  In this paper we discuss the effect of local inhomogeneities on the global
expansion of nearly FLRW universes, in a perturbative setting. We derive a
generic linearized averaging operation for metric perturbations from basic
assumptions, and we explicify the issue of gauge invariance. We derive a gauge
invariant expression for the back-reaction of density inhomogeneities on the
global expansion of perturbed FLRW spacetimes, in terms of observable
quantities, and we calculate the effect quantitatively. Since we do not adopt a
comoving gauge, our result incorporates the back-reaction on the metric due to
scalar velocity and vorticity perturbations. The results are compared with the
results by other authors in this field.

General Relativity and Quantum Cosmology