The shape of primordial non-Gaussianity and the CMB bispectrum

TL;DR

This paper develops advanced methods to compare, compute, and distinguish various primordial non-Gaussian models through their signatures in the CMB bispectrum, facilitating better interpretation of observational data.

Contribution

It introduces improved computational techniques for the CMB bispectrum, classifies primordial non-Gaussian shapes, and proposes a standard normalization for $f_{NL}$ to enable consistent model comparison.

Findings

Identified distinct classes of primordial shapes: equilateral, local, warm, flat, feature.

Developed a fast shape correlator for model comparison.

Provided a standard normalization method for $f_{NL}$.

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.