De Sitter metric as a self-consistent solution of the back reaction problem

The de Sitter metric is a solution of the Einstein equation even when quantum effects of matter fields are included. However between the curvature and the cosmological constant Λ changes drastically. For some values of Λ, there are two or three solutions, while there is none in some other cases. There can be even a positive curvature solution for negative Λ. These features depend on mass and spin of matter fields and the matter-curvature coupling. (orig.)