  After giving how to construct the gauge invariant perturbation variable in an
arbitrarily high order and in the arbitrary background spacetime, we consider
the manifestly gauge invariant theory of the cosmological perturbations in the
long wavelength limit with the spatially flat homogeneous isotropic universe
being the background spacetime. In the previous paper, the physical laws become
manifestly gauge invariant, by writing them in terms of only the single time
background/scalar like objects. In the present paper, by extending our
definition of the background/scalar like objects from the single time case to
the many time case and by writing the solution of the physical law in the form
where many time background/scalar like objects are vanishing, the solutions
become the manifestly gauge invariant. We derive the formula changing the bases
of the many time background/scalar like objects by which we can change the time
slices for many times appearing in the solution including the initial time and
the final time. We use this formula to our treatment of the evolution of the
several slow rolling scalar fields using the $\tau$ function. In the manifestly
gauge invariant manner, we discuss the solution of the many step reheating,
that is, the reheating with the arbitrarily many energy transfer steps. By
using the useful parametrization of the many step reheating, we manifestly
prove that in the many step reheating system the prominent fluctuation
generation process the nearest to the present time erases all the fluctuations
generated by the previous fluctuation generation processes. Therefore in order
to know the first/second order Bardeen parameters at the present time it is
sufficient to calculate only the effects of the the prominent fluctuation
generation processes such as curvaton and the modulated reheating the nearest
to the present time.
