Effects of nonlinear inhomogeneity on the cosmic expansion with
  numerical relativity
  We construct a three-dimensional, fully relativistic numerical model of a
universe filled with an inhomogeneous pressureless fluid, starting from initial
data that represent a perturbation of the Einstein-de Sitter model. We then
measure the departure of the average expansion rate with respect to this
homogeneous and isotropic reference model, comparing local quantities to the
predictions of linear perturbation theory. We find that collapsing
perturbations reach the turnaround point much earlier than expected from the
reference spherical top-hat collapse model and that the local deviation of the
expansion rate from the homogeneous one can be as high as $28\%$ at an
underdensity, for an initial density contrast of $10^{-2}$. We then study, for
the first time, the exact behavior of the backreaction term ${\cal Q}_{\cal
D}$. We find that, for small values of the initial perturbations, this term
exhibits a $1/a$ scaling, and that it is negative with a linearly growing
absolute value for larger perturbation amplitudes, thereby contributing to an
overall deceleration of the expansion. Its magnitude, on the other hand,
remains very small even for relatively large perturbations.
