Large non-Gaussianities in single-field inflation

Abstract

We compute the three-point correlation function for a general model of inflation driven by a single, minimally coupled scalar field. Our approach is based on the numerical evaluation of both the perturbation equations and the integrals which contribute to the three-point function. Consequently, we can analyse models where the potential has a 'feature', in the vicinity of which the slow roll parameters may take on large, transient values. This introduces both scale and shape dependent non-Gaussianities into the primordial perturbations. As an example of our methodology, we examine the 'step' potentials which have been invoked to improve the fit to the glitch in the for , present in both the one-and three-year WMAP (Wilkinson Microwave Anisotropy Probe) data sets. We show that for the typical parameter values, the non-Gaussianities associated with the step are far larger than those in standard slow roll inflation, and may even be within reach of a next generation cosmic microwave background experiment such as Planck. More generally, we use this example to explain that while adding features to a potential can improve the fit to the two-point function, these are generically associated with a greatly enhanced signal at the three-point level. Moreover, this three-point signal will have a very non-trivial shape and scale dependence, which is correlated with the form of the two-point function, and may thus lead to a consistency check on models of inflation with non-smooth potentials.