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Unequal time correlators of stochastic scalar fields in de Sitter space
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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.
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Critical dynamics of a scalar field near four spatial dimensions
The exactly dissipationless critical dynamics of a scalar field is an invariant but unstable surface of the RG flow, and any small friction drives it to Model A, with new two-loop dynamic exponents.
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