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 CMB 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 \Delta \chi ^ { 2 } = -11.4 .
Evidence for oscillations damping before the Planck beam scale is weak : damping only improves the fit to \Delta \chi ^ { 2 } = -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 \Delta \chi ^ { 2 } = -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 .