Density fluctuations in one-field inflation
  Any one-field inflation is actually realized in a multifield configuration because the inflaton must have couplings with other fields to reheat the universe and is coupled to all other fields at least gravitationally. In all single inflaton models, it is explicitly or implicitly assumed that the heavier fields are stuck to their potential minima during inflation, which are time-dependent in general. We present a formalism to calculate curvature perturbations in such a time-dependent background and show that the proper expression can be obtained using a single-field analysis with a reduced potential in which all these heavy fields are situated at their respective, time-dependent minima. Our results provide a firm ground on the conventional calculation. 
Masahide Yamaguchi and Jun'ichi Yokoyama