  Recently a new approach in constructing the conserved charges in cosmological
Einstein's gravity was given. In this new formulation, instead of using the
explicit form of the field equations a covariantly conserved rank four tensor
was used. In the resulting charge expression, instead of the first derivative
of the metric perturbation, the linearized Riemann tensor appears along with
the derivative of the background Killing vector fields. Here we give a detailed
analysis of the first order and the second order perturbation theory in a
gauge-invariant form in cosmological Einstein's gravity. The linearized
Einstein tensor is gauge-invariant at the first order but it is not so at the
second order, which complicates the discussion. This method depends on the
assumption that the first order metric perturbation can be decomposed into
gauge-variant and gauge-invariant parts and the gauge-variant parts do not
contribute to physical quantities.
