Unequal Time Correlators of Stochastic Scalar Fields in de Sitter Space
Résumé
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.