  A spatially flat Robertson-Walker spacetime driven by a cosmological constant
is non-conformally coupled to a massless scalar field. The equations of
semiclassical gravity are explicitly solved for this case, and a
self-consistent de Sitter solution associated with the Bunch-Davies vacuum
state is found (the effect of the quantum field is to shift slightly the
effective cosmological constant). Furthermore, it is shown that the corrected
de Sitter spacetime is stable under spatially-isotropic perturbations of the
metric and the quantum state. These results are independent of the free
renormalization parameters.

General Relativity and Quantum Cosmology