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We provide a parametric representation for position-space Feynman integralsof a massive, self-interacting scalar field in deSitter spacetime, for anarbitrary graph. The expression is given as a multiple contour integral over akernel whose structure is determined by the set of all trees (or forests)within the graph, and it belongs to a class of generalized hypergeometricfunctions. We argue from this representation that connected deSitter $n$-pointvacuum correlation functions have exponential decay for large propertime-separation, and also decay for large spatial separation, to arbitraryorders in perturbation theory. Our results may be viewed as an analog of theso-called cosmic-no-hair theorem in the context of a quantized test scalarfield. This work has significant overlap with a paper by Marolf and Morrison,which is being released simultaneously.

Correlators, Feynman diagrams, and quantum no-hair in deSitter spacetime