Large curvature perturbations near horizon crossing in single-field   inflation models
  We consider the examples of single-field inflation models predicting large amplitudes of the curvature perturbation power spectrum at relatively small scales. It is shown that in models with an inflationary potential of double-well type the peaks in the power spectrum, having, in maximum, the amplitude ~0.1, can exist (if parameters of the potential are chosen appropriately). It is shown also that the spectrum amplitude of the same magnitude (at large k values) is predicted in the model with the running mass potential, if the positive running, n', exists and is about 0.005 at cosmological scales. Estimates of the quantum diffusion effects during inflation in models with the running mass potential are given. 
Edgar Bugaev, Peter Klimai