The theoretical foundations of modern cosmology are built around the Friedmann-Lemaitre-Robertson-Walker solutions that are homogeneous and isotropic. While the Universe is statistically homogeneous and isotropic on large scales, it is inhomogeneous on small scales. This leads to the question of how much do the small scale inhomogeneities effect the evolution of the Universe. This is an extremely important question, because our interpretation of observation data, and thus, our understanding of the Universe, depends on the answer. In recent years, this question has been at the center of a contentious debate. The aim of this proposal is to develop mathematical techniques that will allow for this question to be convincingly answered.