On the trispectrum of Galileon inflation

We present a detailed study of the trispectrum of the curvature perturbation generated within a stable, well dened and predictive theory which comprises an in ationary 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 specic 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 in ationary models, including stable ones. It is therefore both timely and useful to investigate further and turn to observables such as the trispectrum. We nd that, in a number of specic momenta con- gurations, the trispectrum shape-functions present strikingly dierent features as compared to, for example, the entire class of the so-called P(X; ) in ationary models.