Unequal time correlators of stochastic scalar fields in de Sitter space

Abstract

The quantum fluctuations of a test scalar field on superhorizon scale in de Sitter spacetime can be described by an effective one-dimensional stochastic theory corresponding to a particular class of nonequilibrium dynamical systems known as the model A. Using the formulation of the latter in terms of a supersymmetric field theory, we compute various unequal-time correlators at large (superhorizon) time separations and compare with existing quantum field theory computation. This includes perturbative calculations, pushed here up to three-loop order, and a nonperturbative $1/N$ expansion at next-to-leading order. Exploiting the supersymmetry of the stochastic theory, we also derive a spectral representation of the field correlators and a fluctuation-dissipation relation for the infrared modes of the scalar field in de Sitter spacetime.

17 pages, 10 figures; typos corrected, references added, minor changes in Sec. 4C, figures updated

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Cited by in corpus (1)

• Second-order stochastic theory for self-interacting scalar fields in de Sitter spacetime