Graviton and topology contributions to self-consistent cosmology

We study the graviton contribution and the topological effects of antipodal identification in constant curvature solutions of semiclassical Einstein equations. We analyze the curvature R as a function of the cosmological constant Γ, of the topology (labelled here by a discrete parameter σ), and of the trace anomaly λ, the mass m and the coupling ξ 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 Γ>0, R can be negative and even if Γ≠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 ξ and σ. The “back-reaction” effects of the topology appear more important for small ξ and increasing R.