Higher N-point function data analysis techniques for heavy particle production and WMAP results

We explore data analysis techniques for signatures from heavy particle production during inflation. Heavy particules can be produced by time dependent masses and couplings, which are ubiquitous in string theory. These localized excitations induce curvature perturbations with non-zero correlation functions at all orders. In particular, Flauger et. al. 2016 has shown that the signal-to-noise as a function of the order $N$ of the correlation function can peak for $N$ of order $\mathcal{O}(1)$ to $\mathcal{O}(100)$ for an interesting space of models. As previous non-Gaussianity analyses have focused on $N=\{3,4\}$, in principle this provides an unexplored data analysis window with new discovery potential. We derive estimators for arbitrary $N$-point functions in this model and discuss their properties and covariances. To lowest order, the heavy particle production phenomenology reduces to a classical Poisson process, which can be implemented as a search for spherically symmetric profiles in the curvature perturbations. We explicitly show how to recover this result from the $N$-point functions and their estimators. Our focus in this paper is on method development, but we provide an initial data analysis using WMAP data, which illustrates the particularities of higher $N$-point function searches.