Astrophysics and Space Science

, Volume 158, Issue 1, pp 1–7 | Cite as

The problem of the maximum volumes and particle horizon in the Friedmann universe model

  • S. M. Gong (Kung)


The maximum volume of the closed Friedmann universe is further investigated and is shown to be 2π2R3(t), instead of π2R3(t) as found previously. This discrepancy comes from the incomplete use of the volume formula of 3-dimensional spherical space in the astronomical literature. Mathematically, there exists the maximum volume at any cosmic timet in a 3-dimensional spherical case. However, the Friedmann closed universe in expansion reaches its maximum volume only at the timet m of the maximum scale factorR(t m ). The particle horizon has no limitation for the farthest objects in the closed Friedmann universe if the proper distance of objects is compared with the particle horizon as it should be. It will lead to absurdity if the luminosity distance of objects is compared with the proper distance of the particle horizon.


Maximum Volume Universe Model Spherical Case Luminosity Distance Proper Distance 
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  1. Gong, S. M., Li, H. J., and Xia, C. L.: 1986,Scientia Sinica A29, No. 9, 966.Google Scholar
  2. Gong, S. M., Li, H. J., and Xia, C. L.: 1987, in A. Hewitt, G. Burbidge, and Li Zhi Fang (eds.), ‘Observational Cosmology’,IAU Symp. 124, 681.Google Scholar
  3. Heidmann, J.: 1980,Relativistic Cosmology Springer-Verlag, Berlin, Ch. 9.Google Scholar
  4. Longair, M. S. and Scheuer, P. A. G.: 1970,Monthly Notices Roy. Astron. Soc. 151, 45.Google Scholar
  5. Mattig, W.: 1959,Astron. Nachr. 285, 1.Google Scholar
  6. Misner, C. W., Thorne, K. S., and Wheeler, J. A.: 1973,Gravitation, Freeman and Co., San Francisco, p. 723.Google Scholar
  7. Rindler, H.: 1956,Monthly Notices Roy. Astron. Soc. 116, 662.Google Scholar
  8. Sandage, A.: 1961,Astrophys. J. 133 355.Google Scholar
  9. Weinberg, S.: 1972,Gravitation and Cosmology John Wiley and Sons, Inc., New York, Ch. 14 and 15.Google Scholar
  10. Zel'dovich, Ya. B. and Novikov, I. D.: 1983,The Structure and Evolution of the Universe, The Univ. of Chicago Press, Chicago, Ch. 2.Google Scholar

Copyright information

© Kluwer Academic Publishers 1989

Authors and Affiliations

  • S. M. Gong (Kung)
    • 1
  1. 1.Purple Mountain ObservatoryAcademia SinicaNanjingChina

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