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

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 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 N-n, it grows only linearly in N in our formalism. Hence, our formalism is particularly powerful for the inflation models composed of a multi-component scalar field, including the models in which the slow-roll conditions are violated after the horizon crossing time. Explicit formulas obtained by applying our method are provided for n = 2, 3, 4 and 5, which correspond to power-, bi-, tri- and 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.