Manifestly gauge invariant theory of the nonlinear cosmological
  perturbations in the leading order of the gradient expansion
  In the full nonlinear cosmological perturbation theory in the leading order
of the gradient expansion, all the types of the gauge invariant perturbation
variables are defined. The metric junction conditions across the spacelike
transition hypersurface are formulated in a manifestly gauge invariant manner.
It is manifestly shown that all the physical laws such as the evolution
equations, the constraint equations, and the junction conditions can be written
using the gauge invariant variables which we defined only. Based on the
existence of the universal adiabatic growing mode in the nonlinear perturbation
theory and the $\rho$ philosophy where the physical evolution are described
using the energy density $\rho$ as the evolution parameter, we give the
definitions of the adiabatic perturbation variable and the entropic
perturbation variables in the full nonlinear perturbation theory. In order to
give the analytic order estimate of the nonlinear parameter $f_{NL}$, we
present the exponent evaluation method. As the models where $f_{NL}$ changes
continuously and becomes large, using the $\rho$ philosophy, we investigate the
non-Gaussianity induced by the entropic perturbation of the component which
does not govern the cosmic energy density, and we show that in order to obtain
the significant non-Gaussianity it is necessary that the scalar field which
supports the entropic perturbation is extremely small compared with the scalar
field which supports the adiabatic perturbation.
