Inflationary Steps in the Planck Data

We extend and improve the modeling and analysis of large-amplitude, sharp inflationary steps for second order corrections required by the precision of the Planck cosmic microwave background power spectrum and for arbitrary Dirac-Born-Infeld sound speed. With two parameters, the amplitude and frequency of the resulting oscillations, step models improve the fit by $\mathrm{\ensuremath{\Delta}}{\ensuremath{\chi}}^{2}=\ensuremath{-}11.4$. Evidence for oscillations damping before the Planck beam scale is weak: damping only improves the fit to $\mathrm{\ensuremath{\Delta}}{\ensuremath{\chi}}^{2}=\ensuremath{-}14.0$ for one extra parameter, if step and cosmological parameters are jointly fit, in contrast to analyses which fix the latter. Likewise, further including the sound speed as a parameter only marginally improves the fit to $\mathrm{\ensuremath{\Delta}}{\ensuremath{\chi}}^{2}=\ensuremath{-}15.2$ but has interesting implications for the lowest multipole temperature and polarization anisotropy. Since chance features in the noise can mimic these oscillatory features, we discuss tests from polarization power spectra, lensing reconstruction and squeezed and equilateral bispectra that should soon verify or falsify their primordial origin.