic gravitational wave bispectrum and an optimal estimator for its signal-to-noise ratio, then survey early-universe models that could produce such non-...
Galaxy Bispectrum from Massive Spinning Particles
astro-ph.CO 2018-01 conditional novelty 6.0 of 10

A new general-triangle template for the inflationary bispectrum from massive spinning particles, plus a Fisher forecast showing EUCLID and DESI could detect spin-2 and spin-4 signals at f_NL of order one and measure t...
Heavy-Lifting of Gauge Theories By Cosmic Inflation
hep-ph 2017-11 conditional novelty 6.0 of 10

Gauge-Higgs states with Hubble-scale masses can produce observable non-Gaussianity in the squeezed bispectrum, and a curvature coupling can lift low-energy Higgs scales to Hubble size during inflation.
Standard Model Mass Spectrum in Inflationary Universe
hep-th 2016-12 conditional novelty 6.0 of 10

Loop corrections in de Sitter give the Higgs and W/Z bosons masses of order the Hubble scale during inflation, and the authors compute the resulting one-loop bispectrum shapes that would carry that mass spectrum.
Galaxy Bias and Primordial Non-Gaussianity
astro-ph.CO 2015-10 accept novelty 6.0 of 10

The equivalence principle ties the scale-dependent bias in the galaxy power spectrum to the dipole of the galaxy bispectrum, providing a parameter-free test of whether a non-Gaussian clustering signal is primordial.
Ultra large-scale cosmology in next-generation experiments with single tracers
astro-ph.CO 2015-05 accept novelty 6.0 of 10

Full-sky Fisher forecasts across four future survey types show that single-tracer power spectra cannot detect general-relativistic clustering corrections, but can reach sigma(f_NL) of order 1-2 and clearly detect lens...
Effective Theory of Large-Scale Structure with Primordial Non-Gaussianity
astro-ph.CO 2015-05 conditional novelty 6.0 of 10

Primordial non-Gaussianity adds a calculable family of new operators to the effective field theory of large-scale structure, and these operators close under one-loop renormalization for isotropic initial conditions.
On Separate Universes
astro-ph.CO 2015-04 conditional novelty 6.0 of 10

Using conformal Fermi coordinates, the authors show a long-wavelength mode acts on small scales only through a shifted local scale factor, a local curvature, and a Newtonian tidal tensor, so nonlinear gravity generate...
Planck 2013 Results. XXIV. Constraints on primordial non-Gaussianity
astro-ph.CO 2013-03 accept novelty 6.0 of 10

Planck finds no primordial non-Gaussianity at the 5.8 level in the local shape, tightening the constraint by roughly a factor of three over WMAP and bounding the sound speed and curvaton decay fraction.
Signatures of anisotropic sources in the squeezed-limit bispectrum of the cosmic microwave background
astro-ph.CO 2013-02 accept novelty 6.0 of 10

Squeezed-limit primordial bispectra can carry Legendre-polynomial angular dependence, and a cosmic-variance-limited CMB temperature experiment to multipole 2000 could measure the quadrupole coefficient c2 to about 13,...
Observable non-gaussianity from gauge field production in slow roll inflation, and a challenging connection with magnetogenesis
astro-ph.CO 2012-02 accept novelty 6.0 of 10

A dilaton-coupled gauge field in slow-roll inflation generates local-shape non-gaussianity with f_NL of order 10 to 100 and a quadrupolar angular dependence in the squeezed limit.
(Small) Resonant non-Gaussianities: Signatures of a Discrete Shift Symmetry in the Effective Field Theory of Inflation
hep-th 2011-11 conditional novelty 6.0 of 10

Within the Effective Field Theory of Inflation, a softly broken discrete shift symmetry generates oscillatory signals whose signal-to-noise is largest in the two-point function, with higher n-point functions strictly ...
Parity Violation of Gravitons in the CMB Bispectrum
astro-ph.CO 2011-07 conditional novelty 6.0 of 10

With a time-dependent coupling to Weyl-cubed operators, the graviton three-point function violates parity even in exact de Sitter space, leaving a distinctive odd-parity pattern in CMB temperature and polarization bispectra.
Optimal Constraints on Local Primordial Non-Gaussianity from the Two-Point Statistics of Large-Scale Structure
astro-ph.CO 2011-04 conditional novelty 6.0 of 10

Optimal mass weighting plus a multi-tracer Fisher analysis of halo power spectra can tighten local fNL constraints by up to an order of magnitude over a single uniformly weighted halo sample, reaching sigma_fNL around...
Large slow-roll corrections to the bispectrum of noncanonical inflation
astro-ph.CO 2011-03 accept novelty 6.0 of 10

The next-order slow-roll corrections to the inflationary bispectrum for general P(X,phi) Lagrangians are derived in closed form, yielding tens-of-percent corrections in DBI inflation and a new bispectrum shape orthogo...
CMB Bispectrum from Primordial Scalar, Vector and Tensor non-Gaussianities
astro-ph.CO 2010-12 accept novelty 6.0 of 10

A full-sky formalism for CMB bispectra from tensor and vector non-Gaussianity is derived and applied to the two-scalars-one-graviton correlator, yielding a reduced bispectrum scaling as l^-4 and a Planck forecast of |...
Holographic Non-Gaussianity
hep-th 2010-11 conditional novelty 6.0 of 10

For a class of holographic inflationary models, the primordial bispectrum is exactly of equilateral shape with f_NL = 5/36, independent of the dual QFT's field content.
Galileon inflation
hep-th 2010-09 accept novelty 6.0 of 10

In Galileon inflation the bispectrum can scale as steeply as 1/c_s^4 rather than the usual 1/c_s^2, because a dimension-seven operator competes with the dimension-six one.

See all 132 Pith citations

How later papers used it

378 later papers cite it

Evidence: substantial. 372 of the citing papers share no author with it, and 43 of those carry a confident label from Pith's citation classifier.

Pith read 40 of the 537 citing sentences, choosing only those whose citation markers point at this paper alone, and wrote the paraphrases from them. The summary, the counts, the evidence level, the links and the quotes come from code; the summary counts the papers listed below. A later paper is listed under a label when Pith's citation classifier gives one of its sentences that label at probability 0.8 or more (0.95 for support), Pith's reading finds that the citing paper itself did it, and a second check confirms the paraphrase against the sentence. This section lists uses only. It does not list criticism or disagreement, so their absence here says nothing about how the paper has been received. Papers that share an author with this one are listed apart, under "By the same authors". A quote is the citing authors' own sentence, shown when their paper's licence is CC BY, CC BY-SA or CC0. JSON

13 later papers by other authors are listed below: 1 built on it, 8 used its method or tool, 3 used its data or values and 1 compared its own results with it.

Builds on it 1 of 2 papers with this label

Provided an expression for the curvature perturbations in real space that generalizes the simplest local Ansatz of this paper and exhibits directly in coordinate space the effect of scale dependence of non-Gaussian parameters.

Scale-dependent non-Gaussianity probes inflationary physics (2010) · 0.97 · paraphrased: the licence does not allow quoting

Uses its method or tool 8 of 25 papers with this label

Calculated the primordial bispectrum following this paper with the full radiation transfer function using a modified code of CMBFAST for a flat ΛCDM model.

Impact of Secondary non-Gaussianities on the Search for Primordial Non-Gaussianity with CMB Maps (2008) · 1.00 · paraphrased: the licence does not allow quoting
Estimated the precision of a measurement of an n-point function using the Fisher matrix method, citing this paper as an instance.

(Small) Resonant non-Gaussianities: Signatures of a Discrete Shift Symmetry in the Effective Field Theory of Inflation (2011) · 0.99 · paraphrased: the licence does not allow quoting
Defined the Fisher matrix for the bispectrum, citing this paper as an example, and defined the signal-to-noise ratio and degradation parameter.

On the non-Gaussianity from Recombination (2008) · 0.93 · paraphrased: the licence does not allow quoting
Introduced the reduced bispectrum (Komatsu-Spergel estimator) of this paper to replace the full bispectrum without loss of information.

Acoustic signatures in the Cosmic Microwave Background bispectrum from primordial magnetic fields (2010) · 0.90 · paraphrased: the licence does not allow quoting
Used this paper to find, beyond the leading expansion of the curvature perturbation, an estimate of the non-linear parameter.

Systematics of multi-field effects at the end of warped brane inflation (2008) · 0.89 · paraphrased: the licence does not allow quoting
Related the skewness of the filtered map to the reduced bispectrum following this paper.

Exploring the Non-Gaussianity of the Cosmic Infrared Background and Its Weak Gravitational Lensing (2023) · 0.88 · paraphrased: the licence does not allow quoting
Wrote the angular bispectrum of temperature anisotropies using the second order correction to the curvature perturbations and following the derivation in this paper.

A Measurement of Primordial Non-Gaussianity Using WMAP 5-Year Temperature Skewness Power Spectrum (2009) · 0.80 · paraphrased: the licence does not allow quoting
Following the steps outlined in this paper's appendix, wrote the primary CMB angular bispectrum in a given form involving the Gaunt integral.

Non-Gaussianity and the CMB Bispectrum: confusion between Primordial and Lensing-Rees Sciama contribution? (2009) · 0.87 · paraphrased: the licence does not allow quoting

Uses its data or values 3 of 10 papers with this label

Used this paper's numerical estimates of l^2 C_l and b_lll to obtain a final expression for the variance of the estimator.

An Estimator for statistical anisotropy from the CMB bispectrum (2011) · 1.00 · paraphrased: the licence does not allow quoting
Substituted the expected 1σ error on f_NL obtained in this paper into its equation to derive an error on the related quantity.

Measuring chiral gravitational waves in Chern-Simons gravity with CMB bispectra (2018) · 1.00 · paraphrased: the licence does not allow quoting
Noted that with an ideal CMB experiment fundamentally limited by cosmic variance one can constrain |f_NL| < 3, as in this paper.

The trispectrum of 21-cm background anisotropies as a probe of primordial non-Gaussianity (2008) · 0.82 · paraphrased: the licence does not allow quoting

Compares with it 1 of 9 papers with this label

Compared its own squeezed limit bispectrum with the familiar squeezed limit bispectrum of the late-time matter density contrast generated by local primordial non-Gaussianity as in this paper.

Neutrino winds on the sky (2023) · 0.94 · paraphrased: the licence does not allow quoting

How the literature uses it

325 arXiv papers cite this in 469 sentences

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

Papers citing it · 235 sentences without a confident label

Builds on it 2 papers

This allows us to obtain an expression for the curvature perturbation that generalizes the local Ansatz introduced in [ref] , and that contains the aforementioned scale-dependent parameters.

Scale-dependent non-Gaussianity probes inflationary physics · Introduction · 0.90
On general ground, extending the standard definition of $$ for local-type non-Gaussianity [ref] , we can define the polarization-dependent $$ as the bispectrum divided by the power spectrum squared:

New shape of parity-violating graviton non-Gaussianity · Shapes of bispectra · 0.87

Uses its method or tool 23 papers

We also calculate the signal-to-noise (S/N) for the detection of the bispectrum due to inhomogeneous reionization [ref] [equation] This is plotted in Figure [ref] for our two reionization models and for primordial non-Gaussianity with $f_NL=1$.

O-V-S-Z and friends: Non-Gaussianity from inhomogeneous reionization · Introduction · 0.94
To reach these conclusions, we first calculated $B^prim_l_1l_2l_3$ following Ref. [ref] with the full radiation transfer function using a modified code of CMBFAST [ref] for the standard flat $Λ$CDM cosmological model consistent with WMAP with $Ω_b=0.042$, $Ω_c=0.238$, $h=0.732$, $n=0.958$, and $τ=0.089$.

Impact of Secondary non-Gaussianities on the Search for Primordial Non-Gaussianity with CMB Maps · Introduction · 1.00
Using the second order correction to the curvature perturbations $Φ$ in equation ([ref]) and following the derivation in Ref. [ref] , we write the angular bispectrum of temperature anisotropies as [equation] where [equation] and $r$ is the comoving radial coordinate.

A Measurement of Primordial Non-Gaussianity Using WMAP 5-Year Temperature Skewness Power Spectrum · Primordial Non-Gaussianity · 0.80

Uses its data or values 10 papers

We compute the persistence diagrams of sublevel filtrations from a publicly available set of simulations [ref] describing primordial non-Gaussianity of local type [ref] .

Persistent Homology and Non-Gaussianity · Introduction · 0.98
Using the numerical estimates of $l^2 C_l≃6×10^-10$ and $b_lll≃(2/3)×2.4 ×10^-17 f_NL l^-4$ from [ref] , we finally get 1/σ_λ_2M ≃0.1 f_NL (l/2000).

An Estimator for statistical anisotropy from the CMB bispectrum · Signal-to-noise ratio · 1.00
The current bounds from WMAP and COBE are $-4 < f_NL^local < 80$ [ref] , $-151 < f_NL^equil < 253$ [ref] , and $|τ_NL^local| ≲10^8$ [ref] , but Planck is expected to achieve a sensitivity down to $|f_NL^local| ≈5$ [ref] , $|f_NL^equil| ≈66$ (at $1 σ$) [ref] and $|τ_NL^local| ≈560$ [ref] .

Trispectrum versus Bispectrum in Single-Field Inflation · Non-Gaussianities · 0.95

Compares with it 9 papers

For the reduced bispectrum $b^(1)_l_1l_2l_3$ ([ref]), which is seeded by the “local-type” shape $f^(1)(k,q,p)$ ([ref]), both the profile and amplitude look similar to those of the primary CMB anisotropies [ref] , (see Figure [ref], [ref], [ref] and [ref]).

Acoustic signatures in the Cosmic Microwave Background bispectrum from primordial magnetic fields · Conclusion · 0.97
In the case where lensing is not included, signal-to-noise ratio estimates for the bispectrum detection are consistent with previous calculations in the literature [ref] .

Weak Lensing of the Primary CMB Bispectrum · Results & Discussion · 0.97
In Fig. [ref], the red solid lines are the CMB statistically anisotropic bispectra of the intensity mode given by Eq. ([ref]) with $C = 1$, and the green dashed lines are the statistically isotropic one sourced from the local-type non-Gaussianity of curvature perturbations given by [ref] [equation] with $f_NL = 5$ for $ℓ_1 = ℓ_2 = ℓ_3$ and two sets of $m_1, m_2, m_3$.

Violation of the Rotational Invariance in the CMB Bispectrum · Behavior of the CMB statistically anisotropic bispectrum · 0.96

Cites it as background 163 papers

For the primordial non-Gaussianity we will consider the so-called local type characterized by a momentum-independent non-Gaussian parameter -$f_NL$- and refer to [ref] .

Non-Gaussianity and the CMB Bispectrum: confusion between Primordial and Lensing-Rees Sciama contribution? · The Primary and the secondary Lensing-Rees-Sciama CMB bispectrum · 0.98
The local template is the result of assuming that the non-Gaussianity is produced from a background Gaussian field $ζ_g$ by a purely-local process [ref] , so that [equation] a straightforward calculation then yields the bispectrum [equation] Noting that the measured power spectrum $P_ζ(k) ∝k^-3$ and that the wavenumbers must obey $[k]_1+[k]_2+[k]_3=0$, we see that this bispectrum peaks when one of the wavenumbers is much smaller than the other two, e.g. $k_3 ≪k_1 ≈k_2$; this limit is known as the squeezed-limit or local-limit [ref] .

Calculating the local-type fNL for slow-roll inflation with a non-vacuum initial state · Introduction · 0.89
The accepted parametrization of primordial non-Gaussianity is to introduce a quadratic term to the primordial potential $Φ$, written as [equation] where $ϕ$ is a Gaussian random field [ref] .

Systematic effects in large-scale angular power spectra of photometric quasars and implications for constraining primordial nongaussianity · Introduction · 0.80

Discussion

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[1] [1]

L. Verde, L. Wang, A. F. Heavens and M. Kamionkowski, Mon. Not. R. Astron. Soc. 313, 141 (2000)

View on Pith 2000

[2] [2]

K. Sato, Mon. Not. R. Astron. Soc. 195, 467 (1981); Phys. Lett. 99B, 66 (1981)

View on Pith 1981

[3] [3]

A. Guth, Phys. Rev. D 23, 347 (1981)

View on Pith 1981

[4] [4]

A. Albrecht and P. J. Steinhardt, Phys. Rev. Lett. 48, 1220 (1982)

View on Pith 1982

[5] [5]

A. D. Linde, Phys. Lett. 108B, 389 (1982)

View on Pith 1982

[6] [6]

A. Guth and S. Y. Pi, Phys. Rev. Lett. 49, 1110 (1982)

View on Pith 1982

[7] [7]

S. Hawking, Phys. Lett. 115B, 295 (1982)

View on Pith 1982

[8] [8]

J. M. Bardeen, P. J. Steinhardt and M. S. Turner, Phys. Rev . D 28, 679 (1983)

View on Pith 1983

[9] [9]

A. A. Starobinsky, Phys. Lett. 117B, 175 (1982)

View on Pith 1982

[10] [10]

A. A. Starobinsky, in Field Theory, Quantum Gravity, and Strings , edited by H. T. de Vega and N. Sanchez, Lecture Notes in Physics, Vol. 246 (Springer-Verlag, Berlin, 1986), p.10 7

View on Pith 1986

[11] [11]

D. S. Salopek and J. R. Bond, Phys. Rev. D 42, 3936 (1990); ibid. 43, 1005 (1991)

View on Pith 1990

[12] [12]

A. Gangui, F. Lucchin, S. Matarrese and S. Mollerach, As trophys. J. 430, 447 (1994). 14

View on Pith 1994

[13] [13]

E. Calzetta and B. L. Hu, Phys. Rev. D 52, 6770 (1995)

View on Pith 1995

[14] [14]

A. Matacz, Phys. Rev. D 55, 1860 (1997); ibid. 56, R1836 (1997)

View on Pith 1997

[15] [15]

L. Kofman, G. R. Blumenthal, H. Hodges and J. R. Primack, in Large-Scale Structures and Peculiar Motions in the Universe, edited by D. W. Latham and L. N. daCosta, ASP Conference Seri es, Vol. 15, 1991, p.339

View on Pith 1991

[16] [16]

A. Kogut, A. J. Banday, C. L. Bennett, K. M. Gorski, G. Hin shaw, G. F. Smoot and E. L. Wright, Astrophys. J. Lett. 464, L29 (1996)

View on Pith 1996

[17] [17]

P. G. Ferreira, J. Magueijo and K. M. G´ orski, Astrophys . J. Lett. 503, L1 (1998)

View on Pith 1998

[18] [18]

J. Magueijo, Astrophys. J. Lett. 528, L57 (2000)

View on Pith 2000

[19] [19]

A. J. Banday, S. Zaroubi and K. M. G´ orski, Astrophys. J. 533, 575 (2000)

View on Pith 2000

[20] [20]

D. N. Spergel and D. M. Goldberg, Phys. Rev. D 59, 103001 (1999)

View on Pith 1999

[21] [21]

D. M. Goldberg and D. N. Spergel, Phys. Rev. D 59, 103002 (1999)

View on Pith 1999

[22] [22]

A. Cooray and W. Hu, Astrophys. J. 534, 533 (2000)

View on Pith 2000

[23] [23]

W. Hu, Phys. Rev. D 62, 043007 (2000)

View on Pith 2000

[24] [24]

J. R. Bond, G. Efstathiou and M. Tegmark, Mon. Not. R. Ast ron. Soc. 291, L33 (1997)

View on Pith 1997

[25] [25]

L. Wang and M. Kamionkowski, Phys. Rev. D 61, 063504 (2000)

View on Pith 2000

[26] [26]

T. Pyne and S. M. Carroll, Phys. Rev. D 53, 2920 (1996)

View on Pith 1996

[27] [27]

U. Seljak and M. Zaldarriaga, Astrophys. J. 469, 437 (1996)

View on Pith 1996

[28] [28]

E. F. Bunn and M. White, Astrophys. J. 480, 6 (1997)

View on Pith 1997

[29] [29]

Ya. B. Zel’dovich and R. A. Sunyaev, Astrophys. Space. S ci. 4, 301 (1969)

View on Pith 1969

[30] [30]

F. M. Persi, D. N. Spergel, R. Cen and J. P. Ostriker, Astr ophys. J. 442, 1 (1995)

View on Pith 1995

[31] [31]

R. Cen and J. Ostriker, Astrophys. J. 514, 1 (1999)

View on Pith 1999

[32] [32]

A. Refregier, E. Komatsu, D. N. Spergel and U. Pen, Phys. Rev. D 61, 123001 (2000)

View on Pith 2000

[33] [33]

V. Springel, M. White and L. Hernquist, preprint, astro -ph/0008133

View on Pith

[34] [34]

P. Zhang and U. Pen, preprint, astro-ph/0007462

View on Pith Pith review arXiv

[35] [35]

L. Toﬀolatti, F. Arg¨ ueso G´ omez, G. De Zotti, P. Mazzei , A. Franceschini, L. Danese and C. Burigana, Mon. Not. R. Astron. Soc., 297, 117 (1998)

View on Pith 1998

[36] [36]

A. Refregier, D. N. Spergel and T. Herbig, Astrophys. J. 531, 31 (2000)

View on Pith 2000

[37] [37]

X. Luo, Astrophys. J. Lett. 427, L71 (1994)

View on Pith 1994

[38] [38]

A. F. Heavens, Mon. Not. R. Astron. Soc., 299, 805 (1998)

View on Pith 1998

[39] [39]

A. Gangui and J. Martin, Mon. Not. R. Astron. Soc., 313, 323 (2000); Phys. Rev. D 62, 103004 (2000)

View on Pith 2000

[40] [40]

L. Knox, Phys. Rev. D 48, 3502 (1995)

View on Pith 1995

[41] [41]

C. L. Bennett, et al., Astrophys. J. Lett. 464, L1 (1996)

View on Pith 1996

[42] [42]

U. Seljak, Astrophys. J. 463, 1 (1996)

View on Pith 1996

[43] [43]

T. Kitayama and Y. Suto, Astrophys. J. 490, 557 (1997)

View on Pith 1997

[44] [44]

M. Srednicki, Astrophys. J. Lett. 416, L1 (1993)

View on Pith 1993

[45] [45]

M. Tegmark and G. Efstathiou, Mon. Not. R. Astron. Soc. 281, 1297 (1996)

View on Pith 1996

[46] [46]

A. Cooray, W. Hu and M. Tegmark, Astrophys. J. 540, 1 (2000)

View on Pith 2000

[47] [47]

D. J. Schlegel, D. P. Finkbeiner and M. Davis, Astrophys . J. 500, 525 (1998)

View on Pith 1998

[48] [48]

K. M. G´ orski, F. Hivon and B. D. Wandelt, in Proceedings of the MPA/ESO Conference on Evolution of Large -Scale Structure: from Recombination to Garching , edited by A. J. Banday, R. K. Sheth and L. N. daCosta, (1998). 15 TABLE I. The Fisher matrix Fij (Eq.(51)). i and j denote components listed in the ﬁrst row and the ﬁrst column, respectively. T ρ0 is...

View on Pith 1998