Primordial Non-Gaussianities from the Trispectra in Multiple Field Inflationary Models

TL;DR

This paper analyzes the trispectra in multi-field inflation models to understand primordial non-Gaussianities, deriving full perturbation actions and shape functions, and exploring how model parameters influence the trispectrum's form.

Contribution

It provides a comprehensive derivation of the fourth-order perturbation action and characterizes the trispectrum's shape functions in multi-field inflation models.

Findings

Three types of momentum-dependent shape functions identified

Trispectrum expressed in terms of shape functions and model parameters

Shape diagrams facilitate visualization and differentiation of trispectrum shapes

Abstract

We investigate the primordial non-Gaussianities from the trispectra in multi-field inflation models, which can be seen as generalization of multi-field $k$-inflation and multi-DBI inflation. We derive the full fourth-order perturbation action for the inflaton fields and evaluate the four-point correlation functions for the perturbations in the limit $\ca \ll 1$ and $\ce \ll1$. There are three types of momentum-dependent shape functions which arise from three types of four-point interaction vertices. The final trispectrum of the curvature perturbation can be expressed in terms of the deformations and permutations of these three shape functions, and is determined by $\ca$, $\ce$, $\lambda$, $\Pi$ which depend on the non-linear structure of the model and also the transfer function $T_{\Rc\Sc}$. We also discuss the parameter space for the trispectrum and plot the shape diagrams for the trispectrum both for visualization and for distinguishing different shapes from each other.