Manifestly Causal In-In Perturbation Theory about the Interacting Vacuum

TL;DR

This paper resolves a conflict in in-in perturbation theory related to the i*epsilon prescription and causality constraints, ensuring unitarity and well-defined calculations in cosmological contexts.

Contribution

It introduces a modified i*epsilon prescription that preserves unitarity while aligning with causality constraints in in-in perturbation theory.

Findings

The modified i*epsilon prescription maintains exact unitarity.

It agrees with the standard i*epsilon approach to all orders.

The work clarifies the theoretical consistency of in-in perturbation calculations.

Abstract

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.