Probing Inflation with Precision Bispectra

TL;DR

This paper introduces an efficient numerical method using separable basis functions to compute the primordial bispectrum from inflation models, enabling better comparison with observational data.

Contribution

It develops a practical approach with an augmented Legendre basis for rapid, accurate bispectrum calculations across complex inflation models.

Findings

Method achieves high accuracy in bispectrum coefficient calculations.

Approach significantly reduces computational time.

Applicable to a wide range of inflationary phenomenology.

Abstract

Calculating the primordial bispectrum predicted by a model of inflation and comparing it to what we see in the sky is very computationally intensive, necessitating layers of approximations and limiting the models which can be constrained. Exploiting the inherent separability of the tree level in-in formalism using expansions in separable basis functions provides a means by which to obviate some of these difficulties. Here, we develop this approach further into a practical and efficient numerical methodology which can be applied to a much wider and more complicated range of bispectrum phenomenology, making an important step forward towards observational pipelines which can directly confront specific models of inflation. We describe a simple augmented Legendre polynomial basis and its advantages, then test the method on single-field inflation models with non-trivial phenomenology, showing that our calculation of these coefficients is fast and accurate to high orders.