Feynman Rules for Stochastic Inflationary Correlators

Abstract

We elaborate on the functional integral describing the stochastic dynamics of a spectator field during inflation, comparing its diagrammatic expansion to that obtained directly from a perturbative solution of the corresponding Langevin equation. We state Feynman rules for computing arbitrary temporal $n$-point functions and perform some illustrative computations for a $\lambda {\varphi }^4$ interaction, paying attention to the role played by a functional Jacobian determinant in the path integral. We also briefly consider the case when the field contributes to the expansion rate, making the noise multiplicative, which introduces additional vertices.

arXiv comment30 pages

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Cited by in corpus (9)

• Markovian Dynamics in de Sitter
• Large fluctuations and Primordial Black Holes
• Numerical stochastic inflation constrained by frozen noise
• Primordial Black Holes from Effective Field Theory of Stochastic Single Field Inflation at NNNLO
• The $1/N$ expansion for stochastic fields in de Sitter spacetime
• Second-order stochastic theory for self-interacting scalar fields in de Sitter spacetime
• Free scalar correlators in de Sitter via the stochastic approach beyond slow roll
• Spectator dark matter in non-standard cosmologies
• Quantitative classicality in cosmological interactions during inflation