  A new gauge-invariant approach for describing cosmological perturbations is
developed. It is based on a physically motivated splitting of the stress-energy
tensor of the perturbation into two parts - the bare perturbation and the
complementary perturbation associated with stresses in the background
gravitational field induced by the introduction of the bare perturbation. The
complementary perturbation of the stress-energy tensor is explicitly singled
out and taken to the left side of the perturbed Einstein equations so that the
bare stress-energy tensor is the sole source for the perturbation of the metric
tensor and both sides of these equations are gauge invariant with respect to
infinitesimal coordinate transformations. For simplicity we analyze the
perturbations of the spatially-flat Friedmann-Lemaitre-Robertson-Walker dust
model. A cosmological gauge can be chosen such that the equations for the
perturbations of the metric tensor are completely decoupled for the h_{00},
h_{0i}, and h_{ij} metric components and explicitly solvable in terms of
retarded integrals.
