Shape of primordial non-Gaussianity and the CMB bispectrum

By J. Fergusson, E. Shellard. 2008

222 citations recorded by the source corpus.

We present a set of formalisms for comparing, evolving, and constraining primordial non-Gaussian models through the CMB bispectrum. We describe improved methods for efficient computation of the full CMB bispectrum for any general (nonseparable) primordial bispectrum, incorporating a flat sky approximation and a new cubic interpolation. We review all the primordial non-Gaussian models in the present literature and calculate the CMB bispectrum up to $ll2000$ for each different model. This allows us to determine the observational independence of these models by calculating the cross correlation of their CMB bispectra. We are able to identify several distinct classes of primordial shapes---including equilateral, local, warm, flat, and feature (non-scale invariant)---which should be distinguishable given a significant detection of CMB non-Gaussianity. We demonstrate that a simple shape correlator provides a fast and reliable method for determining whether or not CMB shapes are well correlated. We use an eigenmode decomposition of the primordial shape to characterize and understand model independence. Finally, we advocate a standardized normalization method for ${f}_{\mathrm{NL}}$ based on the shape autocorrelator, so that observational limits and errors $\ensuremath{\Delta}{f}_{\mathrm{NL}}$ can be consistently compared for different models.

Subfields: Astronomy and Astrophysics, Oceanography

View Paper: https://www.semanticscholar.org/paper/4353d49d99486e0c5702f638ac6a963451b7e87a

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In Astronomy and Astrophysics

1. Xingang Chen
2. D. Baumann
3. E. Pajer
4. M. Zaldarriaga
5. Volker Springel
6. D. Green
7. Uros Seljak
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In Oceanography

1. E. Pajer
2. Xingang Chen
3. D. Baumann
4. A. Banday
5. H. Eriksen
6. F. Hansen
7. M. Liguori
8. D. Green

Citations in the corpus

• Signatures of Initial State Modifications on Bispectrum Statistics (2009, background): “Thus far only the local and equilateral type of non-Gaussianities have been constrained by the data [33, 35], although recently a strong case has been made for a more general set-up [ 53 ].”
• General CMB and primordial bispectrum estimation: Mode expansion, map making, and measures of F NL (2009, methodology): “Despite these three shapes being a good approximation to non-Gaussianity from a number of classes of inflation models, they are not exhaustive in their coverage of known primordial models [11], nor other types of late-time non-Gaussianity, such as that from cosmic strings [12, 13]; they cannot be ex”
• Planck2018 results (2018, methodology): “Using modal techniques developed by Fergusson & Shellard (2009) and Fergusson et al. (2010, 2012), any shape can be factorized, with a close-to-optimal estimator.”
• Building a boostless bootstrap for the bispectrum (2020, methodology): “ly the total energy, and so in the following we will write k T instead of e 1. We are not the rst to use ESPs to write scalar bispectra, and examples have already appeared in the literature, see e.g. [70,71]. However, it is worth stressing a few additional points: • The fact that the decomposition i”
• Resonant non-gaussianity (2010, methodology): “ experiments. Implementing this is slightly subtle because of the three-dimensional nature of the primordial non-Gaussian shapes as opposed to the two-dimensional nature of the observations (see e.g. [14,15] for a discussion). The interesting issue of defining a scalar product suitable for non-scale-”
• Review of local non-Gaussianity from multi-field inflation (2010, methodology): “There are several different fNL’s used in the literature which parameterise different shape dependences of the bispectrum [41, 42], the most popular being the local model discussed in this paper and the so-called equilateral model which can arise from models of inflation with noncanonical kinetic te”
• Equilateral Non-Gaussianity and New Physics on the Horizon (2011, methodology): “We introduced a weight function in the integral, ω(x1, x2) ≡ (1+x1 +x2), to achieve that the scalar product exhibits the same scaling as the optimal CMB estimator [30].”
• Constraining primordial non-Gaussianity with future galaxy surveys (2011, methodology): “The bispectra for the three cases are given in the Appendix A. c© 2012 RAS, MNRAS 000, 1–22 The analysis of CMB bispectra from the Planck satellite is currently considered to be the most promising tool for distinguishing between these scenarios (Fergusson & Shellard 2009).”
• Primordial Non-Gaussianities from Inflation Models (2010, background): “and normalize it to get the shape correlator [60, 63] C(S, S ) ≡ S · S ′ (S · S)1/2(S ′ · S ′)1/2 .”
• Primordial non-Gaussianity from the large-scale structure (2010, methodology): “hape of the primordial bispectrum can be extremely complex in some models, there are broadly three classes of shape characterizing the local, equilateral and folded type of primordial non-Gaussianity [24, 25]. The magnitude of each template “X” is controlled by a dimensionless nonlinear parameter fX”
• Primordial Non-Gaussianity and Bispectrum Measurements in the Cosmic Microwave Background and Large-Scale Structure (2010, methodology): “All five primordial models are normalised relative to the constant solution (48) and are taken from the study by Fergusson and Shellard in [9].”