The two-loop correction to the diffusion coefficient in stochastic inflation is computed for the first time via composite-operator renormalisation and matching in SdSET.
Effective long wavelength scalar dynamics in de Sitter
5 Pith papers cite this work. Polarity classification is still indexing.
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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 $\phi$.
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A generalized Fokker-Planck equation for stochastic inflation is derived from a Polchinski-type renormalization group flow on the density matrix, incorporating dissipative and diffusive corrections beyond the leading order.
The conventional truncation in stochastic inflation is inconsistent because quadratic-noise contributions are the same perturbative order as the deterministic non-Markovian corrections.
Derives stochastic equations from Schwinger-Keldysh formalism that include quantum diffusion and classical metric perturbations for non-perturbative ultra-slow-roll inflation, validated on Starobinsky and critical Higgs models.
Explicit one-loop computation shows the constraint effective potential for scalars in de Sitter is free of infrared problems and supports its use in stochastic Starobinsky-Yokoyama inflation.
citing papers explorer
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Quantum correction to the diffusion term in stochastic inflation from composite-operator matching in Soft de Sitter Effective Theory
The two-loop correction to the diffusion coefficient in stochastic inflation is computed for the first time via composite-operator renormalisation and matching in SdSET.
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Stochastic inflation from a non-equilibrium renormalization group
A generalized Fokker-Planck equation for stochastic inflation is derived from a Polchinski-type renormalization group flow on the density matrix, incorporating dissipative and diffusive corrections beyond the leading order.
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A consistent formulation of stochastic inflation I: Non-Markovian effects and issues beyond linear perturbations
The conventional truncation in stochastic inflation is inconsistent because quadratic-noise contributions are the same perturbative order as the deterministic non-Markovian corrections.
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Nonperturbative stochastic inflation in perturbative dynamical background
Derives stochastic equations from Schwinger-Keldysh formalism that include quantum diffusion and classical metric perturbations for non-perturbative ultra-slow-roll inflation, validated on Starobinsky and critical Higgs models.
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Scalar field effective potentials in de Sitter spacetime
Explicit one-loop computation shows the constraint effective potential for scalars in de Sitter is free of infrared problems and supports its use in stochastic Starobinsky-Yokoyama inflation.