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Cosmic Microwave Background Bispectrum from the Lensing--Rees-Sciama Correlation Reexamined: Effects of Non-linear Matter Clustering
Cosmology and Nongalactic Astrophysics · Submitted 17 Apr 2012
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim We find that the difference between the linear and non-linear predictions is undetectable, and does not alter the contamination of the local-form primordial non-Gaussianity.
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The abstract, sentence by sentence
The bispectrum of the cosmic microwave background (CMB) generated by a correlation between a time-dependent gravitational potential and the weak gravitational lensing effect provides a direct measurement of the influence of dark energy on CMB. This bispectrum is also known to yield the most important contamination of the so-called "local-form" primordial bispectrum, which can be used to rule out all single-field inflation models. In this paper, we reexamine the effect of non-linear matter clustering on this bispectrum. We compare three different approaches: the 3rd-order perturbation theory (3PT), and two empirical fitting formulae available in the literature, finding that detailed modeling of non-linearity appears to be not very important, as most of the signal-to-noise comes from the squeezed triangle, for which the correlation in the linear regime dominates. The expected signal-to-noise ratio for an experiment dominated by the cosmic variance up to $l_{\rm max}=1500$ is about 5, which is much smaller than the previous estimates including non-linearity, but agrees with the estimates based on the linear calculation. We find that the difference between the linear and non-linear predictions is undetectable, and does not alter the contamination of the local-form primordial non-Gaussianity.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | The bispectrum of the cosmic microwave background (CMB) generated by a correlation between a time-dependent gravitational potential and the weak gravitational lensing effect provides a direct measurement of the influence of dark energy on CMB. | background 1.00 | 0.09 | 0.05 | asserted 1.00 |
| s1 | This bispectrum is also known to yield the most important contamination of the so-called "local-form" primordial bispectrum, which can be used to rule out all single-field inflation models. | background 1.00 | 0.05 | 0.03 | asserted 1.00 |
| s2 | In this paper, we reexamine the effect of non-linear matter clustering on this bispectrum. | contribution 1.00 | 0.76 | 0.03 | unclear 0.66 |
| s3 | We compare three different approaches: the 3rd-order perturbation theory (3PT), and two empirical fitting formulae available in the literature, finding that detailed modeling of non-linearity appears to be not very important, as most of the signal-to-noise comes from the squeezed triangle, for which the correlation in the linear regime dominates. | method 0.49 | 0.95 | 0.47 | asserted 0.94 |
| s4 | The expected signal-to-noise ratio for an experiment dominated by the cosmic variance up to $l_{\rm max}=1500$ is about 5, which is much smaller than the previous estimates including non-linearity, but agrees with the estimates based on the linear calculation. | result 1.00 | 0.85 | 0.15 | asserted 0.97 |
| s5 | We find that the difference between the linear and non-linear predictions is undetectable, and does not alter the contamination of the local-form primordial non-Gaussianity. | result 0.87 | 0.96 | 0.70 | asserted 1.00 |
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The paper
Original abstract
The bispectrum of the cosmic microwave background (CMB) generated by a correlation between a time-dependent gravitational potential and the weak gravitational lensing effect provides a direct measurement of the influence of dark energy on CMB. This bispectrum is also known to yield the most important contamination of the so-called "local-form" primordial bispectrum, which can be used to rule out all single-field inflation models. In this paper, we reexamine the effect of non-linear matter clustering on this bispectrum. We compare three different approaches: the 3rd-order perturbation theory (3PT), and two empirical fitting formulae available in the literature, finding that detailed modeling of non-linearity appears to be not very important, as most of the signal-to-noise comes from the squeezed triangle, for which the correlation in the linear regime dominates. The expected signal-to-noise ratio for an experiment dominated by the cosmic variance up to $l_{\rm max}=1500$ is about 5, which is much smaller than the previous estimates including non-linearity, but agrees with the estimates based on the linear calculation. We find that the difference between the linear and non-linear predictions is undetectable, and does not alter the contamination of the local-form primordial non-Gaussianity.
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References
How the literature uses it
7 arXiv papers cite this in 10 sentences
Papers citing it · 9 sentences without a confident label
Cites it as support 1 paper
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The linear theory calculation is an excellent approximation, as non-linear effects have no impact on the contamination of $f_NL$ [ref] .
Removing the ISW-lensing bias from the local-form primordial non-Gaussianity estimation · The bias due to the ISW-lensing bispectrum · 1.00
What it cites · 31 sentences without a confident label
Contests 7 papers
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This suggests that the previous work based on MA99 [ref] would require a reexamination.
Dark energy and cosmic microwave background bispectrum · Comparing $P(k,z)$ · contest 0.79
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This suggests that the previous work based on MA99 [ref] would require a reexamination.
Constraining the dark energy dynamics with the cosmic microwave background bispectrum · Comparing $P(k,z)$ · contest 0.79
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Our results do not agree with those of [ref] , who find $χ^2_X-LIN$ of order unity for $X=HALOFIT$.
Non-Gaussianity and the CMB Bispectrum: confusion between Primordial and Lensing-Rees Sciama contribution? · $χ^2$ difference between linear and non-linear models · contest 0.72
Uses the method or tool of 4 papers
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Lewis, Challinor and Hanson [ref] have shown that the sub-leading-order correction can be incorporated by simply replacing $C_l^P$ above with the lensed CMB power spectrum, $C_l$: [equation] We shall use this formula for computing the lensing-ISW (RS) bispectrum.
The shape of the CMB lensing bispectrum · Lensing-RS Bispectrum · 0.94
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One popular calibrated formula is due to Smith et al. [ref] , which will be called “HALOFIT.” They model the power spectrum as $P(k)=P_Q(k)+P_H(k)$, where $P_Q(k)$ is the quasi-linear 2-halo term: [equation] where $f(y)≡y/4+y^2/8$ with $y=k/k_σ$, and $α_n$, $β_n$, and $k_σ$ are free parameters which need to be determined from simulations (see Appendix C of [ref] ).
Stable clustering, the halo model and nonlinear cosmological power spectra · Halo Model (HALOFIT) · 0.96
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The expected signal-to-noise ratio is given by [ref] [equation] where $Δ_l_1l_2l_3=1$ if all $l$'s are different, $Δ_l_1l_2l_3=2$ if two $l$'s are equal (isosceles configuration), and $Δ_l_1l_2l_3=6$ if all $l$'s are equal (equilateral configuration).
The Microwave Background Bispectrum, Paper I: Basic Formalism · Signal-to-noise ratio · 0.85
Uses data or values from 1 paper
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Throughout this paper, we shall use the cosmological parameters given by the WMAP 5-year best-fit parameters (WMAP+BAO+$H_0$ ML; [ref] ): $Ω_M=0.277$, $Ω_Λ=0.723$, $h=0.702$, $n_s=0.962$, and $σ_8=0.817$.
Five-Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Cosmological Interpretation · Introduction · 1.00
Compares with 5 papers
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The values of $δf_NL(l_max)$ that we find agree well with those from the linear calculation of [ref] .
CMB lensing and primordial non-Gaussianity · Contamination of the local-form primordial non-Gaussianity · 0.95
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We then compare these results with another empirical model [ref] used by most of the previous work on the lensing-RS bispectrum.
The Mass Power Spectrum in Quintessence Cosmological Models · Empirical Models · 0.93
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Our $S/N$ estimate agrees well with that from the linear calculation of [ref] .
Algorithms for bispectra: forecasting, optimal analysis, and simulation · Signal-to-noise ratio · 0.83
Cites as background 4 papers
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This correlation has been studied in the past [ref] with different empirical methods for computing the non-linear matter power spectrum.
Dark energy and cosmic microwave background bispectrum · Introduction · 0.92
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This correlation has been studied in the past [ref] with different empirical methods for computing the non-linear matter power spectrum.
Non-Gaussianity and the CMB Bispectrum: confusion between Primordial and Lensing-Rees Sciama contribution? · Introduction · 0.92
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This correlation has been studied in the past [ref] with different empirical methods for computing the non-linear matter power spectrum.
Constraining the dark energy dynamics with the cosmic microwave background bispectrum · Introduction · 0.92
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