General Relativity and Gravitation

, Volume 32, Issue 1, pp 105–125 | Cite as

On Average Properties of Inhomogeneous Fluids in General Relativity: Dust Cosmologies

  • Thomas Buchert


For general relativistic spacetimes filled with irrotational ‘dust’ a generalized form of Friedmann's equations for an ‘effective’ expansion factor a D of inhomogeneous cosmologies is derived. Contrary to the standard Friedmann equations, which hold for homogeneous-isotropic cosmologies, the new equations include the ‘backreaction effect’ of inhomogeneities on the average expansion of the model. A universal relation between ‘backreaction’ and average scalar curvature is also given. For cosmologies whose averaged spatial scalar curvature is proportional to a D -2, the expansion law governing a generic domain can be found. However, as the general equations show, ‘backreaction’ acts as to produce average curvature in the course of structure formation, even when starting with space sections that are spatially flat on average.

Irrotational dust model 


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  1. 1.
    Arnowitt, R., Deser, S., Misner, C. W. (1962). In Gravitation: an Introduction to Current Research, L. Witten, ed. (Wiley, New York).Google Scholar
  2. 2.
    Buchert, T. (1996). In Mapping, Measuring and Modelling the Universe (València 1995), P. Coles, V. J. Martínez, M. J. Pons–Bordería, eds.(ASP Conference Series), 349–356.Google Scholar
  3. 3.
    Buchert, T. (1997). In 2nd SFB Workshop on Astro-particle Physics, Report SFB/P002, Ringberg (Tegernsee) 1996, R. Bender, T. Buchert, P. Schneider, F. von Feilitzsch, eds.(T echnical University of Munich, Munich), p. 71-82.Google Scholar
  4. 4.
    Buchert, T., Ehlers, J. (1997). Astron. Astrophys. 320, 1.Google Scholar
  5. 5.
    Buchert, T., Kerscher, M., Sicka, C. (1999). Preprint.Google Scholar
  6. 6.
    Carfora, M., Piotrkowska, K. (1995). Phys. Rev. D 52, 4393.Google Scholar
  7. 7.
    Ellis, G. F. R.(1984). In General Relativity and Gravitation 10, B. Bertotti, F. de Felice and A. Pascolini, eds.(Reidel, Dordrecht), 215–288.Google Scholar
  8. 8.
    Kasai, M. (1995). Phys. Rev. D 52, 5605.Google Scholar
  9. 9.
    Kofman, L., Pogosyan, D. (1995). Astrophys. J. 442, 30.Google Scholar
  10. 10.
    Maartens, R., Ellis G. F. R., Stoeger W. R. (1995). Phys. Rev. D 51, 5942.Google Scholar
  11. 11.
    Matarrese, S. (1996). In Proc. Int. School of Physics “Enrico Fermi,” CXXXII -- Dark Matter in the Universe (Varenna 1995), S. Bonometto, J. Primack, A. Provenzale, eds. (IOS Press, Amsterdam), 601-628.Google Scholar
  12. 12.
    Matarrese, S., Terranova, D. (1996). Mon. Not. R. Astron. Soc. 283, 400.Google Scholar
  13. 13.
    Peebles, P. J. E.(1980). The Large Scale Structure of the Universe (Princeton University Press, Princeton, NJ).Google Scholar
  14. 14.
    Russ, H., Morita, M., Kasai, M., Börner, G.(1996). Phys. Rev. D 53, 6881.Google Scholar
  15. 15.
    Russ, H., Soffel, M. H., Kasai, M., Börner, G.(1997). Phys. Rev. D 56, 2044.Google Scholar
  16. 16.
    Stoeger, W. R., Helmi, A., Torres, D. F. (1999). Preprint gr-qc/9904020.Google Scholar
  17. 17.
    Takada M., Futamase T. (1999). Gen. Rel. Grav. 31, 461.Google Scholar
  18. 18.
    Wainwright, J., Ellis, G. F. R.(1997). Dynamical Systems in Cosmology (Cambridge University Press, Cambridge).Google Scholar
  19. 19.
    Wertz, J. R. (1971). Astrophys. J. 164, 227.Google Scholar
  20. 20.
    Yodzis, P. (1974). Proc. Royal IrishA cad. 74A, 61.Google Scholar
  21. 21.
    York, J. W., Jr. (1979). In Sources of Gravitational Radiation, L. Smarr, ed.(Cambridge University Press, Cambridge), p. 83.Google Scholar

Copyright information

© Plenum Publishing Corporation 2000

Authors and Affiliations

  • Thomas Buchert
    • 1
    • 2
  1. 1.Theory DivisonCERNGenève 23Switzerland
  2. 2.Theoretische PhysikLudwig-Maximilians-UniversitätMünchenGermany

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