On the full trispectrum in single field DBI-inflation

TL;DR

This paper calculates the four-point correlation function of primordial curvature perturbations in general single field inflation models, highlighting the significance of scalar exchange and contact interactions, especially in DBI-inflation.

Contribution

It provides the first comprehensive computation of the full trispectrum in general single field models including DBI-inflation, emphasizing the role of scalar exchange diagrams.

Findings

Scalar exchange and contact interaction diagrams contribute comparably to the trispectrum.

In DBI-inflation, the trispectrum peaks when the four momenta form equal angles.

Scalar exchange trispectrum can be an order of magnitude larger than contact interaction in equilateral configurations.

Abstract

We compute the tree-level connected four-point function of the primordial curvature perturbation for a fairly general minimally coupled single field inflationary model, where the inflaton's Lagrangian is a general function of the scalar field and its first derivatives. This model includes K-inflation and DBI-inflation as particular cases. We show that, at the leading order in the slow-roll expansion and in the small sound speed limit, there are two important tree-level diagrams for the trispectrum. One is a diagram where a scalar mode is exchanged and the other is a diagram where the interaction occurs at a point, i.e. a contact interaction diagram. The scalar exchange contribution is comparable to the contact interaction contribution. For the DBI-inflation model, in the so-called equilateral configuration, the scalar exchange trispectrum is maximized when the angles between the four momentum vectors are equal and in this case the amplitude of the trispectrum from the scalar exchange is one order of magnitude higher than the contact interaction trispectrum.