Effects of discontinuities of the derivatives of the inflaton potential

Abstract

We study the effects of a class of features of the inflaton potential, corresponding to discontinuties in its derivatives. We perform fully numerical calculations and derive analytical approximations for the curvature pertubations spectrum and the bispectrum which are in good agreement with the numerical results. The spectrum of primordial perturbations has oscillations around the scale $k_0$ which leaves the horizon at the time $\tau_0$ when the feature occurs, with the amplitude and phase of the oscillations determined by the size and the order of the discontinuity. The large scale bispectrum in the squeezed and equilateral limits have a very similar form and are linearly suppressed. Both in the squeezed and equilateral small scale limit the bispectrum has an oscillatory behavior whose phase depends on the parameters determining the discontinuity, and whose amplitude is inversely proportional to the scale. Given the generality of this class of features they could be used to model or classify phenomenologically different types of non Gaussian features encountered in observational data such as the cosmic microwave background radiation or large scale structure.