Non-gaussianity from the trispectrum in general single field inflation

TL;DR

This paper develops a comprehensive, gauge-consistent framework to compute the primordial trispectrum in general single-field inflation with a Lagrangian P(X,φ). By deriving the full fourth-order action in both comoving and uniform curvature gauges and including second-order tensor perturbations, the authors establish the correct leading-order trispectrum for ζ_n and relate it to ζ, demonstrating agreement with prior results in the slow-roll regime. They also lay out how to obtain next-to-leading corrections, which can be potentially observable for models with small sound speed, and discuss implications for δN formalism and Planck-era constraints. The work provides a robust, technically detailed method for analyzing higher-order non-Gaussianity in broad inflationary scenarios and highlights when tensor sourcing materially affects the trispectrum.

Abstract

We compute the fourth order action in perturbation theory for scalar and second order tensor perturbations for a minimally coupled single field inflationary model, where the inflaton's lagrangian is a general function of the field's value and its kinetic energy. We obtain the fourth order action in two gauges, the comoving gauge and the uniform curvature gauge. Using the comoving gauge action we calculate the trispectrum at leading order in slow-roll, finding agreement with a previously known result in the literature. We point out that in general to obtain the correct leading order trispectrum one cannot ignore second order tensor perturbations as previously done by others. The next-to-leading order corrections may become detectable depending on the shape and we provide the necessary formalism to calculate them.