Correlators, Feynman Diagrams, and Quantum No-hair in deSitter Spacetime

• DOI: 10.1007/s00220-012-1653-2
• Publication Date: 2013-02-27T06:45:57Z
• Authors: Stefan Hollands
• Keywords: Propagator

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.<br/>57 pages, Latex, several figures. v2: more details given on derivation of parametric formula in sec.5, and exponential decay result in sec. 6, references added, figures added, typos removed<br/>