Applicability of the linearly perturbed FRW metric and Newtonian cosmology

It has been argued that the effect of cosmological structure formation on the average expansion rate is negligible, because the linear approximation to the metric remains applicable in the regime of nonlinear density perturbations. We discuss why the arguments based on the linear theory are not valid. We emphasize the difference between Newtonian gravity and the weak field, small velocity limit of general relativity in the cosmological setting.