Effective theories of single field inflation when heavy fields matter
  We compute the low energy effective field theory (EFT) expansion for
single-field inflationary models that descend from a parent theory containing
multiple other scalar fields. By assuming that all other degrees of freedom in
the parent theory are sufficiently massive relative to the inflaton, it is
possible to derive an EFT valid to arbitrary order in perturbations, provided
certain generalized adiabaticity conditions are respected. These conditions
permit a consistent low energy EFT description even when the inflaton deviates
off its adiabatic minimum along its slowly rolling trajectory. By generalizing
the formalism that identifies the adiabatic mode with the Goldstone boson of
this spontaneously broken time translational symmetry prior to the integration
of the heavy fields, we show that this invariance of the parent theory dictates
the entire non-perturbative structure of the descendent EFT. The couplings of
this theory can be written entirely in terms of the reduced speed of sound of
adiabatic perturbations. The resulting operator expansion is distinguishable
from that of other scenarios, such as standard single inflation or DBI
inflation. In particular, we re-derive how certain operators can become
transiently strongly coupled along the inflaton trajectory, consistent with
slow-roll and the validity of the EFT expansion, imprinting features in the
primordial power spectrum, and we deduce the relevant cubic operators that
imply distinct signatures in the primordial bispectrum which may soon be
constrained by observations.
