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A spatially flat Robertson-Walker spacetime driven by a cosmological constantis non-conformally coupled to a massless scalar field. The equations ofsemiclassical gravity are explicitly solved for this case, and aself-consistent de Sitter solution associated with the Bunch-Davies vacuumstate is found (the effect of the quantum field is to shift slightly theeffective cosmological constant). Furthermore, it is shown that the correctedde Sitter spacetime is stable under spatially-isotropic perturbations of themetric and the quantum state. These results are independent of the freerenormalization parameters.

Stability of de Sitter spacetime under isotropic perturbations in semiclassical gravity