  We study the analytic structure of in-in correlation functions in a deSitter
background. The aim of this study is to probe the initial conditions for
inflation through the features of correlation functions of the field
fluctuations, and understand precisely how an in-in correlator responds to
particles in the initial state. We emphasize that the choice of vacuua and the
corresponding particle interpretation for these fluctuations is flexible, and
we clarify the role of this choice at the level of calculations and their
diagrammatic interpretation. We consider several possibilities aside from the
standard Bunch Davies vacuum prescription for the initial state, and trace the
change in pole structure as one begins adding excitations; starting from just a
single particle, to highly excited states and special cases such as a coherent
state. We illustrate - with the example of coherent states - the subtleties in
concluding a Bunch Davies initial state from the absence of physical poles in
the bispectrum, which is interesting in light of some recent literature.
Initial states with a finite number of excitations are plagued with
disconnected diagrams isolated in phase space, and we highlight their
implications on the observation of these signals, and how the situation changes
as one begins to excite more and more particles. We also comment about the
implications of various initial conditions on the squeezed limit of the
bispectrum. These new pole structures are a direct consequence of mixing of
positive and negative frequency modes which is a characteristic of curved
spacetimes; in particular, we see in detail how particles in an initial state
replicate mode mixing structures. This study aims to clarify the missing
details that link quantum and classical initial conditions, and sharpen our
understanding of in-in correlators in inflation.
