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Astrophysics and Space Science

, Volume 154, Issue 2, pp 207–216 | Cite as

Closed-form expressions for the rate of growth of perturbations in zero-pressure Friedmann-Lemaître universes

  • D. J. Heath
Article

Abstract

The general solutions to the density perturbation equation derived by Bonnor are pressented for the zero-pressure Friedmann-Lemaître universes in terms of elliptic functions. The particular solutions already published to this equation in terms of elementary functions are exhibited as special cases arising from the general solutions. These occur when the elliptic functions simplify to either trigonometric or hyperbolic functions.

Keywords

General Solution Elementary Function Elliptic Function Density Perturbation Hyperbolic Function 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. Bonnor, W. B.: 1957,Monthly Notices Roy. Astron. Soc. 117, 104.Google Scholar
  2. Edwards, D.: 1972,Monthly Notices Roy. Astron. Soc. 159, 51.Google Scholar
  3. Jeans, J. H.: 1902,Phil. Trans. 199A, 1.Google Scholar
  4. Lifshitz, E. M.: 1946,J. Phys. USSR 10, 116.Google Scholar
  5. Neville, E. H.: 1951,Jacobian Elliptic Functions, Clarendon Press, Oxford, p. 249.Google Scholar
  6. Peebles, P. J. E.: 1980,The Large-Scale Structure of the Universe, Princeton University Press.Google Scholar
  7. Tinsley, B.: 1978,Nature 273, 208.Google Scholar
  8. Weinberg, S.: 1972,Gravitation and Cosmology, Wiley and Sons, New York.Google Scholar
  9. Whittaker, E. T. and Watson, G. N.: 1978,A Course of Modern Analysis, Cambridge University Press, Cambridge, p. 517.Google Scholar

Copyright information

© Kluwer Academic Publishers 1989

Authors and Affiliations

  • D. J. Heath
    • 1
  1. 1.Faculty of Applied SciencesLuton College of Higher EducationLutonU.K.

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