Non-Gaussianity from Step Features in the Inflationary Potential

TL;DR

This paper derives analytic solutions for the power spectrum and bispectrum caused by sharp step features in the inflationary potential, highlighting their potential observability and impact on cosmic microwave background data.

Contribution

It provides the first analytic solutions for the non-Gaussian signatures from sharp step features in the inflationary potential, enabling better assessment of their observational prospects.

Findings

Bispectrum exhibits strong scale dependence and oscillatory amplitude.

Sharp steps on scales > 2 Gpc could be detectable by Planck.

Features can improve WMAP7 likelihood by approximately 12 units.

Abstract

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 non-linearity 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 ~ 2 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 ~ 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.