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General Relativity and Gravitation

, Volume 42, Issue 10, pp 2453–2475 | Cite as

Imitating accelerated expansion of the Universe by matter inhomogeneities: corrections of some misunderstandings

  • Andrzej Krasiński
  • Charles Hellaby
  • Krzysztof Bolejko
  • Marie-Noëlle Célérier
Research Article

Abstract

A number of misunderstandings about modeling the apparent accelerated expansion of the Universe and about the ‘weak singularity’ are clarified: (1) Of the five definitions of the deceleration parameter given by Hirata and Seljak (HS), only q 1 is a correct invariant measure of acceleration/deceleration of expansion. The q 3 and q 4 are unrelated to acceleration in an inhomogeneous model. (2) The averaging over directions involved in the definition of q 4 does not correspond to what is done in observational astronomy. (3) HS’s equation (38) connecting q 4 to the flow invariants gives self-contradictory results when applied at the centre of symmetry of the Lemaître–Tolman (L–T) model. The intermediate equation (31) that determines q 3' is correct, but approximate, so it cannot be used for determining the sign of the deceleration parameter. Even so, at the centre of symmetry of the L–T model, it puts no limitation on the sign of q 3'(0). (4) The ‘weak singularity’ of Vanderveld et al. is a conical profile of mass density at the centre—a perfectly acceptable configuration. (5) The so-called ‘critical point’ in the equations of the ‘inverse problem’ for a central observer in an L–T model is a manifestation of the apparent horizon (AH)—a common property of the past light cones in zero-lambda L–T models, perfectly manageable if the equations are correctly integrated.

Keywords

Exact solutions Cosmology Inhomogeneous cosmological models 

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References

  1. 1.
    Vanderveld R.A., Flanagan E.E., Wasserman I.: Phys. Rev. D 74, 023506 (2006)CrossRefADSGoogle Scholar
  2. 2.
    Hirata C.M., Seljak U.: Phys. Rev. D 72, 083501 (2005)CrossRefADSGoogle Scholar
  3. 3.
    Iguchi H., Nakamura T., Nakao K.: Progr. Theor. Phys. 108, 809 (2002)MATHCrossRefADSGoogle Scholar
  4. 4.
    Lemaître, G.: Ann. Soc. Sci. Bruxelles A53, 51 (1933); English translation, with historical comments: Gen. Relativ. Gravit. 29, 637 (1997)Google Scholar
  5. 5.
    Tolman, R.C..: Proc. Nat. Acad. Sci. USA 20, 169 (1933); reprinted, with historical comments: Gen. Relativ. Gravit. 29, 931 (1997)Google Scholar
  6. 6.
    Tipler F.: Phys. Lett. 64A, 8 (1977)MathSciNetADSGoogle Scholar
  7. 7.
    Ellis, G.F.R.: In: Sachs, R.K. (ed.) Proceedings of the International School of Physics ‘Enrico Fermi’, Course 47: General Relativity and Cosmology, pp. 104–182. Academic Press, New York, (1971), reprinted, with historical comments, in Gen. Relativ. Gravit. 41, 581 (2009)Google Scholar
  8. 8.
    Hoyle F.: Cosmological tests of gravitational theories. In: Moller, C. (eds) Proc. Enrico Fermi School of Physics, Course XX, Varenna, “Evidence for Gravitational Theories”, pp. 141–174. Academic Press, New York (1961)Google Scholar
  9. 9.
    McCrea W.E.: Observable Relations in Relativistic Cosmology. Zeits. Astrophys. 9, 290–314 (1934)ADSGoogle Scholar
  10. 10.
    Lu T.H.-C., Hellaby C.: Obtaining the spacetime metric from cosmological observations. Class. Quant. Grav. 24, 4107–4131 (2007)MATHCrossRefMathSciNetADSGoogle Scholar
  11. 11.
    Hellaby C.: The mass of the cosmos. Mon. Not. Roy. Astron. Soc. 370, 239–244 (2006)ADSGoogle Scholar
  12. 12.
    McClure M.L., Hellaby C.: Determining the metric of the cosmos: stability, accuracy, and consistency. Phys. Rev. D 78, 044005 (2008)CrossRefADSGoogle Scholar
  13. 13.
    Riess A.G., Filippenko A.V., Challis P., Clocchiatti A., Diercks A., Garnavich P.M., Gilliland R.L., Hogan C.J., Jha S., Krishner R.P., Leibundgut B., Phillips M.M., Reiss D., Schmidt B.P., Schommer R.A., Smith R.C., Spyromilio J., Stubbs C., Suntzeff N.B., Tonry J.: Astron. J. 116, 1009 (1998)CrossRefADSGoogle Scholar
  14. 14.
    Perlmutter S., Aldering G., Goldhaber G., Knop R.A., Nugent P., Castro P.G., Deustua S., Fabbro S., Goobar A., Groom D.E., Hook I.M., Kim A.G., Kim M.Y., Lee L.C., Nunes N.J., Pain R., Pennypacker C.R., Quimby R., Lidman C., Ellis R.S., Irwin M., McMahon R.G., Ruiz-Lapuente P., Walton N., Schaefer B., Boyle B.J., Filippenko A.V., Matheson T., Fruchter A.S., Panagia N., Newberg H.J.M., Couch W.J.: Astrophys. J. 517, 565 (1999)CrossRefADSGoogle Scholar
  15. 15.
    Krasiński A.: Inhomogeneous Cosmological Models. Cambridge University Press, Cambridge (1997)MATHCrossRefGoogle Scholar
  16. 16.
    Plebański J., Krasiński A.: An Introduction to General Relativity and Cosmology. Cambridge University Press, Cambridge (2006)MATHCrossRefGoogle Scholar
  17. 17.
    Bondi, H.: Mon. Not. Roy. Astron. Soc. 107, 410 (1947); reprinted, with historical comments, in Gen. Relativ. Gravit. 31, 1777 (1999)Google Scholar
  18. 18.
    Flanagan E.E.: Phys. Rev. D 71, 103521 (2005)CrossRefADSGoogle Scholar
  19. 19.
    Barausse E., Matarrese S., Riotto A.: Phys. Rev. D 71, 063537 (2005)CrossRefADSGoogle Scholar
  20. 20.
    Goldberg, J., Sachs, R.K.: Acta Phys. Polon. 22 (Suppl.), 13 (1962); reprinted, with historical comments, in Gen. Relativ. Gravit. 41, 433 (2009)Google Scholar
  21. 21.
    Synge J.L.: Relativity: The General Theory. North-Holland, Amsterdam (1960)MATHGoogle Scholar
  22. 22.
    Visser M.: Phys. Rev. D 47, 2395 (1993)CrossRefMathSciNetADSGoogle Scholar
  23. 23.
    Navarro J.F., Frenk C.S., White S.D.: Astrophys. J. 462, 563 (1996)CrossRefADSGoogle Scholar
  24. 24.
    Célérier M.N.: Astron. Astrophys. 353, 63 (2000)Google Scholar
  25. 25.
    Mustapha N., Hellaby C., Ellis G.F.R.: Mon. Not. R. Astron. Soc. 292, 817 (1997)ADSGoogle Scholar
  26. 26.
    Hellaby C., Lake K.: Astrophys. J. 290, 381 (1985) + erratum Astrophys. J. 300, 461 (1986)Google Scholar
  27. 27.
    Mustapha N., Hellaby C.: Gen. Relativ. Gravit. 33, 455 (2001)MATHCrossRefMathSciNetADSGoogle Scholar
  28. 28.
    Humphreys, N.P., Maartens, R., Matravers, D.R.: arXiv:gr-qc/9804023 (1998)Google Scholar
  29. 29.
    Hellaby C., Alfedeel A.H.A.: Phys. Rev. D 79, 043501 (2009)CrossRefADSGoogle Scholar
  30. 30.
    Hellaby, C.: Some Properties of Singularities in the Tolman Model. PhD Thesis, Queen’s University, Kingston, Ontario. http://www.mth.uct.ac.za/~cwh/CWH_PhD.pdf (1985)
  31. 31.
    Hellaby C.: Class. Quant. Grav. 4, 635 (1987)MATHCrossRefMathSciNetADSGoogle Scholar
  32. 32.
    Krasiński A., Hellaby C.: Phys. Rev. D 69, 043502 (2004)CrossRefADSGoogle Scholar
  33. 33.
    Alnes H., Amarzguioui M., Grøn Ø.: Phys.Rev. D 73, 083519 (2006)CrossRefADSGoogle Scholar
  34. 34.
    Hellaby, C.: Modelling Inhomogeneity in the Universe. In: 5th International School on Field Theory and Gravitation, Cuiabá, Brazil, 20–24 April 2009, Proc. Sci. PoS(ISFTG)005 (2009)Google Scholar
  35. 35.
    Araújo, M.E., Stoeger, W.R.: arXiv:0705.1846 [astro-ph] (2007)Google Scholar
  36. 36.
    Chung D.J.H., Romano A.E.: Phys. Rev. D 74, 103507 (2006)CrossRefADSGoogle Scholar
  37. 37.
    Hellaby C., Lake K.: Astrophys. J. 282, 1–10 (1984)CrossRefMathSciNetADSGoogle Scholar
  38. 38.
    Bolejko K., Wyithe J.S.B.: J. Cosm. Astropart. Phys. 02, 020 (2009)CrossRefADSGoogle Scholar
  39. 39.
    Yoo C.M., Kai T., Nakao K-I.: Prog. Theor. Phys. 120, 937 (2008)MATHCrossRefADSGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  • Andrzej Krasiński
    • 1
  • Charles Hellaby
    • 2
  • Krzysztof Bolejko
    • 1
    • 2
  • Marie-Noëlle Célérier
    • 3
  1. 1.N. Copernicus Astronomical Centre, Polish Academy of SciencesWarszawaPoland
  2. 2.Astrophysics, Cosmology and Gravity Centre, Department of Mathematics and Applied MathematicsUniversity of Cape TownRondeboschSouth Africa
  3. 3.Laboratoire Univers et Théories (LUTH), Observatoire de Paris, CNRSUniversité Paris-DiderotMeudonFrance

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