A Modal Approach to the Numerical Calculation of Primordial non-Gaussianities

TL;DR

This paper introduces a novel numerical method leveraging modal techniques and the separability of the In-In formalism to efficiently compute and analyze higher-order primordial non-Gaussianities across various early-universe models.

Contribution

It presents a new, accurate, and efficient numerical approach for calculating primordial non-Gaussianities using modal techniques and the separability of the In-In formalism, applicable to diverse early-universe scenarios.

Findings

Validated method on single-field inflation models with analytical results

Successfully verified the single-field consistency relation

Automatically incorporates the i epsilon prescription in calculations

Abstract

We propose a new method to numerically calculate higher-order correlation functions of primordial fluctuations generated from any early-universe scenario. Our key-starting point is the realization that the tree-level In-In formalism is intrinsically separable. This enables us to use modal techniques to efficiently calculate and represent non-Gaussian shapes in a separable form well suited to data analysis. We prove the feasibility and the accuracy of our method by applying it to simple single-field inflationary models in which analytical results are available, and we perform non-trivial consistency checks like the verification of the single field consistency relation. We also point out that the i epsilon prescription is automatically taken into account in our method, preventing the need for ad-hoc tricks to implement it numerically.