Effective long wavelength scalar dynamics in de Sitter

Abstract

We discuss the effective infrared theory governing a light scalar's long wavelength dynamics in de Sitter spacetime. We show how the separation of scales around the physical curvature radius $k/a\sim H$ can be performed consistently with a window function and how short wavelengths can be integrated out in the Schwinger-Keldysh path integral formalism. At leading order, and for time scales $\Delta t\gg H^{-1}$, this results in the well-known Starobinsky stochastic evolution. However, our approach allows for the computation of quantum UV corrections, generating an effective potential on which the stochastic dynamics takes place. The long wavelength stochastic dynamical equations are now second order in time, incorporating temporal scales $\Delta t\sim H^{-1}$ and resulting in a Kramers equation for the probability distribution - more precisely the Wigner function - in contrast to the more usual Fokker-Planck equation. This feature allows us to non-perturbatively evaluate, within the stochastic formalism, not only expectation values of field correlators, but also the stress-energy tensor of $\varphi$.

25 pages, 2 figures; v2: small changes, matches published JCAP version

References in corpus (16)

• Stochastic Inflationary Scalar Electrodynamics
• Generation of fluctuations during inflation: comparison of stochastic and field-theoretic approaches
• Stochastic growth of quantum fluctuations during slow-roll inflation
• On Resumming Inflationary Perturbations beyond One-loop
• On the proper treatment of massless fields in Euclidean de Sitter space
• Classical approximation to quantum cosmological correlations
• Cosmology With Many Light Scalar Fields: Stochastic Inflation and Loop Corrections
• Feynman Diagrams for Stochastic Inflation and Quantum Field Theory in de Sitter Space
• Perturbative Quantum Gravity Comes of Age
• Critical Number of Fields in Stochastic Inflation
• Vacuum Fluctuations of a Scalar Field during Inflation: Quantum versus Stochastic Analysis
• Nonperturbative renormalization group for scalar fields in de Sitter space: beyond the local potential approximation
• $O(N)$ model in Euclidean de Sitter space: beyond the leading infrared approximation
• Thermal Interpretation of Infrared Dynamics in de Sitter
• Large-Scale Suppression from Stochastic Inflation
• Decoherence Can Relax Cosmic Acceleration

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• A manifestly covariant theory of multifield stochastic inflation in phase space: solving the discretisation ambiguity in stochastic inflation
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