Feynman diagrams for stochastic inflation and quantum field theory in de Sitter space

摘要: We consider a massive scalar field with quartic self-interaction $\ensuremath{\lambda}/4!{\ensuremath{\phi}}^{4}$ in de Sitter spacetime and present diagrammatic expansion that describes the as driven by stochastic noise. This is compared Feynman diagrams Keldysh basis of amphichronous (closed-time-path) theoretical formalism. For all orders expansion, we find agree when evaluated leading infrared approximation, i.e. to order ${m}^{2}/{H}^{2}$, where $m$ mass $H$ Hubble rate. As consequence, correlation functions computed both approaches also order. perturbative correspondence shows theory exactly equivalent infrared. The former can then offer nonperturbative resummation diagram including fields $0\ensuremath{\le}{m}^{2}\ensuremath{\ll}\sqrt{\ensuremath{\lambda}}{H}^{2}$ for which perturbation fails at late times.