  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. This work has significant overlap with a paper by Marolf and Morrison,
which is being released simultaneously.
