Enhancement of superhorizon scale inflationary curvature perturbations

We show that there exists a simple mechanism which can enhance the amplitude of curvature perturbations on superhorizon scales, relative to their amplitude at horizon crossing, even in some single-field inflation models. We give a criterion for this enhancement in general single-field inflation models; the condition for a significant effect is that the quantity a phi /H become sufficiently small, as compared to its value at horizon crossing, for some time interval during inflation.