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There is an ongoing debate in the literature concerning the effects ofaveraging out inhomogeneities (``backreaction'') in cosmology. In particular,some simple models of structure formation studied in the literature seem toindicate that the backreaction can play a significant role at late times, andit has also been suggested that the standard perturbed FLRW framework is nolonger a good approximation during structure formation, when the densitycontrast becomes nonlinear. In this work we use Zalaletdinov's covariantaveraging scheme (macroscopic gravity or MG) to show that as long as the metricof the Universe can be described by the perturbed FLRW form, the correctionsdue to averaging remain negligibly small. Further, using a fully relativisticand reasonably generic model of pressureless spherical collapse, we show thatas long as matter velocities remain small (which is true in our model), theperturbed FLRW form of the metric can be explicitly recovered. Together, theseresults imply that the backreaction remains small even during nonlinearstructure formation, and we confirm this within the toy model with a numericalcalculation.

Nonlinear Structure Formation, Backreaction and Weak Gravitational Fields