The angular bispectrum of the cosmic microwave background

Luo, Xiaochun

doi:10.1086/187367

Cited by 87 publications

(119 citation statements)

References 14 publications

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“…The signal-to-noise ratio for trispectra with fixed field configurations can be obtained from expression (28) by using the recoupling relations (15) to permute the field symbols into that of the fixed field representation. The results can be simplified by using the following identities for the 6-j symbols, …”

Section: Discussionmentioning

confidence: 99%

“…The constraints (15) and (19) express redundancies in the definition of the trispectrum, where a physical configuration can be labeled by 4! = 24 different permutations of the field labels and pairings.…”

Section: B Rotational and Parity Invariancementioning

confidence: 99%

“…Non-Gaussian signatures in the three-point function or bispectrum of the temperature distribution [2,8,11,12,13] and polarization [14] as well as techniques for their extraction [15,16,17,18,19,20] have been studied extensively in the past few years. The four-point function or trispectrum has recently received much attention due to its use in the study of the gravitational lensing of the CMB [6,9,21,22].…”

Section: Introductionmentioning

confidence: 99%

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Angular trispectra of CMB temperature and polarization

2002

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We develop the formalism necessary to study four-point functions of the cosmic microwave background (CMB) temperature and polarization fields. We determine the general form of CMB trispectra, with the constraints imposed by the assumption of statistical isotropy of the CMB fields, and derive expressions for their estimators, as well as their Gaussian noise properties. We apply these techniques to initial non-Gaussianity of a form motivated by inflationary models. Due to the large number of four-point configurations, the sensitivity of the trispectra to initial non-Gaussianity approaches that of the temperature bispectrum at high multipole moment. These trispectra techniques will also be useful in the study of secondary anisotropies induced for example by the gravitational lensing of the CMB by the large scale structure of the universe.

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Section: Discussionmentioning

confidence: 99%

Section: B Rotational and Parity Invariancementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Angular trispectra of CMB temperature and polarization

2002

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“…(25) in terms of the (processed) matter power spectra using Eq. (19) to obtain the matter bispectrum,…”

Section: The Bispectrum For Galaxy Surveysmentioning

confidence: 99%

Non-Gaussianity from self-ordering scalar fields

2010

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The Universe may harbor relics of the post-inflationary epoch in the form of a network of selfordered scalar fields. Such fossils, while consistent with current cosmological data at trace levels, may leave too weak an imprint on the cosmic microwave background and the large-scale distribution of matter to allow for direct detection. The non-Gaussian statistics of the density perturbations induced by these fields, however, permit a direct means to probe for these relics. Here we calculate the bispectrum that arises in models of self-ordered scalar fields. We find a compact analytic expression for the bispectrum, evaluate it numerically, and provide a simple approximation that may be useful for data analysis. The bispectrum is largest for triangles that are aligned (have edges k1 ≃ 2k2 ≃ 2k3) as opposed to the local-model bispectrum, which peaks for squeezed triangles (k1 ≃ k2 ≫ k3), and the equilateral bispectrum, which peaks at k1 ≃ k2 ≃ k3. We estimate that this non-Gaussianity should be detectable by the Planck satellite if the contribution from self-ordering scalar fields to primordial perturbations is near the current upper limit.

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“…It is the intent of this Letter to probe for the scale-scale correlations in the COBE-DMR 4-year sky maps, and, as an example, show that this measure is effective in testing models of the initial density perturbations. In contrast with other techniques, such as the bispectrum, [12], higher order cumulants [13], Minkowski functionals [14], or double Fourier analysis [15], scale-scale correlations are localized, and can localize the areas on the sky where the signal comes from, and with a resolution that depends on the scale considered.…”

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confidence: 99%

Evidence for Scale-Scale Correlations in the Cosmic Microwave Background Radiation

1998

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We perform a discrete wavelet analysis of the COBE-DMR 4yr sky maps and find a significant scale-scale correlation on angular scales from about 11 to 22 degrees, only in the DMR face centered on the North Galactic Pole. This non-Gaussian signature does not arise either from the known foregrounds or the correlated noise maps, nor is it consistent with upper limits on the residual systematic errors in the DMR maps. Either the scale-scale correlations are caused by an unknown foreground contaminate or systematic errors on angular scales as large as 22 degrees, or the standard inflation plus cold dark matter paradigm is ruled out at the > 99% confidence level.Most attempts at quantifying the non-Gaussianity in the cosmic microwave background radiation are motivated by the belief that non-Gaussianity can distinguish inflationary models of structure formation from topological models. While standard inflation predicts a Gaussian distribution of anisotropies [1], spontaneous symmetry breaking produces topological defects whose networks create non-Gaussian patterns on the microwave background radiation on small scales [2]. Minute non-Gaussian features can however be generated by gravitational waves [3] or by the Rees-Sciama [4] and Sunyaev-Zeldovich effects.It is generally held that cosmic gravitational clustering can be roughly described by three régimes: linear, quasilinear, and fully developed nonlinear clustering. Whilst quasi-linear and non-linear clustering induce non-Gaussian distribution functions, if the initial density perturbations are Gaussian, scale-scale correlations and other non-Gaussian features of the density field can not be generated during the linear régime. Hence the linear régime is best suited to study the primordial non-Gaussian fluctuations. Since the amplitudes of the cosmic temperature fluctuations revealed by COBE are as small as ∆T /T 10 −5 , the gravitational clustering should remain in the linear régime on scales larger than about 30 h −1 Mpc and at redshifts higher than 2. Current limits on non-Gaussianity from galaxy surveys probe redshifts smaller than about 1 [5]. Interestingly, at redshifts between 2 and 3, and scales on the order of 40 to 80 h −1 Mpc, there are positive detections of scale-scale correlations in the distribution of Lyα absorption lines in quasar spectra [6]. These clouds are likely to be pre-collapsed and continuously distributed intergalactic gas clouds, and are therefore fair tracers of the cosmic density field, especially on large scales [7]. This may indicate that the primordial fluctuations are scale-scale correlated.While on small angular scales ( 150) there may be some indications of non-Gaussianity [8], studies by traditional non-Gaussian detectors have concluded that there is no evidence of non-Gaussianity in the cosmic temperature fluctuations on large scales [9]. (See however [10].) This does not rule out the existence of scale-scale correlations. Because each non-Gaussian feature is non-Gaussian in its own way, there is no single statistical indicator for ...

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The angular bispectrum of the cosmic microwave background

Cited by 87 publications

References 14 publications

Angular trispectra of CMB temperature and polarization

Angular trispectra of CMB temperature and polarization

Non-Gaussianity from self-ordering scalar fields

Evidence for Scale-Scale Correlations in the Cosmic Microwave Background Radiation

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