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General relativistic corrections to the expansion rate of the Universe arisewhen the Einstein equations are averaged over a spatial volume in a locallyinhomogeneous cosmology. It has been suggested that they may contribute to theobserved cosmic acceleration. In this paper, we propose a new scheme thatutilizes numerical simulations to make a realistic estimate of the magnitude ofthese corrections for general inhomogeneities in (3+1) spacetime. We thenquantitatively calculate the volume averaged expansion rate using N-bodylarge-scale structure simulations and compare it with the expansion rate in astandard FRW cosmology. We find that in the weak gravitational field limit, theconverged corrections are slightly larger than the previous claimed 10^{-5}level, but not large enough nor even of the correct sign to drive the currentcosmic acceleration. Nevertheless, the question of whether the cumulativeeffect can significantly change the expansion history of the Universe needs tobe further investigated with strong-field relativity.

Effects of structure formation on the expansion rate of the Universe: An estimate from numerical simulations