Fluctuation-dissipation and equilibrium for scalar fields in de Sitter

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The infrared dynamics of a minimally coupled scalar field in de Sitter spacetime can be described as Brownian motion of a particle in a medium of de Sitter temperature TDS=H/2π. The system obeys a fluctuation-dissipation relation and its equilibrium distribution is Maxwell-Boltzmann, implying kinetic and potential energies of comparable magnitudes. The transition to equilibrium is a semi-classical process beyond the scope of perturbation theory for interacting fields. The stochastic kinetic energy of the field causes de Sitter spacetime to cool down slowly with a corresponding decrease of the effective vacuum energy.