Full nonlinear growing and decaying modes of superhorizon curvature
  perturbations
  We clarify the behavior of curvature perturbations in a nonlinear theory in
case the inflaton temporarily stops during inflation. We focus on the evolution
of curvature perturbation on superhorizon scales by adopting the spatial
gradient expansion and show that the nonlinear theory, called the {\it beyond}
$\delta N$-formalism for a general single scalar field as the next-leading
order in the expansion. Both the leading-order in the expansion ($\delta
N$-formalism) and our nonlinear theory include the solutions of full-nonlinear
orders in the standard perturbative expansion. Additionally, in our formalism,
we can deal with the time evolution in contrast to $\delta N$-formalism, where
curvature perturbations remain just constant, and show decaying modes do not
couple with growing modes as similar to the case with linear theory. We can
conclude that although the decaying mode diverges when $\dot{\phi}$ vanishes,
there appears no trouble for both the linear and nonlinear theory since these
modes will vanish at late times.
