The quantum Fokker-Planck equation of stochastic inflation

Collins, Hael; Holman, R.; Vardanyan, Tereza

doi:10.1007/jhep11(2017)065

Cited by 23 publications

(19 citation statements)

References 30 publications

(61 reference statements)

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“…Ref [39]. showed that time evolution of the density matrix in λφ 4 , corrected perturbatively at fixed O(λ)gives Fokker-Planck evolution for the diagonal entries.…”

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confidence: 99%

De Sitter diagrammar and the resummation of time

Baumgart

Sundrum

2020

J. High Energ. Phys.

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Light scalars in inflationary spacetimes suffer from logarithmic infrared divergences at every order in perturbation theory. This corresponds to the scalar field values in different Hubble patches undergoing a random walk of quantum fluctuations, leading to a simple toy "landscape" on superhorizon scales, in which we can explore questions relevant to eternal inflation. However, for a sufficiently long period of inflation, the infrared divergences appear to spoil computability. Some form of renormalization group approach is thus motivated to resum the log divergences of conformal time. Such a resummation may provide insight into De Sitter holography. We present here a novel diagrammatic analysis of these infrared divergences and their resummation. Basic graph theory observations and momentum power counting for the in-in propagators allow a simple and insightful determination of the leading-log contributions. One thus sees diagrammatically how the superhorizon sector consists of a semiclassical theory with quantum noise evolved by a first-order, interacting classical equation of motion. This rigorously leads to the "Stochastic Inflation" ansatz developed by Starobinsky to cure the scalar infrared pathology nonperturbatively. Our approach is a controlled approximation of the underlying quantum field theory and is systematically improvable.

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“…Ref [39]. showed that time evolution of the density matrix in λφ 4 , corrected perturbatively at fixed O(λ)gives Fokker-Planck evolution for the diagonal entries.…”

mentioning

confidence: 99%

De Sitter diagrammar and the resummation of time

Baumgart

Sundrum

2020

J. High Energ. Phys.

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“…This allows us to neglect deep-IR modes beyond the observable scales in calculating observable correlation functions. 2 Recently several papers appeared which try to extend Stochastic Formalism, in Schrödinger picture [24], or by using path integral method [25]. 3 This stochastic formalism is also called Starobinsky's stochastic formalism.…”

Section: Ir Secular Growth and Stochastic Formalismmentioning

confidence: 99%

Statistical nature of infrared dynamics on de Sitter background

Tokuda

Tanaka

2018

J. Cosmol. Astropart. Phys.

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In this study, we formulate a systematic way of deriving an effective equation of motion(EoM) for long wavelength modes of a massless scalar field with a general potential V(φ) on de Sitter background, and investigate whether or not the effective EoM can be described as a classical stochastic process. Our formulation gives an extension of the usual stochastic formalism to including sub-leading secular growth coming from the nonlinearity of short wavelength modes. Applying our formalism to λφ 4 theory, we explicitly derive an effective EoM which correctly recovers the nextto-leading secularly growing part at a late time, and show that this effective EoM can be seen as a classical stochastic process. Our extended stochastic formalism can describe all secularly growing terms which appear in all correlation functions with a specific operator ordering. The restriction of the operator ordering will not be a big drawback because the commutator of a light scalar field becomes negligible at large scales owing to the squeezing.

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“…The stochastic approach has been shown to reproduce the correct IR behaviour of the full QFT statistical propagator to leading order in the coupling [3,[17][18][19][20] and was recently favourably compared at two-loop order in perturbation theory [21]. Other authors have studied the evolution of the density matrix for the IR modes to recover a Fokker-Planck equation [22,23], and ref. [24] argued the emergence of the stochastic formalism from a leading-log diagrammatic analysis at coincident points.…”

Section: Introductionmentioning

confidence: 99%

“…[25,26] for example applications), and in recent years there has been an upsurge in activity aiming to extend it e.g. to beyond leading order in the coupling [22,27,28], the slow-roll approximation [16,29], or to include derivative interactions [30]. However, compared to its extensive use, studies of the embedding and range of validity of the stochastic approach in QFT remain scarce (see however [31,32]), which has motivated the present work.…”

Section: Introductionmentioning

confidence: 99%

Stochastic inflation from quantum field theory and the parametric dependence of the effective noise amplitude

Andersen

Eriksson

Tranberg

2022

J. High Energ. Phys.

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The non-linear dynamics of long-wavelength cosmological fluctuations may be phrased in terms of an effective classical, but stochastic evolution equation. The stochastic noise represents short-wavelength modes that continually redshift into the long-wavelength domain. The effective evolution may be derived from first principles quantum field theory in an expanding background, through a sequence of approximations calling for additional scrutiny. We perform such an analysis, putting particular emphasis on the amplitude of the stochastic noise, which ultimately determines the cosmological correlations and provides a non-perturbative IR regulator to the dynamics.

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The quantum Fokker-Planck equation of stochastic inflation

Cited by 23 publications

References 30 publications

De Sitter diagrammar and the resummation of time

De Sitter diagrammar and the resummation of time

Statistical nature of infrared dynamics on de Sitter background

Stochastic inflation from quantum field theory and the parametric dependence of the effective noise amplitude

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