Primordial non-Gaussianity and the CMB bispectrum

Fergusson, J.; Shellard, E. P. S.

doi:10.1103/physrevd.76.083523

Cited by 86 publications

(143 citation statements)

References 29 publications

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“…[16,65]), but with one crucial difference: the shape of the intrinsic second-order nonGaussianity is not separable, meaning that the integration cannot be split into three onedimensional integrations. We obviate this problem by using the fact that T (2) (k, k 1 , k 2 ) is smooth in k 1 and k 2 as a consequence of the line of sight integral acting only on k. After integrating over the highly oscillatory direction k, we interpolate the result in the smooth directions.…”

Section: Bispectrum Computationmentioning

confidence: 99%

The intrinsic bispectrum of the cosmic microwave background

Pettinari

Fidler

Crittenden

et al. 2013

J. Cosmol. Astropart. Phys.

129

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Abstract. We develop a new, efficient code for solving the second-order Einstein-Boltzmann equations, and use it to estimate the intrinsic CMB non-Gaussianity arising from the nonlinear evolution of density perturbations. The full calculation involves contributions from recombination and less tractable contributions from terms integrated along the line of sight. We investigate the bias that this intrinsic bispectrum implies for searches of primordial nonGaussianity. We find that the inclusion or omission of certain line of sight terms can make a large impact. When including all physical effects but lensing and time-delay, we find that the local-type f NL would be biased by f intr NL = 0.5, below the expected sensitivity of the Planck satellite. The speed of our code allows us to confirm the robustness of our results with respect to a number of numerical parameters.

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Section: Bispectrum Computationmentioning

confidence: 99%

The intrinsic bispectrum of the cosmic microwave background

Pettinari

Fidler

Crittenden

et al. 2013

J. Cosmol. Astropart. Phys.

129

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“…Using the integral form of the delta functions and the spherical wave expansion we perform the integrations over the angular parts of (k 1 , k 2 , k 3 , k 4 , K), with algebra similar to [12,14,24], to give…”

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confidence: 99%

Cosmic Microwave Background Trispectrum and Primordial Magnetic Field Limits

Trivedi¹,

Seshadri²,

Subramanian³

2012

Phys. Rev. Lett.

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Primordial magnetic fields will generate non-Gaussian signals in the cosmic microwave background (CMB) as magnetic stresses and the temperature anisotropy they induce depend quadratically on the magnetic field. We compute a new measure of magnetic non-Gaussianity, the CMB trispectrum, on large angular scales, sourced via the Sachs-Wolfe effect. The trispectra induced by magnetic energy density and by magnetic scalar anisotropic stress are found to have typical magnitudes of approximately a few times 10 −29 and 10 −19 , respectively. Observational limits on CMB non-Gaussianity from WMAP data allow us to conservatively set upper limits of a nG, and plausibly sub-nG, on the present value of the primordial cosmic magnetic field. This represents the tightest limit so far on the strength of primordial magnetic fields, on Mpc scales, and is better than limits from the CMB bispectrum and all modes in the CMB power spectrum. Thus, the CMB trispectrum is a new and more sensitive probe of primordial magnetic fields on large scales.Magnetic fields are ubiquitous in the Universe from planets and stars to galaxies and galaxy clusters [1,2], yet the origin and evolution of large-scale magnetic fields remains a puzzle. A popular paradigm is that magnetic fields in collapsed structures could arise from dynamo amplification of seed magnetic fields [2]. The seed field could in turn be generated in astrophysical batteries [3] or due to processes in the early universe [4,5]. Indeed recent γ-ray observations claim to find a lower limit to an all-pervasive intergalactic magnetic field that fills most of the cosmic volume [6], which would perhaps favor a primordial origin. A primordial magnetic field can be generated at inflation [4], or arise out of other phase transitions in the early Universe [5]. As yet there is no compelling mechanism which produces strong coherent primordial fields. Equally, the dynamo paradigm is not without its own challenges in producing sufficiently coherent fields and sufficiently rapidly [2]. Therefore, it is useful to keep open the possibility that primordial magnetic fields originating in the early universe play a crucial role in explaining the observed cosmic magnetism.In this context it is important to investigate every observable signature of the putative primordial magnetic fields. Constraints on large-scale primordial magnetic fields have already been derived using the cosmic microwave background (CMB) power spectrum [7,8] and Faraday rotation [9]. However, the effects of a magnetic field on the CMB are relatively more prominent in its non-Gaussian correlations. This is because magnetic fields induce non-Gaussian signals at lowest order as the magnetic energy density and stress are quadratic in the field. On the other hand, the standard inflationary perturbations, dominated by their linear component, can source non-Gaussian correlations only with higher-order perturbations and thus necessarily produce a small amplitude of CMB non-Gaussianity (cf. [10,11]). Primordial magnetic fields can induce apprec...

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“…We have modified CAMB [48] by adding a module that computes this bispectrum 5 using the parametrization above. As was pointed out in [47], because of the substructure in the tetrahedral, it requires quite a lot of sampling in the α, β plane to get small errors. They suggested a recursion step to speed up the calculation.…”

Section: Figmentioning

confidence: 99%

“…to address the accuracy of our code, we use the following approximation for the constant bispectrum shape [47] in the SW limit. The constant shape is given by…”

Section: Figmentioning

confidence: 99%

Optimal estimator for resonance bispectra in the CMB

2015

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We propose an (optimal) estimator for a CMB bispectrum containing logarithmically spaced oscillations. There is tremendous theoretical interest in such bispectra, and they are predicted by a plethora of models, including axion monodromy models of inflation and initial state modifications. The number of resolved logarithmical oscillations in the bispectrum is limited due to the discrete resolution of the multipole bispectrum. We derive a simple relation between the maximum number of resolved oscillations and the frequency. We investigate several ways to factorize the primordial bispectrum, and conclude that a one dimensional expansion in the sum of the momenta ki = kt is the most efficient and flexible approach. We compare the expansion to the exact result in multipole space and show for ω eff = 100 that O(10 3 ) modes are sufficient for an accurate reconstruction. We compute the expected σ f NL and find that within an effective field theory (EFT) the overall signal to noise scales as S/N ∝ ω 3/2 . Using only the temperature data we find S/N ∼ O(1 − 10 2 ) for the frequency domain set by the EFT.

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Primordial non-Gaussianity and the CMB bispectrum

Cited by 86 publications

References 29 publications

The intrinsic bispectrum of the cosmic microwave background

The intrinsic bispectrum of the cosmic microwave background

Cosmic Microwave Background Trispectrum and Primordial Magnetic Field Limits

Optimal estimator for resonance bispectra in the CMB

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