Probing inflation with precision bispectra

Philip Clarke,E.P.S Shellard

doi:10.1088/1475-7516/2021/08/002

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.

Highlights

The primordial bispectrum is one of the main characteristics used to distinguish between models of inflation
While it is well known that the physics of inflation must have been extremely close to linear, and the initial seeds of structure it laid down very close to Gaussian, there is expected to have been some level of coupling between the Fourier modes of the perturbations
In the simplest example of an inflation model this is expected to be unobservable [1], but the possibility remains that inflation was driven by more complex physics that may have left an observable imprint on our universe today

Summary

Introduction

The primordial bispectrum is one of the main characteristics used to distinguish between models of inflation. Some models of inflation have interactions that predict nonGaussian correlations at observable levels. Ways this can happen include self-interactions [2, 3], interactions between multiple fields [4], sharp features [5] and periodic features [6]. Constraining such imprints is extremely difficult observationally. Much progress has been made by course-graining the model space into a small number of approximate templates, and leveraging the simplifying characteristic of separability with respect to the three parameters of the bispectrum [7, 8]

Objectives

Methods

Findings

Conclusion