Graviton and topology contributions to self-consistent cosmology

We study the graviton contribution and the topology effects of antipodal identification in constant curvature solutions of semiclassical Einstein equations. We analyze the curvature R as a function of the cosmological constant Λ, of the topology (labelled here by a discrete parameter σ), and of the trace anomaly γ, the mass m and the coupling ζ of quantum matter fields. For m=0, we find eight possible (some of them classically forbidden) configurations depending on the graviton-matter balance. Even if Λ>0, R can be negative and even if Λ≠0, R goes to zero when N (the number of matter fields) goes to infinity. For m≠0 we find five characteristic types of behaviours depending on the values of ζ and σ. The 'back-reaction' effects of the topology appear more important for small ζ and increasing R. (orig.)