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

Abstract

We consider a massive scalar field with quartic self-interaction $\lambda /4!{\varphi }^4$ 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. As a consequence, the correlation functions computed in both approaches also agree to leading infrared order. This perturbative correspondence shows that the stochastic Theory is exactly equivalent to the Field Theory in the infrared. The former can then offer a non-perturbative resummation of the Field Theoretical Feynman diagram expansion, including fields with $0\le m^2\ll \sqrt{\lambda }{H}^2$ for which the perturbation expansion fails at late times.

25 pages, 4 figures

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• Nonperturbative renormalization group for scalar fields in de Sitter space: beyond the local potential approximation
• Review on stochastic approach to inflation
• The quantum Fokker-Planck equation of stochastic inflation
• Large fluctuations and Primordial Black Holes
• Quantum Diffusion in Sharp Transition to Non-Slow-Roll Phase
• Numerical stochastic inflation constrained by frozen noise
• Swampland conjectures in hybrid metric-Palatini gravity
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• Stochastic Effects in Anisotropic Inflation
• Quantum corrections to inflation: the importance of RG-running and choosing the optimal RG-scale
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• Computing First-Passage Times with the Functional Renormalisation Group
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• Stochastic inflation from quantum field theory and the parametric dependence of the effective noise amplitude
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• Classicality of Stochastic Noise Away From Quasi-de Sitter Inflation
• Stochastic Inflation with Interacting Noises
• Time-reversed Stochastic Inflation
• Emergent particles of de Sitter: thermal interpretation of the stochastic formalism and beyond
• Deviations from Gaussian White Noise in Stochastic Inflation
• Scalar field effective potentials in de Sitter spacetime
• A Tail of Eternal Inflation
• Sub-Leading Logarithms for Scalar Potential Models on de Sitter