Efficient diagrammatic computation method for higher order correlation functions of local type primordial curvature perturbations

Abstract

We present a new efficient method for computing the non-linearity parameters of the higher order correlation functions of local type curvature perturbations in inflation models having a $\cal N$-component scalar field, focusing on the non-Gaussianity generated during the evolution on super-horizon scales. In contrast to the naive expectation that the number of operations necessary to compute the $n$-point functions is proportional to ${\cal N}^n$, it grows only linearly in ${\cal N}$ in our formalism. Hence, our formalism is particularly powerful for the inflation models composed of a multi-component scalar field. Explicit formulas obtained by applying our method are provided for $n=2,3,4$ and 5, which correspond to power-, bi-, tri- and {\it quad}-spectra, respectively. We also discuss how many parameters we need to parameterize the amplitude and the shape of the higher order correlation functions of local type.

17 pages, 11 figures, 2 tables, minor revisions