Manifestly Causal In-In Perturbation Theory about the Interacting Vacuum
  In-In perturbation theory is a vital tool for cosmology and nonequilibrium
physics. Here, we reconcile an apparent conflict between two of its important
aspects with particular relevance to De Sitter/inflationary contexts: (i) the
need to slightly deform unitary time evolution with an i*epsilon prescription
that projects the free ("Bunch-Davies") vacuum onto the interacting vacuum and
renders vertex integrals well-defined, and (ii) Weinberg's "nested commutator"
reformulation of in-in perturbation theory which makes manifest the constraints
of causality within expectation values of local operators, assuming exact
unitarity. We show that a modified i*epsilon prescription maintains the exact
unitarity on which the derivation of (ii) rests, while nontrivially agreeing
with (i) to all orders of perturbation theory.
