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We clarify the behavior of curvature perturbations in a nonlinear theory incase the inflaton temporarily stops during inflation. We focus on the evolutionof curvature perturbation on superhorizon scales by adopting the spatialgradient expansion and show that the nonlinear theory, called the {\it beyond}$\delta N$-formalism for a general single scalar field as the next-leadingorder in the expansion. Both the leading-order in the expansion ($\deltaN$-formalism) and our nonlinear theory include the solutions of full-nonlinearorders in the standard perturbative expansion. Additionally, in our formalism,we can deal with the time evolution in contrast to $\delta N$-formalism, wherecurvature perturbations remain just constant, and show decaying modes do notcouple with growing modes as similar to the case with linear theory. We canconclude that although the decaying mode diverges when $\dot{\phi}$ vanishes,there appears no trouble for both the linear and nonlinear theory since thesemodes will vanish at late times.

Full nonlinear growing and decaying modes of superhorizon curvature perturbations