  It is well-known that spacetime averaging is an operation that does not
commute with building the Einstein tensor. In the framework of Macroscopic
gravity (MG), a covariant averaging procedure, this non-commutativity gives
averaged field equations with an additional correction term known as
back-reaction. It is important to explore whether such a term, even if known to
be small, may or may not cause any systematic effect for precision cosmology.
In this work, we explore the application of the MG formalism to an almost
Friedmann-Lema\^itre-Robertson-Walker (FLRW) model. Namely, we find solutions
to the field equations of MG taking the averaged universe to be almost-FLRW
modelled using a linearly perturbed FLRW metric. We study several solutions
with different functional forms of the metric perturbations including plane
waves ansatzes. We find that back-reaction terms are present not only at the
background level but also at perturbed level, reflecting the non-linear nature
of the averaging process. Thus, the averaging effect can extend to both the
expansion and the growth of structure in the universe.
