Built on

A. Starobinsky, A new type of isotropic cosmological models without singularity , Physics Letters B 91
1980
Earlier work this paper cites.
A. H. Guth, Inflationary universe: A possible solution to the horizon and flatness problems , Phys. Rev. D 23
1981
Earlier work this paper cites.
A. D. Linde, A New Inflationary Universe Scenario: A Possible Solution of the Horizon, Flatness, Homogeneity, Isotropy and Primordial Monopole Problems , Phys. Lett. 108B
1982
Earlier work this paper cites.
A. A. Starobinsky, Dynamics of Phase Transition in the New Inflationary Universe Scenario and Generation of Perturbations , Phys. Lett. 117B
1982
Earlier work this paper cites.
A. D. Linde, Chaotic Inflation , Phys. Lett. 129B
1983
Earlier work this paper cites.
H.Risken, The Fokker-Planck Equation , Springer (1984)
Original
1984
Earlier work this paper cites.
A. A. Starobinsky, STOCHASTIC DE SITTER (INFLATIONARY) STAGE IN THE EARLY UNIVERSE , Lect. Notes Phys. 246
1986
Earlier work this paper cites.
A. D. Linde, Eternally Existing Selfreproducing Chaotic Inflationary Universe , Phys. Lett. B175
1986
Earlier work this paper cites.
K.-i. Nakao, Y. Nambu and M. Sasaki, Stochastic Dynamics of New Inflation , Prog. Theor. Phys. 80
1988
Earlier work this paper cites.
Y. Nambu and M. Sasaki, Stochastic Approach to Chaotic Inflation and the Distribution of Universes , Phys. Lett. B219
1989
Earlier work this paper cites.

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M. Morikawa, Dissipation and Fluctuation of Quantum Fields in Expanding Universes , Phys. Rev. D42
1990
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1994
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Then

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D.Baumann and L.McAllister, Inflation and String Theory. , Cambridge University Press (2015)
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V. K. Onemli, Vacuum Fluctuations of a Scalar Field during Inflation: Quantum versus Stochastic Analysis , Phys. Rev. D91
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2017

Statistical nature of infrared dynamics on de Sitter background

Tokuda, Junsei, Tanaka, Takahiro

Understand

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 $V(\phi)$ 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 $\lambda \phi^4$ theory, we explicitly derive an effective EoM which correctly recovers the next-to-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, which will not be a big drawback because the commutator of a light scalar field becomes negligible at large scales owing to the squeezing.

Built on

A. Starobinsky, A new type of isotropic cosmological models without singularity , Physics Letters B 91
1980
Earlier work this paper cites.
A. H. Guth, Inflationary universe: A possible solution to the horizon and flatness problems , Phys. Rev. D 23
1981
Earlier work this paper cites.
A. D. Linde, A New Inflationary Universe Scenario: A Possible Solution of the Horizon, Flatness, Homogeneity, Isotropy and Primordial Monopole Problems , Phys. Lett. 108B
1982
Earlier work this paper cites.
A. A. Starobinsky, Dynamics of Phase Transition in the New Inflationary Universe Scenario and Generation of Perturbations , Phys. Lett. 117B
1982
Earlier work this paper cites.
A. D. Linde, Chaotic Inflation , Phys. Lett. 129B
1983
Earlier work this paper cites.
H.Risken, The Fokker-Planck Equation , Springer (1984)
Original
1984
Earlier work this paper cites.
A. A. Starobinsky, STOCHASTIC DE SITTER (INFLATIONARY) STAGE IN THE EARLY UNIVERSE , Lect. Notes Phys. 246
1986
Earlier work this paper cites.
A. D. Linde, Eternally Existing Selfreproducing Chaotic Inflationary Universe , Phys. Lett. B175
1986
Earlier work this paper cites.
K.-i. Nakao, Y. Nambu and M. Sasaki, Stochastic Dynamics of New Inflation , Prog. Theor. Phys. 80
1988
Earlier work this paper cites.
Y. Nambu and M. Sasaki, Stochastic Approach to Chaotic Inflation and the Distribution of Universes , Phys. Lett. B219
1989
Earlier work this paper cites.

Similar

M. Morikawa, Dissipation and Fluctuation of Quantum Fields in Expanding Universes , Phys. Rev. D42
1990
Cited alongside, same era.
A. A. Starobinsky and J. Yokoyama, Equilibrium state of a selfinteracting scalar field in the De Sitter background , Phys. Rev. D50
1994
Cited alongside, same era.
N. C. Tsamis and R. P. Woodard, Stochastic quantum gravitational inflation , Nucl. Phys. B724
2005
Cited alongside, same era.
Y. Urakawa and T. Tanaka, Influence on Observation from IR Divergence during Inflation. I. , Prog. Theor. Phys. 122
Original
2009
Cited alongside, same era.
F. Finelli, G. Marozzi, A. A. Starobinsky, G. P. Vacca and G. Venturi, Generation of fluctuations during inflation: Comparison of stochastic and field-theoretic approaches , Phys. Rev. D79
Original
2009
Cited alongside, same era.