Transporting non-Gaussianity from sub to super-horizon scales

TL;DR

This paper develops a quantum extension of the moment transport method to accurately compute inflationary perturbations on sub-horizon scales, linking quantum and classical descriptions during inflation.

Contribution

It introduces quantum transport equations for inflationary perturbations, bridging sub- and super-horizon scales and connecting to existing formalisms like In-In.

Findings

Quantum transport equations valid on all scales.

Reduction to classical equations after horizon crossing.

Connections established between transport and In-In formalisms.

Abstract

We extend the `moment transport method' for calculating the statistics of inflationary perturbations to the quantum phase of evolution on sub-horizon scales. The quantum transport equations form a set of coupled ordinary differential equations for the evolution of quantum correlation functions during inflation, which are valid on sub- and super-horizon scales, and reduce to the known classical transport equations after horizon crossing. The classical and quantum equations follow directly from the field equations of cosmological perturbation theory. In this paper, we focus on how the evolution equations arise, and explore how transport methods relate to other approaches, and in particular how formal integral solutions to the transport equations connect to those of the In-In formalism.