Moment transport equations for non-Gaussianity

TL;DR

This paper introduces a new, efficient transport equation-based method for calculating primordial non-Gaussianity during inflation, improving upon existing techniques by separating sources and handling multiple fields.

Contribution

The paper develops a novel transport equation approach for evolving the distribution of inflationary fields, enabling efficient and clear calculation of non-Gaussianity.

Findings

Method agrees well with existing literature results.

Efficiently separates multiple sources of non-Gaussianity.

Generalizes to multiple fields and higher moments.

Abstract

We present a novel method for calculating the primordial non-Gaussianity produced by super-horizon evolution during inflation. Our method evolves the distribution of coarse-grained inflationary field values using a transport equation. We present simple evolution equations for the moments of this distribution, such as the variance and skewness. This method possesses some advantages over existing techniques. Among them, it cleanly separates multiple sources of primordial non-Gaussianity, and is computationally efficient when compared with popular alternatives, such as the "delta N" framework. We adduce numerical calculations demonstrating that our new method offers good agreement with those already in the literature. We focus on two fields and the fNL parameter, but we expect our method will generalize to multiple scalar fields and to moments of arbitrarily high order. We present our expressions in a field-space covariant form which we postulate to be valid for any number of fields.