A Map Between Primordial Power Spectra and the Effective Field Theory of
  Inflation
  We have developed a precise dictionary between the spectrum of primordial
density fluctuations and the parameters of the effective field theory (EFT) of
inflation that determine the primordial power spectrum (PPS). At lowest order
the EFT contains two parameters: the slow-roll parameter $\epsilon$, which acts
as an order parameter, and the speed of sound $c_s$. Applying second-order
perturbation theory, we provide maps from the PPS to the EFT parameters that
are precise up to the cube of the fractional change in the PPS $(\Delta
\mathcal{P}/\mathcal{P})^3$, or less than $1\%$ for spectral features that
modulate the PPS by $20\%$. While such features are not required when the
underlying cosmological model is assumed to be $\Lambda$CDM they are necessary
for alternative models that have no cosmological constant/dark energy. We
verify the dictionary numerically and find those excursions in the slow-roll
parameter that reproduce the PPS needed to fit Planck data for both $\Lambda$
and no-$\Lambda$ cosmological models.
