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.

arXiv comment25 pages, no figures

References in corpus (22)

• Equilibrium State of a Massless Self-Interacting Scalar Field in the De Sitter Background
• Stochastic Quantum Gravitational Inflation
• Super-Hubble de Sitter Fluctuations and the Dynamical RG
• Quantum Fluctuations, Decoherence of the Mean Field, and Structure Formation in the Early Universe
• Stochastic Inflationary Scalar Electrodynamics
• Infrared effects in inflationary correlation functions
• Generation of fluctuations during inflation: comparison of stochastic and field-theoretic approaches
• Decoherence during Inflation: the generation of classical inhomogeneities
• Power spectrum for inflation models with quantum and thermal noises
• Stochastic growth of quantum fluctuations during slow-roll inflation
• Open EFTs, IR Effects and Late-Time Resummations: Systematic Corrections in Stochastic Inflation
• Infrared Correlations in de Sitter Space: Field Theoretic vs. Stochastic Approach
• Stochastic inflation in phase space: Is slow roll a stochastic attractor?
• 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
• A New Theory of Stochastic Inflation
• Effective long wavelength scalar dynamics in de Sitter
• The Zeta-Zeta Correlator Is Time Dependent
• Lagrangian Formulation of Stochastic Inflation: A Recursive Approach
• Stochastic Dynamics of Coarse-Grained Quantum Fields in Inflationary Universe
• Thermal Interpretation of Infrared Dynamics in de Sitter

Cited by in corpus (23)

• Non-Gaussian tail of the curvature perturbation in stochastic ultra-slow-roll inflation: implications for primordial black hole production
• Implications of stochastic effects for primordial black hole production in ultra-slow-roll inflation
• De Sitter Diagrammar and the Resummation of Time
• Characters of different secular effects in various patches of de Sitter space
• A manifestly covariant theory of multifield stochastic inflation in phase space: solving the discretisation ambiguity in stochastic inflation
• Statistical nature of infrared dynamics on de Sitter background
• Unitarity of quantum-gravitational corrections to primordial fluctuations in the Born-Oppenheimer approach
• Higgs vacuum (in)stability during inflation: the dangerous relevance of de Sitter departure and Planck-suppressed operators
• Observations in Quantum Cosmology
• Massive scalar field in de Sitter spacetime: a two-loop calculation and a comparison with the stochastic approach
• Inflationary stochastic anomalies
• Numerical stochastic inflation constrained by frozen noise
• Power-counting during single-field slow-roll inflation
• Renormalization group inspired autonomous equations for secular effects in de Sitter space
• Multipoint correlators in multifield cosmology
• Gravity, Horizons and Open EFTs
• Stochastic inflation from quantum field theory and the parametric dependence of the effective noise amplitude
• Non-Gaussianity from Entanglement During Inflation
• Non-Gaussian statistics of de Sitter spectators: A perturbative derivation of stochastic dynamics
• From the Fokker-Planck equation to perturbative QFT's results in de Sitter space
• Fokker-Planck equations for a trapped particle in a quantum-thermal Ohmic bath: general theory and applications to Josephson junctions
• Unification of Stochastic and Quantum Thermodynamics in Scalar Field Theory via a Model with Brownian Thermostat
• Emergent particles of de Sitter: thermal interpretation of the stochastic formalism and beyond