  We generalize the Effective Field Theory of Inflation to include additional
light scalar degrees of freedom that are in their vacuum at the time the modes
of interest are crossing the horizon. In order to make the scalars light in a
natural way we consider the case where they are the Goldstone bosons of a
global symmetry group or are partially protected by an approximate
supersymmetry. We write the most general Lagrangian that couples the scalar
mode associated to the breaking of time translation during inflation to the
additional light scalar fields. This Lagrangian is constrained by
diffeomorphism invariance and the additional symmetries that keep the new
scalars light. This Lagrangian describes the fluctuations around the time of
horizon crossing and it is supplemented with a general parameterization
describing how the additional fluctuating fields can affect cosmological
perturbations. We find that multifield inflation can reproduce the
non-Gaussianities that can be generated in single field inflation but can also
give rise to new kinds of non-Gaussianities. We find several new three-point
function shapes. We show that in multifield inflation it is possible to
naturally suppress the three-point function making the four-point function the
leading source of detectable non-Gaussianities. We find that under certain
circumstances, i.e. if specific shapes of non-Gaussianities are detected in the
data, one could distinguish between single and multifield inflation and
sometimes even among the various mechanisms that kept the additional fields
light.
