Topological nonrealization results via the Goodwillie tower approach to   iterated loopspace homology
  We prove a strengthened version of a theorem of Lionel Schwartz that says that certain modules over the Steenrod algebra cannot be the mod 2 cohomology of a space.   What is most interesting is our method, which replaces his iterated use of the Eilenberg--Moore spectral sequence by a single use of the spectral sequence converging to the mod 2 cohomology of Omega^nX obtained from the Goodwillie tower for the suspension spectrum of Omega^nX. Much of the paper develops basic properties of this spectral sequence. 
Nicholas J. Kuhn