The shape of primordial non-Gaussianity and the CMB bispectrum

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 (non-separable) 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 characterise and understand model independence. Finally, we advocate a standardised normalisation method for $f_{NL}$ based on the shape autocorrelator, so that observational limits and errors can be consistently compared for different models.

32 pages, 20 figures

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Cited by in corpus (12)

• Primordial Non-Gaussianities from Inflation Models
• Primordial non-Gaussianity from the DBI Galileons
• CMB Constraints on Primordial non-Gaussianity from the Bispectrum (f_{NL}) and Trispectrum (g_{NL} and τ_{NL}) and a New Consistency Test of Single-Field Inflation
• Large non-Gaussianities in the Effective Field Theory Approach to Single-Field Inflation: the Trispectrum
• Primordial non-Gaussianity in the large scale structure of the Universe
• Analytic formulae of the CMB bispectra generated from non-Gaussianity in the tensor and vector perturbations
• Nongaussianity from Particle Production During Inflation
• Non-Gaussianity in single field models without slow-roll
• Path Integral for Inflationary Perturbations
• Minimal cut-off vacuum state constraints from CMB bispectrum statistics
• Primordial Features as Evidence for Inflation
• Non-Gaussian Distribution and Clustering of Hot and Cold Pixels in the WMAP Five-Year Sky