Anatomy of bispectra in general single-field inflation -- modal expansions

TL;DR

This paper analyzes the bispectra of general single-field inflation models, providing a modal expansion method for efficient comparison with CMB data and exploring the shapes' convergence properties.

Contribution

It introduces a modal expansion framework for bispectra in single-field inflation, including models with non-trivial features, enabling efficient data analysis and model comparison.

Findings

Rapid convergence of modal expansions, typically over 95% with fewer than 30 modes.

Identification of basic shape contributions and their scaling as slow roll is relaxed.

Effective recovery of complex shapes from particle production during inflation using Fourier basis.

Abstract

We discuss bispectra of single-field inflationary models described by general Lorentz invariant Lagrangians that are at most first order in field derivatives, including the fast-roll models investigated by Noller and Magueijo. Based on a factor analysis, we identify the least correlated basic contributions to the general shape and show quantitatively which templates provide a good approximation. We compute how relative contributions of basic shapes to the total bispectrum scale as slow roll is relaxed. To enable future comparison with CMB observations, we provide a modal expansion of these non-separable bispectra in Fourier space, employing the formalism by Shellard et al. Convergence is rapid, usually better than ninety-five percent with less than thirty modes, due to the smoothness of these primordial shapes. Truncated polynomial modal expansions have restrictions, which we highlight using an example with slow convergence. The particular shape originates from particle production during inflation (common in trapped inflation) and entails both localized and oscillatory features. We show that this shape can be recovered efficiently using a Fourier basis and outline the prospect of future model parameter extraction and N-body simulations based on modal techniques.