On the Trispectrum of Galileon Inflation

TL;DR

This paper analyzes the trispectrum of curvature perturbations in Galileon inflation, revealing distinctive shape-function features that differentiate it from other inflationary models, thus providing new observational signatures.

Contribution

It provides a detailed calculation of the trispectrum in Galileon inflation, highlighting unique shape-function features that distinguish it from other models like $P(X,)$ inflation.

Findings

Trispectrum shape-functions show distinctive features in specific momentum configurations.

Galileon inflation's trispectrum differs significantly from $P(X,)$ models.

The model remains stable and unitary under quantum corrections.

Abstract

We present a detailed study of the trispectrum of the curvature perturbation generated within a stable, well defined and predictive theory which comprises an inflationary phase. In this model the usual shift symmetry is enhanced up to the so-called Galileon symmetry. The appeal of this type of theories rests on being unitary and stable under quantum corrections. Furthermore, in the specific model under consideration here, these properties have been shown to approximately hold in realistic scenarios which account for curved spacetime and the coupling with gravity. In the literature, the analysis of the bispectrum of the curvature perturbation for this theory revealed non-Gaussian features which are shared by a number of inflationary models, including stable ones. It is therefore both timely and useful to investigate further and turn to observables such as the trispectrum. We find that, in a number of specific momenta configurations, the trispectrum shape-functions present strikingly different features as compared to, for example, the entire class of the so-called $P(X,\phi)$ inflationary models.