On the primordial origin of the smoothing excess in the Planck temperature power spectrum in light of LSS data

The Planck DR3 measurements of the temperature and polarization anisotropies power spectra of the cosmic microwave background (CMB) show an excess of smoothing of the acoustic peaks with respect to ACDM, often quantified by a phenomenological parameter AL. A specific feature superimposed to the primordial power spectrum has been suggested as a physical solution for this smoothing excess. Here, we investigate the impact of this specific localized oscillation with a frequency linear in the wavenumber, designed to mimic the smoothing of CMB temperature spectrum corresponding to AL <^> 1.1-1.2 on the matter power spectrum. We verify the goodness of the predictions in perturbation theory at next-to-leading order with a set of N-body simulations, a necessary step to study the non-linear damping of these primordial oscillations. We show that for a large portion of the parameter space, the amplitude of this primordial oscillation can be strongly damped on the observed nonlinear matter power spectrum at z = 0, but a larger signal is still persistent at z < 2 and is therefore a target for future galaxy surveys at high redshifts. From an analysis of the BOSS DR12 two-point correlation function, we find Alin < 0.26 at 95% CL by keeping the frequency fixed to the best-fit of Planck data.