Cosmological acceleration from structure formation

We discuss the Buchert equations, which describe the average expansion of an inhomogeneous dust universe. In the limit of small perturbations, they reduce to the Friedmann–Robertson–Walker equations. However, when the universe is very inhomogeneous, the behavior can be qualitatively different from the FRW case. In particular, the average expansion rate can accelerate even though the local expansion rate decelerates everywhere. We clarify the physical meaning of this paradoxical feature with a simple toy model, and demonstrate how acceleration is intimately connected with gravitational collapse. This provides a link to structure formation, which in turn has a preferred time around the era when acceleration has been observed to start.