Transport equations for the inflationary trispectrum

TL;DR

This paper introduces a transport method to calculate the evolution of the inflationary trispectrum, including parameters tauNL and gNL, in multi-field inflation models, providing explicit formulas for practical computation.

Contribution

It presents a novel transport technique for tracking the trispectrum parameters during inflation and derives a third-order relation between field fluctuations and curvature perturbations.

Findings

The method accurately tracks tauNL and gNL over inflation.

Provides explicit formulas for inflationary observable calculations.

Clarifies the relation between different formalisms.

Abstract

We use transport techniques to calculate the trispectrum produced in multiple-field inflationary models with canonical kinetic terms. Our method allows the time evolution of the local trispectrum parameters, tauNL and gNL, to be tracked throughout the inflationary phase. We illustrate our approach using examples. We give a simplified method to calculate the superhorizon part of the relation between field fluctuations on spatially flat hypersurfaces and the curvature perturbation on uniform density slices, and obtain its third-order part for the first time. We clarify how the 'backwards' formalism of Yokoyama et al. relates to our analysis and other recent work. We supply explicit formulae which enable each inflationary observable to be computed in any canonical model of interest, using a suitable first-order ODE solver.