Abstract
We consider time-ordered (or Feynman) propagators between two different $\alpha-$states of a linear de Sitter Quantum Field in the global de Sitter manifold and in the Poincar\'e patch. We separately examine $\alpha-\beta$, In-In and In-Out propagators and find the imaginary contribution to the effective actions. The In-In propagators are real in both the Poincar\'e patch and in the global de Sitter manifold. On the other side the In-Out propagators at coincident points contain finite imaginary contributions in both patches in even dimensions, but they are not equivalent. In odd dimensions in both patches the imaginary contributions are zero. For completeness, we also consider the Static patch and identify in our construction the state that is equivalent to the Bunch-Davies one in the Poincar\'e patch.
Highlights
To explain the point of our study let us consider a real massive scalar field in a curved space
We separately examine α − β, in–in and in–out propagators and find the imaginary contribution to the effective actions
The in–in propagators are real in both the Poincarepatch and in the global de Sitter manifold
Summary
To explain the point of our study let us consider a real massive scalar field in a curved space. The Feynman propagators in de Sitter space having an imaginary part at coincident points is the object of study of this note. In particular we observe that the rate is zero in any odd dimensional de Sitter spacetime; the in-in propagator is real and provides vanishing imaginary contribution to the effective action in any dimension. In the concluding section we present a heuristic explanation why the pair creation rate should be zero in odd dimensions and explain why there still can be nontrivial stress-energy flux the rate is vanishing
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