International Journal of Theoretical Physics

, Volume 28, Issue 9, pp 967–981 | Cite as

Is the cosmological singularity thermodynamically possible?

  • Jacob D. Bekenstein
Article

Abstract

The four broad approaches that have been suggested heretofore to eliminate the initial singularity from cosmology are briefly reviewed. None is satisfactory, basically because one does not know enough about the microphysics involved in the process. Thermodynamics has often been used in such dilemmas, and it is proposed to answer the question of whether there was a Friedmann-like singularity in the universe by exploiting the bound on specific entropy that has been established for finite system. It is made applicable to the universe by considering only a causally connected spacelike region within the particle horizon of a given observer. It is found that the specific entropy of radiation in such a region can exceed the bound if the observer is too early in the universe. Faith in the bound leads to the conclusion that the Friedmann models cannot be extrapolated back to nearer than a few Planck-Wheeler times from the singularity. The Friedmann initial singularity thus appears to be thermodynamically unacceptable.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Anderson, P. (1983).Physical Review D,28, 271.Google Scholar
  2. Bekenstein, J. D. (1973).Physical Review D,7, 2333.Google Scholar
  3. Bekenstein, J. D. (1975).Physical Review D,11, 2072.Google Scholar
  4. Bekenstein, J. D. (1977).Physical Review D,15, 1458.Google Scholar
  5. Bekenstein, J. D. (1981a).Physical Review D,23, 287.Google Scholar
  6. Bekenstein, J. D. (1981b).Physical Review Letters,46, 623.Google Scholar
  7. Bekenstein, J. D. (1982).General Relativity and Gravitation,14, 355.Google Scholar
  8. Bekenstein, J. D. (1983).Physical Review D,27, 2262.Google Scholar
  9. Bekenstein, J. D. (1984).Physical Review D,30, 1669.Google Scholar
  10. Bekenstein, J. D. (1988).Physical Review A,37, 3434.Google Scholar
  11. Bekenstein, J. D., and Guendelman, E. I. (1987).Physical Review D,35, 716.Google Scholar
  12. Bekenstein, J. D., and Meisels, A. (1978).Physical Review D,18, 4378.Google Scholar
  13. Bekenstein, J. D., and Meisels, A. (1980).Astrophysical Journal,237, 342.Google Scholar
  14. Bowick, M. J., Smolin, L., and Wijewardhana, L. C. R. (1986).Physical Review Letters,56, 424.Google Scholar
  15. Dehnen, H., and Honl, H. (1975).Astrophysics and Space Science,33, 49.Google Scholar
  16. De Sitter, W. (1917).Proceedings Koninlijk Nederlansch Akademie van Wetenschappen,20, 229.Google Scholar
  17. Friedmann, A. (1922).Zeitschrift für Physik,10, 377.Google Scholar
  18. Friedmann, A. (1924).Zeitschrift für Physik,21, 326.Google Scholar
  19. Fulling, S. and Parker, L. (1973).Physical Review D,7, 2357.Google Scholar
  20. Geroch, R. P. (1966).Physical Review Letters,17, 445.Google Scholar
  21. Ginzburg, V. L. (1971).Comments on Astrophysics and Space Physics,3, 7.Google Scholar
  22. Guth, A. H. (1981).Physical Review D,23, 347.Google Scholar
  23. Fischetti, M., Hartle, J. B., and Hu, B.-L. (1979).Physical Review D,20, 1757.Google Scholar
  24. Hartle, J. B. (1983). InThe Very Early Universe, G. W. Gibbons, S. W. Hawking, and S. T. C. Siklos, eds., Cambridge University Press, Cambridge.Google Scholar
  25. Hawking, S. W. (1965).Physical Review Letters,15, 689.Google Scholar
  26. Hawking, S. W. (1966).Physical Review Letters,17, 444.Google Scholar
  27. Hawking, S. W. (1975).Communications on Mathematical Physics,43, 212.Google Scholar
  28. Hawking, S. W. (1979). InGeneral Relativity: An Einstein Centennary Survey, S. W. Hawking and W. Israel, eds., Cambridge University Press, Cambridge.Google Scholar
  29. Hawking, S. W., and Ellis, G. F. R. (1973).The Large Scale Structure of Spacetime, Cambridge University Press, Cambridge.Google Scholar
  30. Hawking, S. W., and Halliwell, J. (1985).Physical Review D,31, 1777.Google Scholar
  31. Hubble, E. P. (1929).Proceedings of the National Academy of Sciences,15, 168.Google Scholar
  32. Kahn, I., and Qadir, A. (1984).Lettere al Nuovo Cimento,41, 493.Google Scholar
  33. Linde, A. D. (1982).Physics Letters,108B, 389.Google Scholar
  34. Murphy, G. L. (1973).Physical Review D,8, 4231.Google Scholar
  35. Nariai, H., and Tomita, K. (1971).Progress of Theoretical Physics,46, 776.Google Scholar
  36. Narlikar, J. V., and Padmanabhan, T, (1986).Gravity, Gauge Theories and Quantum Cosmology, Reidel, Dordrecht.Google Scholar
  37. Penrose, R., and Hawking, S. W. (1970).Proceedings of the Royal Society of London,314A, 529.Google Scholar
  38. Qadir, A. (1983).Physics Letters,95A, 285.Google Scholar
  39. Rosen, N. (1974). Unpublished.Google Scholar
  40. Schiffer, M. (1988). Unpublished.Google Scholar
  41. Schiffer, M., and Bekenstein, J. D. (1989).Physical Review D 39, 1109.Google Scholar
  42. Sorkin, R. D., Wald, R. M. and Jiu, Z. Z. (1981).General Relativity and Gravitation,13, 1127.Google Scholar
  43. Starobinsky, A. A. (1980).Physics Letters,91B, 99.Google Scholar
  44. Tolman, R. C. (1934).Relativity, Thermodynamics and Cosmology, Oxford University Press, London.Google Scholar
  45. Unruh, W. G., and Wald, R. M. (1982).Physical Review D,25, 942.Google Scholar
  46. Vilenkin, A. (1983).Physical Review D,27, 2848.Google Scholar
  47. Vilenkin, A. (1989).International Journal of Theoretical Physics, this issue.Google Scholar
  48. Weinberg, S. (1972).Gravitation and Cosmology, Wiley, New York.Google Scholar

Copyright information

© Plenum Publishing Corporation 1989

Authors and Affiliations

  • Jacob D. Bekenstein
    • 1
  1. 1.Physics DepartmentBen-Gurion UniversityBeershevaIsrael

Personalised recommendations