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 $\sim 10\%$ in amplitude), although of only marginal
significance in the framework of $\Lambda$CDM cosmology. On the other hand if
the underlying cosmology is assumed to be Einstein-de Sitter, larger features
in the PPS (up to $\sim 20\%$) 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,
$\Delta\mathcal{P}_\mathcal{R}/\mathcal{P}_\mathcal{R}$ is such that
$(\Delta\mathcal{P}_\mathcal{R}/\mathcal{P}_\mathcal{R})^3$ falls within the
$1\,\sigma$ confidence interval of the reconstruction for features induced by
variations of either the sound speed $c_\mathrm{s}$ or the slow-roll parameter
$\epsilon$. 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.
