The Effect of Structure Formation on the Expansion of the Universe

Observations of the expansion rate of the universe at late times disagree by a factor of 1.5-2 with the prediction of homogeneous and isotropic models based on ordinary matter and gravity. We discuss how the departure from linearly perturbed homogeneity and isotropy due to structure formation could explain this discrepancy. We evaluate the expansion rate in a dust universe which contains nonlinear structures with a statistically homogeneous and isotropic distribution. The expansion rate is found to increase relative to the exactly homogeneous and isotropic case by a factor of 1.1-1.3 at some tens of billions of years. The time scale follows from the cold dark matter transfer function and the amplitude of primordial perturbations without additional free parameters.