The quantum Fokker-Planck equation of stochastic inflation

Abstract

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.

25 pages, no figures

References in corpus (8)

• Stochastic Inflationary Scalar Electrodynamics
• Generation of fluctuations during inflation: comparison of stochastic and field-theoretic approaches
• Power spectrum for inflation models with quantum and thermal noises
• Stochastic growth of quantum fluctuations during slow-roll inflation
• Feynman Diagrams for Stochastic Inflation and Quantum Field Theory in de Sitter Space
• Two loop stress-energy tensor for inflationary scalar electrodynamics
• Two Loop Scalar Bilinears for Inflationary SQED
• The Zeta-Zeta Correlator Is Time Dependent

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