Non-Gaussianity of superhorizon curvature perturbations beyond $\delta$
  N formalism
  We develop a theory of nonlinear cosmological perturbations on superhorizon
scales for a single scalar field with a general kinetic term and a general form
of the potential. We employ the ADM formalism and the spatial gradient
expansion approach, characterised by $O(\epsilon^m)$, where $\epsilon=1/(HL)$
is a small parameter representing the ratio of the Hubble radius to the
characteristic length scale $L$ of perturbations. We obtain the general
solution for a full nonlinear version of the curvature perturbation valid up
through second-order in $\epsilon$ ($m=2$). We find the solution satisfies a
nonlinear second-order differential equation as an extension of the equation
for the linear curvature perturbation on the comoving hypersurface. Then we
formulate a general method to match a perturbative solution accurate to
$n$-th-order in perturbation inside the horizon to our nonlinear solution
accurate to second-order ($m=2$) in the gradient expansion on scales slightly
greater than the Hubble radius. The formalism developed in this paper allows us
to calculate the superhorizon evolution of a primordial non-Gaussianity beyond
the so-called $\delta N$ formalism or separate universe approach which is
equivalent to leading order ($m=0$) in the gradient expansion. In particular,
it can deal with the case when there is a temporary violation of slow-roll
conditions. As an application of our formalism, we consider Starobinsky's
model, which is a single field model having a temporary non-slow-roll stage due
to a sharp change in the potential slope. We find that a large non-Gaussianity
can be generated even on superhorizon scales due to this temporary suspension
of slow-roll inflation.
