Advertisement

General Relativity and Gravitation

, Volume 37, Issue 12, pp 2063–2082 | Cite as

Evolution of density perturbations in a realistic universe

  • Marek Demianski
  • Zdzisław A. Golda
  • Andrzej Woszczyna
Research Article

Abstract

Prompted by the recent more precise determination of the basic cosmological parameters and growing evidence that the matter-energy content of the universe is now dominated by dark energy and dark matter we present the general solution of the equation that describes the evolution of density perturbations in the linear approximation. It turns out that as in the standard CDM model the density perturbations grow very slowly during the radiation dominated epoch and their amplitude increases by a factor of about 4000 in the matter and later dark energy dominated epoch of expansion of the universe.

Keywords

Cosmology Density Expansion 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Bahcall, N.A., Ostriker, J.P., Perlmutter, S., Steinhardt P.J.: Science 284, 1481 (1999)CrossRefADSGoogle Scholar
  2. 2.
    Brandenberger, R., Kahn, R., Press W.H.: Phys. Rev. D 28, 1809 (1983)CrossRefADSMathSciNetGoogle Scholar
  3. 3.
    Kodama, H., Sasaki, M.: Prog. Theor. Phys. 78, 1 (1984)CrossRefGoogle Scholar
  4. 4.
    Ellis, G.F.R., Bruni, M.: Phys. Rev. D 40, 1804 (1989)CrossRefADSMathSciNetGoogle Scholar
  5. 5.
    Padmanabhan, T.: Structure Formation in the Universe. Cambridge University Press, Cambridge (1993)Google Scholar
  6. 6.
    Peebles, P.J.E.: The Large Scale Structure of the Universe. Princeton Series in Physics, Princeton, New Jersey (1980)Google Scholar
  7. 7.
    Ince, E.L.: Ordinary Differential Equations. Dover Publikations, New York (1956)Google Scholar
  8. 8.
    Heune, K.: Math. Ann. 33, 161–179 (1889)CrossRefGoogle Scholar
  9. 9.
    Ronveux, A. (Ed.): Heun's Differential Equations. Oxford University Press, Oxford (1995)Google Scholar
  10. 10.
    Whittaker, E.T., Watson, G.N.: A Course in Modern Analysis, 4th ed. Cambridge University Press, Cambridge p. 576 (1990)Google Scholar
  11. 11.
    Snow, C.: In Hypergeometric and Legendre Functions with Applications to Integral Equations of Potential Theory. Nat. Bur. Stand. Appl. Math. Ser. No. 19 (U.S. GPO, Chap. VII, pp. 87–101 Washington, D.C. (1952)Google Scholar
  12. 12.
    Lifshitz, E.M.: ZhETPh 16, 587 (1946)MathSciNetGoogle Scholar
  13. 13.
    Groth, E.J., Peebles, P.J.E.: Astronomy Astroph. 41, 143 (1975)ADSGoogle Scholar
  14. 14.
    Mészáros, P.: Astroph J. 238, 781 (1980)CrossRefGoogle Scholar
  15. 15.
    Weinberg, S.: Gravitation and Cosmology, John Wiley and Sons, New York (1972)Google Scholar
  16. 16.
    Guyot, M., Zeldovich, Ya. B.: Astronomy Astroph. 9, 227 (1970)ADSGoogle Scholar
  17. 17.
    Rozgacheva, I.K., Syunyaev, R.A.: Pis'ma Astron. Zh. 6, 323 (1981)ADSGoogle Scholar
  18. 18.
    Heath, D.: Mon. Not. R. Astron. Soc. 179, 351 (1977)ADSGoogle Scholar
  19. 19.
    Chernin, A.D., Nagirner, D.I., Starikova, S.V.: Astronomy Astroph. 399, 19 (2003)CrossRefMATHADSGoogle Scholar
  20. 20.
    Eisenstein, D.J.: SISA (1997) astro-ph/9709054Google Scholar
  21. 21.
    Bildhauer, S., Buchert, T., Kasai, M.: Astronomy Astroph. 263, 23 (1992)ADSGoogle Scholar
  22. 22.
    Goliath, M., Ellis, G.F.R.: Phys. Rev. D 60, 023502 (1999)CrossRefADSMathSciNetGoogle Scholar
  23. 23.
    Sierpiński, W.: Principles of Higher Algebra with an appendix by Andrzej Mostowski, Outline of Galois Theory. (in Polish) (PTM, Warszawa-Wrocław 1951)Google Scholar
  24. 24.
    Friedman, A.: Zeits. für Phys. 10, 377 (1922)CrossRefADSGoogle Scholar
  25. 25.
    Robertson, H.P.: Rev. of Mod. Phys. 5, 62 (1933)CrossRefMATHADSGoogle Scholar
  26. 26.
    Stabell, R., Refsdal, S.: Mon. Not. R. Astron. Soc. 132, 453 (1966)Google Scholar
  27. 27.
    Harrison, E.R.: Mon. Not. R. Astron. Soc. 137, 69 (1967)ADSGoogle Scholar
  28. 28.
    Ehlers, J., Rindler, W.: Mon. Not. R. Astron. Soc. 238, 503 (1989)MATHADSGoogle Scholar
  29. 29.
    Belinsky, V.A., Khalatnikov, I.M.: ZhETPh 60, 401 (1975)ADSGoogle Scholar

Copyright information

© Springer-Verlag 2005

Authors and Affiliations

  • Marek Demianski
    • 1
  • Zdzisław A. Golda
    • 2
  • Andrzej Woszczyna
    • 2
  1. 1.Institute of Theoretical PhysicsUniversity of WarsawWarsawPoland
  2. 2.Astronomical ObservatoryJagellonian UniversityCracowPoland

Personalised recommendations