Reconstructing the EFT of inflation from cosmological data

Reconstructions of the primordial power spectrum (PPS) of curvature perturbations from cosmic microwave background anisotropies and large-scale structure data suggest that the usually assumed power-law PPS has localised features (up to ~ 10% in amplitude), although of only marginal significance in the framework of Lambda CDM cosmology. On the other hand if the cosmology is taken to be Einstein-de Sitter, larger features in the PPS (up to ~ 20% in amplitude) are required to accurately fit the observed acoustic peaks. Within the context of single clock inflation, we show that any given reconstruction of the PPS can be mapped on to functional parameters of the underlying effective theory of the adiabatic mode within a 2nd-order formalism, provided the best fit fractional change of the PPS, ΔP_R/P_R is such that (ΔP_R/P_R)³ falls within the 1 σ confidence interval of the reconstruction for features induced by variations of either the sound speed c_s or the slow-roll parameter ε. Although there is a degeneracy amongst these functional parameters (and the models that project onto them), we can identify simple representative inflationary models that yield such features in the PPS. Thus we provide a dictionary (more accurately, a thesaurus) to go from observational data, via the reconstructed PPS, to models that reproduce them to per cent level precision.