Large non-Gaussianities in single-field inflation

Abstract

We compute the three-point correlation function for a general model of inflation driven bya single, minimally coupled scalar field. Our approach is based on the numerical evaluationof both the perturbation equations and the integrals which contribute to the three-pointfunction. Consequently, we can analyse models where the potential has a ‘feature’, in thevicinity of which the slow roll parameters may take on large, transient values. Thisintroduces both scale and shape dependent non-Gaussianities into the primordialperturbations. As an example of our methodology, we examine the ‘step’ potentials whichhave been invoked to improve the fit to the glitch in the for , present in both the one-and three-year WMAP (Wilkinson Microwave AnisotropyProbe) data sets. We show that for the typical parameter values, the non-Gaussianitiesassociated with the step are far larger than those in standard slow roll inflation, and mayeven be within reach of a next generation cosmic microwave background experimentsuch as Planck. More generally, we use this example to explain that while addingfeatures to a potential can improve the fit to the two-point function, these aregenerically associated with a greatly enhanced signal at the three-point level.Moreover, this three-point signal will have a very non-trivial shape and scaledependence, which is correlated with the form of the two-point function, andmay thus lead to a consistency check on models of inflation with non-smoothpotentials.