Feynman Diagrams for Stochastic Inflation and Quantum Field Theory in de Sitter Space

Understand

We consider a massive scalar field with quartic self-interaction $\lambda/4!\,\phi^4$ in de~Sitter spacetime and present a diagrammatic expansion that describes the field as driven by stochastic noise.

• This is compared with the Feynman diagrams in the Keldysh basis of the Amphichronous (Closed-Time-Path) Field Theoretical formalism.
• For all orders in the expansion, we find that the diagrams agree when evaluated in the leading infrared approximation, i.e.
• to leading order in $m^2/H^2$, where $m$ is the mass of the scalar field and $H$ is the Hubble rate.