A note on calm excited states of inflation

We identify a two-parameter family of excited states within slow-roll inflation for which either the corrections to the two-point function or the characteristic signatures of excited states in the three-point function - i.e. the enhancement for the flattened momenta configurations- are absent. These excited states may nonetheless violate the adiabaticity condition maximally. We dub these initial states of inflation calm excited states. We show that these two sets do not intersect, i.e., those that leave the power-spectrum invariant can be distinguished from their bispectra, and vice versa. The same set of calm excited states that leave the two-point function invariant for slow-roll inflation, do the same task for DBI inflation. However, at the level of three-point function, the calm excited states whose flattened configuration signature is absent for slow-roll inflation, will lead to an enhancement for DBI inflation generally, although the signature is smaller than what suggested by earlier analysis. This example also illustrates that imposing the Wronskian condition is important for obtaining a correct estimate of the non-Gaussian signatures.