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

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Abstract

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.

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  1. School of Mathematics, Cardiff University, Cardiff, UK

    Stefan Hollands

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Hollands, S. Correlators, Feynman Diagrams, and Quantum No-hair in deSitter Spacetime. Commun. Math. Phys. 319, 1–68 (2013). https://doi.org/10.1007/s00220-012-1653-2

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