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We undertake a thorough search for signatures of sharp oscillatory featuresin the WMAP9 power spectrum and bispectrum as well as in the Planck powerspectrum. For the first time, we carry out searches in both the power spectrumand bispectrum simultaneously, employing well-defined look-elsewhere statisticsto assess significances in a rigorous manner. Developing efficient methods toscan power spectrum likelihoods for oscillatory features, we present resultsfor the phenomenological bare sine and cosine modulations, allowing validationagainst existing Planck Likelihood surveys, as well as templates that includethe correct sharp feature scaling. In particular, we study degeneracies betweenfeature and cosmological parameters. For frequencies beyond the scale set bythe acoustic peaks, the dependencies are realised through uninterestingadjustments of the comoving distance to last scattering. Hence, it issufficient to keep cosmological parameters fixed and employ fast Gaussianapproximations to the likelihood as a function of the feature model amplitude.In cases where results can be compared to the literature, our method showsexcellent agreement. We supplement results from the Planck Likelihood with ananalysis based on the Planck SMICA component separation map that, working onthe assumption that the component separation algorithm is reliable, allows forthe inclusion of a larger sky fraction. In principle, this allows us to placethe most stringent constraints to date on the amplitudes of feature models inthe temperature power spectrum. Invoking the WMAP bispectrum, we perform acombined power spectrum and bispectrum survey. We use and slightly generalisestatistics developed in previous work to reliably judge the significance oflarge feature model amplitude estimates. We conclude that our results areentirely consistent with a featureless realisation of a Gaussian CMB.

Polyspectra searches for sharp oscillatory features in cosmic microwave sky data