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The quantum Fokker-Planck equation of stochastic inflation

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arxiv 1706.07805 v1 pith:2S6VDJDO submitted 2017-06-23 hep-th astro-ph.COgr-qc

Hael Collins , Richard Holman , Tereza Vardanyan This is my paper
classification hep-thastro-ph.COgr-qc
keywords theoryequationfieldfokker-planckquantumstochasticmasslessscalar
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We derive the stochastic description of a massless, interacting scalar field in de Sitter space directly from the quantum theory. This is done by showing that the density matrix for the effective theory of the long wavelength fluctuations of the field obeys a quantum version of the Fokker-Planck equation. This equation has a simple connection with the standard Fokker-Planck equation of the classical stochastic theory, which can be generalised to any order in perturbation theory. We illustrate this formalism in detail for the theory of a massless scalar field with a quartic interaction.

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Cited by 4 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Stochastic inflation as an open quantum system II: open effective field theory and stochastic matching

    hep-th 2026-05 unverdicted novelty 7.0 of 10

    Develops open EFT for stochastic inflation with a distinct stochastic RG channel, derives nonlocal master equations including Fokker-Planck and Klein-Kramers forms, and demonstrates stochastic renormalization with an ...

  2. Stochastic inflation from a non-equilibrium renormalization group

    hep-th 2026-05 unverdicted novelty 7.0 of 10

    Stochastic inflation is the leading infrared limit of a coarse-grained Schwinger–Keldysh effective theory, and the same Fokker–Planck dynamics follows from a Polchinski-type renormalization-group flow for the reduced ...

  3. Renormalisation and matching of massless scalar correlation functions in Soft de Sitter Effective Theory

    hep-th 2026-03 conditional novelty 6.0 of 10

    SdSET is shown to renormalise and match like a flat-space EFT: tree-level trispectrum and six-point matching plus a one-loop power-spectrum match determine the SdSET couplings and initial-condition functions.

  4. Stochastic inflation as an open quantum system

    hep-th 2025-07 conditional novelty 6.0 of 10

    Stochastic inflation emerges from an open-quantum-system derivation, with a Lindblad master equation that reduces to and corrects Starobinsky's Fokker-Planck equation.

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