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

Xinghai Zhao1,2,3,* and Grant J. Mathews1,2,†

  • 1Department of Physics, University of Notre Dame, Notre Dame, Indiana 46556, USA
  • 2Center for Astrophysics, University of Notre Dame, Notre Dame, Indiana 46556, USA
  • 3The Joint Institute for Nuclear Astrophysics, University of Notre Dame, Notre Dame, Indiana 46556, USA

  • *xzhao@nd.edu
  • †gmathews@nd.edu
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Phys. Rev. D 83, 023524 – Published 26 January, 2011

DOI: https://doi.org/10.1103/PhysRevD.83.023524

Abstract

General relativistic corrections to the expansion rate of the Universe arise when the Einstein equations are averaged over a spatial volume in a locally inhomogeneous cosmology. It has been suggested that they may contribute to the observed cosmic acceleration. In this paper, we propose a new scheme that utilizes numerical simulations to make a realistic estimate of the magnitude of these corrections for general inhomogeneities in (3+1) spacetime. We then quantitatively calculate the volume averaged expansion rate using N-body large-scale structure simulations and compare it with the expansion rate in a standard FRW cosmology. We find that in the weak gravitational field limit, the converged corrections are slightly larger than the previous claimed 10−5 level, but not large enough nor even of the correct sign to drive the current cosmic acceleration. Nevertheless, the question of whether the cumulative effect can significantly change the expansion history of the Universe needs to be further investigated with strong-field relativity.

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Phys. Rev. D 83, 023524– Published 26 January, 2011
  • Received 24 December 2009
Article part of CHORUS

© 2011 American Physical Society

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