  It is generally assumed that on sufficiently large scales the Universe is
well-described as a homogeneous, isotropic FRW cosmology with a dark energy.
Does the formation of nonlinear cosmic inhomogeneities produce a significant
effect on the average large-scale FLRW dynamics? As an answer, we suggest that
if the length scale at which homogeneity sets in is much smaller than the
Hubble length scale, the back-reaction due to averaging over inhomogeneities is
negligible. This result is supported by more than one approach to study of
averaging in cosmology. Even if no single approach is sufficiently rigorous and
compelling, they are all in agreement that the effect of averaging in the real
Universe is small. On the other hand, it is perhaps fair to say that there is
no definitive observational evidence yet that there indeed is a homogeneity
scale which is much smaller than the Hubble scale, or for that matter, if
today's Universe is indeed homogeneous on large scales. If the Copernican
principle can be observationally established to hold, or is theoretically
assumed to be valid, this provides strong evidence for homogeneity on large
scales. However, even this by itself does not say what the scale of homogeneity
is. If that scale is today comparable to the Hubble radius, only a fully
non-perturbative analysis can establish or rule out the importance of
cosmological back-reaction. This brief elementary report summarizes some recent
theoretical developments on which the above inferences are based.
