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It is not known whether or not the stable rational cohomology groupsH * (Aut(F∞); Q) always vanish (see Hatcher in  and Hatcher and Vogtmann in  where they pose the question and show that it does vanish in the first 6 dimensions). We show that either the rational cohomology does not 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. Thisdoi:10.5565/publmat_46102_06 fatcat:gznrlv3ymzefhl3447sh2ti3r4