The semiclassical stability of de Sitter spacetime

de Sitter spacetime and Bunch-Davies vacuum are a solution to the semiclassical Einstein-Schrödinger equations describing the evolution of spacetime geometry and a massive scalar quantum field with arbitrary coupling to curvature. The stability of this solution is proven by calculating the renormalized energy momentum tensor expectation value for small spatially homogeneous deviations from the de Sitter – Bunch-Davies system and solving the linearized backreaction problem. A renormalization scheme is developed. All momentum integrations are carried out analytically. The general solution is given in terms of its Laplace transform. It contains only two artificial instabilities: a constant gauge mode and an instability on the Planck time scale lying outside of the scope of our semiclassical theory.