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

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.

36 pages, 8 eps figures; v2 more general two-field model considered, JCAP version

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• Primordial non-Gaussianity from the DBI Galileons
• Cosmological Bootstrap in Slow Motion
• A note on the role of the boundary terms for the non-Gaussianity in general k-inflation
• Resonant Trispectrum and a Dozen More Primordial N-point functions
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