Lensing anomaly and oscillations in the primordial power spectrum

The latest analysis of the cosmic microwave background by the Planck team finds more smoothing of the acoustic peaks in the temperature power spectrum than predicted by $\Lambda$CDM. Here we investigate whether this additional smoothing can be mimicked by an oscillatory feature, generated during inflation, that is similar to the acoustic peaks but out of phase. We consider oscillations generated by oscillating modulations of the background -- e.g., due to heavy fields or modulated potentials -- and by sharp features. We show that it is difficult to induce oscillations that are linear (or almost linear) in $k$ by oscillatory modulations of the background. We find, however, that a sharp bumpy feature in the sound speed of perturbations is able to produce the desired oscillations. The scenario can be tested by combining CMB and BAO data.