Einstein's Universe: Cosmological structure formation in numerical
  relativity
  We perform large-scale cosmological simulations that solve Einstein's
equations directly via numerical relativity. Starting with initial conditions
sampled from the cosmic microwave background, we track the emergence of a
cosmic web without the need for a background cosmology. We measure the
backreaction of large-scale structure on the evolution of averaged quantities
in a matter-dominated universe. Although our results are preliminary, we find
the global backreaction energy density is of order $10^{-8}$ compared to the
energy density of matter in our simulations, and is thus unlikely to explain
accelerating expansion under our assumptions. Sampling scales above the
homogeneity scale of the Universe ($100-180\,h^{-1}$Mpc), in our chosen gauge,
we find $2-3\%$ variations in local spatial curvature.
