We provide analytic solutions for the power spectrum and bispectrum of curvature fluctuations produced by a step feature in the inflaton potential, valid in the limit that the step is short and sharp. In this limit, the bispectrum is strongly scale dependent and its effective nonlinearity attains a large oscillatory amplitude. The perturbations to the curvature power spectrum, on the other hand, remain a small component on top of the usual spectrum of fluctuations generated by slow roll. We utilize our analytic solutions to assess the observability of the predicted non-Gaussian signatures and show that, if present, only very sharp steps on scales larger than $\sim 2\mathrm{Gpc}$ are likely to be able to be detected by Planck. Such features are not only consistent with WMAP7 data, but can also improve its likelihood by $2\Delta \ln L\approx 12$ for two extra parameters, the step location and height. If this improvement were due to a slow roll violating step as considered here, a bispectrum or corresponding polarization power spectrum detection would provide definitive checks as to its primordial origin.

• Received 21 October 2011

DOI:https://doi.org/10.1103/PhysRevD.85.023531