Non-gaussianity from the trispectrum in general single field inflation

TL;DR

This paper derives the fourth order action for scalar and tensor perturbations in single field inflation, computes the trispectrum at leading order, and emphasizes the importance of including second order tensor perturbations for accurate results.

Contribution

It provides the first comprehensive derivation of the fourth order action in two gauges and highlights the necessity of including second order tensor perturbations in trispectrum calculations.

Findings

Leading order trispectrum matches previous results.

Second order tensor perturbations are essential for accuracy.

Formalism for next-to-leading order corrections is provided.

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.