A Note on Calm Excited States of Inflation

TL;DR

The paper investigates whether excited initial states in inflation can be 'calm', i.e., leave the power spectrum unmodified while still imprinting non-Gaussian signatures. By constructing two-parameter families of Bogoliubov coefficients and enforcing the Wronskian condition, it shows that in slow-roll inflation such calm states exist and may exhibit no flattened-configuration enhancement in some cases, whereas in DBI inflation the flattened-configuration enhancement generally persists. The work emphasizes the crucial role of the Wronskian in accurately estimating non-Gaussian signals and demonstrates that distinguishing initial-state effects requires combining two-point and three-point measurements. These results constrain the microphysical origin of initial states and guide future observational probes of inflationary initial conditions.

Abstract

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.