Résumé
While the simplest inflationary models predict a power-law form of the primordial power spectrum (PPS), various UV complete scenarios predict features on top of the standard power law that leave characteristic imprints in the late-time distribution of matter, encoded in the galaxy power spectrum. In this work, we assess the validity of the Effective Field Theory of Large Scale Structure (EFTofLSS) and the IR-resummation scheme of PyBird in the context of primordial (oscillatory) features. We find an excellent agreement at the level of the matter power spectrum between N-body simulations and the one-loop EFT predictions, for models commonly studied in the literature. We then apply the EFTofLSS to the galaxy power spectrum measurements from BOSS LRG and eBOSS QSO to constrain specific global and local features in the PPS. We demonstrate that while such features can improve the fit to cosmic microwave background (CMB) data, they may result in a poorer fit to clustering measurements at low redshift. The resulting constraints on the amplitude of the primordial oscillations are competitive with those obtained from CMB data, despite the well-known damping of oscillations due to non-linear structure formation processes. For the first time in this context, we jointly analyze the galaxy power spectrum (monopole and quadrupole) in combination with Planck CMB data to derive strong constraints on the amplitude of primordial features. This work highlights the EFTofLSS as a powerful tool for testing early universe scenarios on scales that complement CMB observations.