Averaging of a locally inhomogeneous realistic universe

Toshifumi Futamase

Research output: Contribution to journalArticlepeer-review

85 Citations (Scopus)


We present an averaging scheme in general relativity which allows us to study the effect of local inhomogeneity on the global behavior of the universe. The scheme uses 3+1 splitting of spacetime and introduces Isaacson averaging on the spatial hypersurface to get the averaged geometry. As a result of the averaging, the Friedmann-Robertson-Walker (FWR) geometry is derived in the first-order approximation for a wide class of inhomogeneous nonlinear matter distribution. The deviation from the FRW expansion is derived to the next order in terms of the anisotropic distribution of an effective stress-energy tensor. Using a simple model of inhomogeneity we show that the average effect of the inhomogeneity behaves like a negative spatial curvature term and thus has a tendency to extend the age of the universe.

Original languageEnglish
Pages (from-to)681-689
Number of pages9
JournalPhysical Review D - Particles, Fields, Gravitation and Cosmology
Issue number2
Publication statusPublished - 1996

ASJC Scopus subject areas

  • Nuclear and High Energy Physics
  • Physics and Astronomy (miscellaneous)


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