From the Fokker-Planck equation to perturbative QFT's results in de Sitter space

2025/04/29 by Kamenshchik, Alexander, Petriakova, Polina · 2 citations
#FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #High Energy Physics - Theory (hep-th)

paper · doi:10.48550/arxiv.2504.20646

Abstract

A technique to build perturbative series for the spectator field's correlation functions in de Sitter space through the Fokker-Planck equation is proposed. We derive from the first-order differential equation the iterative integral relation for equal- and multi-time correlation functions. With an appropriate integration, the obtained two-point and four-point correlation functions are in agreement with quantum field theory's ones.

Citations

• Recent Developments in Stochastic Inflation
• Borel resummation of secular divergences in stochastic inflation
• Vacuum Fluctuations of a Scalar Field during Inflation: Quantum versus Stochastic Analysis
• Feynman Diagrams for Stochastic Inflation and Quantum Field Theory in de Sitter Space
• Infrared Correlations in de Sitter Space: Field Theoretic vs. Stochastic Approach
• Infrared dynamics in de Sitter space from Schwinger-Dyson equations
• Fluctuation-dissipation and equilibrium for scalar fields in de Sitter
• Quantum Stability of a w < - 1 Phase of Cosmic Acceleration
• Stochastic Quantum Gravitational Inflation
• A Leading Logarithm Approximation for Inflationary Quantum Field Theory
• Attractor states and infrared scaling in de Sitter space
• Matter Contributions to the Expansion Rate of the Universe
• Equilibrium State of a Massless Self-Interacting Scalar Field in the De Sitter Background
• Birth of inflationary universes

Cited by

• Confronting infrared divergences in de Sitter: loops, logarithms and the stochastic formalism
• Scalar field stochastic dynamics in de Sitter spacetime from exact solutions of quantum deficient oscillators

Related

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• Non-Gaussian statistics of de Sitter spectators: A perturbative derivation of stochastic dynamics