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

Understand

We provide a parametric representation for position-space Feynman integrals of a massive, self-interacting scalar field in deSitter spacetime, for an arbitrary graph.

• The expression is given as a multiple contour integral over a kernel whose structure is determined by the set of all trees (or forests) within the graph, and it belongs to a class of generalized hypergeometric functions.
• We argue from this representation that connected deSitter $n$-point vacuum correlation functions have exponential decay for large proper time-separation, and also decay for large spatial separation, to arbitrary orders in perturbation theory.
• Our results may be viewed as an analog of the so-called cosmic-no-hair theorem in the context of a quantized test scalar field.