  Effective Field Theory (EFT) is an efficient method for parametrizing unknown
high energy physics effects on low energy data. When applied to time-dependent
backgrounds, EFT must be supplemented with initial conditions. In these
proceedings, I briefly describe such approach, especially in the case of
inflationary, almost-de Sitter backgrounds. I present certain self-consistency
constraints that bound the size of possible deviations of the initial state
from the standard thermal vacuum. I also estimate the maximum size of
non-Gaussianities due to a non-thermal initial state which is compatible with
all bounds. These non-Gaussianities can be much larger than those due to
nonlinearities in the action describing single-scalar slow roll inflation
