Robust predictions for an oscillatory bispectrum in Planck 2015 data from transient reductions in the speed of sound of the inflaton

We update the search for features in the cosmic microwave background (CMB) power spectrum due to transient reductions in the speed of sound, using Planck 2015 CMB temperature and polarization data. We enlarge the parameter space to much higher oscillatory frequencies of the feature, and define a robust prior independent of the ansatz for the reduction, guaranteed to reproduce the assumptions of the theoretical model. This prior exhausts the regime in which features coming from a Gaussian reduction are easily distinguishable from the baseline cosmology. We find a fit to the $\ensuremath{\ell}\ensuremath{\approx}20--40\text{ }\text{ }\mathrm{minus}/\mathrm{plus}$ structure in Planck TT power spectrum, as well as features spanning along higher $\ensuremath{\ell}$'s ($\ensuremath{\ell}\ensuremath{\approx}100--1500$). None of those fits is statistically significant, either in terms of their improvement of the likelihood or in terms of the Bayes ratio. For the higher-$\ensuremath{\ell}$ ones, their oscillatory frequency (and their amplitude to a lesser extent) is tightly constrained, so they can be considered robust, falsifiable predictions for their correlated features in the CMB bispectrum. We compute said correlated features, and assess their signal to noise and correlation with the secondary bispectrum of the correlation between the gravitational lensing of the CMB and the integrated Sachs-Wolfe effect. We compare our findings to the shape-agnostic oscillatory template tested in Planck 2015, and we comment on some tantalizing coincidences with some of the traits described in Planck's 2015 bispectrum data.