Shape of primordial non-Gaussianity and the CMB bispectrum

2008/12/17 by J. R. Fergusson, J. Fergusson, E. P. S. Shellard · 1 voice · 220 citations
Earth and Planetary Sciences · Mathematics · Physics and Astronomy · #Anisotropy #Astrophysics #Bispectrum #Cosmic microwave background #Cosmology and Gravitation Theories #Galaxies: Formation, Evolution, Phenomena #Gaussian #Geophysics and Gravity Measurements #Mathematics #Non-Gaussianity #Physics #Quantum mechanics #Spectral density #Statistical physics #Statistics #astro-ph

paper · pdf · doi:10.1103/physrevd.80.043510

published in Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields 80(4) (American Physical Society) · 32 pages, 20 figures

arxiv created 2009/08/12 · openalex publication_date 2009/08/14 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

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 l<2000 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_NL based on the shape autocorrelator, so that observational limits and errors \ensuremathΔf_NL can be consistently compared for different models.

Cited by

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Discussions

• Today's #JanuArty theme is triangles. This illustration is based on the paper "The shape of primordial non-Gaussianity and the CMB bispectrum" arxiv.org/abs/0812.3413 So, I um, I dunno? I made some [bsky, 38 points, 0 comments]

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