The Supersymmetric Effective Field Theory of Inflation
  We construct the Supersymmetric Effective Field Theory of Inflation, that is
the most general theory of inflationary fluctuations when time-translations and
supersymmetry are spontaneously broken. The non-linear realization of these
invariances allows us to define a complete SUGRA multiplet containing the
graviton, the gravitino, the Goldstone of time translations and the Goldstino,
with no auxiliary fields. Going to a unitary gauge where only the graviton and
the gravitino are present, we write the most general Lagrangian built out of
the fluctuations of these fields, invariant under time-dependent spatial
diffeomorphisms, but softly-breaking time diffeomorphisms and gauged SUSY. With
a suitable St\"uckelberg transformation, we introduce the Goldstone boson of
time translation and the Goldstino of SUSY. No additional dynamical light field
is needed. In the high energy limit, larger than the inflationary Hubble scale
for the Goldstino, these fields decouple from the graviton and the gravitino,
greatly simplifying the analysis in this regime. We study the phenomenology of
this Lagrangian. The Goldstino can have a non-relativistic dispersion relation.
Gravitino and Goldstino affect the primordial curvature perturbations at loop
level. The UV modes running in the loops generate three-point functions which
are degenerate with the ones coming from operators already present in the
absence of supersymmetry. Their size is potentially as large as corresponding
to $f_{\rm NL}^{\rm equil.,\,orthog.}\sim 1$ or, for particular operators, even
$\gg 1$. The non-degenerate contribution from modes of order $H$ is estimated
to be very small.
