  The total Hamiltonian in general relativity, which involves the first class
Hamiltonian and momentum constraints, weakly vanishes. However, when the action
is expanded around a classical solution as in the case of a single scalar field
inflationary model, there appears a non-vanishing Hamiltonian and additional
first class constraints; but this time the theory becomes perturbative in the
number of fluctuation fields. We show that one can reorganize this expansion
and solve the Hamiltonian constraint exactly, which yield an explicit all order
action. On the other hand, the momentum constraint can be solved perturbatively
in the tensor modes $\gamma_{ij}$ by still keeping the curvature perturbation
$\zeta$ dependence exact. In this way, after gauge fixing, one can obtain a
semi-exact Hamiltonian for $\zeta$ which only gets corrections from the
interactions with the tensor modes (hence the Hamiltonian becomes exact when
the tensor perturbations set to zero). The equations of motion clearly exhibit
when the evolution of $\zeta$ involves a logarithmic time dependence, which is
a subtle point that has been debated in the literature. We discuss the long
wavelength and late time limits, and obtain some simple but non-trivial
classical solutions of the $\zeta$ zero-mode.
