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arXiv · 1708.01734

Statistical nature of infrared dynamics on de Sitter background

Junsei Tokuda·Takahiro Tanaka
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Abstract

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.

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Junsei Tokuda, Takahiro Tanaka. 2017-08-05. Statistical nature of infrared dynamics on de Sitter background. https://doi.org/10.1088/1475-7516%2F2018%2F02%2F014

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