Polyspectra searches for sharp oscillatory features in cosmic microwave sky data

Despite numerous efforts, the search for oscillatory signatures in primordial spectra has not produced any convincing evidence for feature models to date. We undertake a thorough search for signatures of sharp features in the WMAP9 power spectrum and bispectrum as well as in the Planck power spectrum. For the first time, we carry out searches in both the power spectrum and bispectrum simultaneously, employing well-defined look-elsewhere statistics to assess significances in a rigorous manner. Developing efficient methods to scan power spectrum likelihoods for oscillatory features, we present results for the phenomenological bare sine and cosine modulations, allowing validation against existing Planck likelihood surveys, as well as templates that include the correct sharp feature scaling. In particular, we study degeneracies between feature and cosmological parameters. For frequencies beyond the scale set by the acoustic peaks, the dependencies are realized through uninteresting adjustments of the comoving distance to last scattering. Hence, it is sufficient to keep cosmological parameters fixed and employ Gaussian approximations to the likelihood as a function of the feature model amplitude. In cases where results can be compared to the literature, our method shows excellent agreement. We supplement results from the Planck likelihood with an analysis based on the Planck spectral matching independent component analysis (SMICA) map that, working on the assumption that the component separation algorithm is reliable, allows for the inclusion of a larger sky fraction. In principle, this allows us to place the most stringent constraints to date on the amplitudes of feature models in the temperature power spectrum. Invoking the WMAP bispectrum, we perform a combined power spectrum and bispectrum survey. We use and slightly generalize statistics developed in previous work to reliably judge the significance of large feature model amplitude estimates. We conclude that our results are entirely consistent with a featureless realization of a Gaussian cosmic microwave background.