Stable rational cohomology of automorphism groups of free groups and the integral cohomology of moduli spaces of graphs

It is not-known whether or riot the stable rational cohomology groups (H) over tilde*(Aut(F-infinity);Q) always vanish (see Hatcher in [5] and Hatcher and Vogtmann in [7] where they pose the question and show that it does vanish in the first 6 dimensions). We show that either the rational cohomology does riot vanish in certain dimensions, or the integral cohomology of a moduli space of pointed graphs does not stabilize in certain other dimensions. Similar results are stated for groups of outer automorphisms. This yields that H-5((Q) over cap (m); Z), H-6((Q) over cap (m); Z), and H-5(Q(m); Z) never stabilize as m --> infinity, where the moduli spaces (Q) over cap (m) and Q(m) are the quotients of the spines (X) over cap (m) and X-m of "outer space" and "auter space", respectively, introduced in [3] by Culler and Vogtmann and [6] by Hatcher and Vogtmann.