Constraining fast-roll inflation
  We present constraints on how far single field inflation may depart from the familiar slow-roll paradigm. Considering a fast-roll regime while requiring a (near)-scale-invariant power spectrum introduces large self-interactions for the field and consequently large and scale-dependent non-Gaussianities. Employing this signal, we use the requirement of weak-coupling together with WMAP constraints to derive bounds on generic $P(X,\phi)$ theories of single field inflation. 
Johannes Noller
astro-ph.CO gr-qc hep-th