Advertisement

Springer Nature is making Coronavirus research free. View research | View latest news | Sign up for updates

5D generalized inflationary cosmology

  • 41 Accesses

  • 9 Citations

Abstract

We consider a 5D Kaluza-Klein type cosmological model with the fifth coordinate being a generalization of the invariant “historical” timeτ of the covariant theory of Horwitz and Piron. We distinguish between vacuum-, off-shell matter-, and on-shell matter-dominated eras as the solutions of the corresponding 5D gravitational field equations, and build an inflationary scenario according to which passage from the off-shell matter-dominated era to the on-shell one occurs, probably as a phase transition. We study the effect of this phase transition on the expansion rate in both cases of localO(4,1) andO(3,2) invariance of the extended (x µ,τ) manifold and show that it does not change in either case. The expansion of the model we consider is not adiabatic; the thermodynamic entropy is a growing function of cosmic time for the closed universe, and can be a growing function of historical time for the open and the flat universe. A complete solution of the 5D gravitational field equations is obtained for the on-shell matter-dominated universe. The open and the closed universe are shown to tend asymptotically to the standard 4D cosmological models, in contrast to the flat universe which does not have the corresponding limit. Finally, possible cosmological implications are briefly discussed.

This is a preview of subscription content, log in to check access.

References

  1. 1.

    Forgacs, P., and Horvath, Z. (1979)Gen. Rel. Grav. 11, 205.

  2. 2.

    Chodos, A., and Detweiler, S. (1980).Phys. Rev. D 21, 2167.

  3. 3.

    Guth, A. H. (1981).Phys. Rev. D 23, 347.

  4. 4.

    Freund, P. G. O. (1982).Nucl. Phys. B 209, 146.

  5. 5.

    Appelquist, T., and Chodos, A. (1983).Phys. Rev. Lett. 50, 141.

  6. 6.

    Alvarez, E., and Gavela, M. B. (1983).Phys. Rev. Lett. 51, 931.

  7. 7.

    Randjbar-Daemi, S., Salam, A., and Strathdee, J. (1984).Phys. Lett. B 135, 388.

  8. 8.

    Marciano, W. J. (1984).Phys. Rev. Lett. 52, 489.

  9. 9.

    Stueckelberg, E. C. G. (1941).Helv. Phys. Acta 14, 372; (1942).ibid. 15, 23.

  10. 10.

    Horwitz, L. P. and Piron, C. (1973).Helv. Phys. Acta 46, 316.

  11. 11.

    Saad, D., Horwitz, L. P. and Arshansky, R. I. (1989).Found. Phys. 19, 1125.

  12. 12.

    Land, M. S. Horwitz, L. P. and Shnerb, N. (1995).J. Math. Phys., in press.

  13. 13.

    Shnerb, N., and Horwitz, L. P. (1993).Phys. Rev. A 48, 4068.

  14. 14.

    Burakovsky, L. and Horwitz, L. P. (1994). “Manifestly Covariant Relativistic Thermodynamics and Avoidance of Gravitational Singularities.” Preprint TAUP-217394.

  15. 15.

    Burakovsky, L., and Horwitz, L. P. (1993).Physica A 201, 666.

  16. 16.

    Burakovsky, L., and Horwitz, L. P. (1995).Found. Phys. 25, 785.

  17. 17.

    Horwitz, L. P., Schieve, W. C., and Piron, C. (1981).Ann. Phys. (NY) 137, 306.

  18. 18.

    Burakovsky, L., and Horwitz, L. P. (1994). “Covariant Thermodynamics and “Realistic” Friedmann Model.” Preprint TAUP-2180-94.

  19. 19.

    Burakovsky, L. (1994). “On Relativistic Statistical Mechanics, Thermodynamics and Cosmology in 1 +D Dimensions.” Preprint TAUP-2187-94.

  20. 20.

    Burakovsky, L., Horwitz, L. P., and Schieve, W. C. (1994). “On Relativistic Bose-Einstein Condensation.” Preprint TAUP-2149-94.

  21. 21.

    Mann, R. B., and Vincent, D. E. (1985).Phys. Lett. A 107, 75.

  22. 22.

    Ishihara, H. (1984).Prog. Theor. Phys. 72, 376.

  23. 23.

    Chao, W. Z. (1984).Phys. Lett. B 146, 307.

  24. 24.

    Lorenz-Petzold, D. (1985).Phys. Rev. D 31, 929.

  25. 25.

    Wesson, P. S. (1992).Phys. Lett. B 276, 299; (1992).Space Sci. Rev. 59, 365; (1992).Astrophys. J. 394, 19.

  26. 26.

    Ponce de Leon, J., and Wesson, P. S. (1992).J. Math. Phys. 33, 3883; (1993).ibid. 34, 4080.

  27. 27.

    Shafi, Q., and Wetterich, C. (1985).Phys. Lett. B 152, 51; (1987).Nucl. Phys. B 289, 787.

  28. 28.

    Grøn, Ø. (1988).Astron. Astrophys. 193, 1.

  29. 29.

    Wesson, P. S. (1984).Gen. Rel. Grav. 16, 193; (1990).ibid. 22, 707.

  30. 30.

    Weinberg, S. (1972).Gravitation and Cosmology (Wiley, New York).

  31. 31.

    Kaluza, T. (1921).Sitzungsber. Preuss. Akad. Wiss. Berlin, Phys. Math.,K1 33, 966.

  32. 32.

    Rindler, W. (1986).Essential Relativity (Springer-Verlag, New York).

  33. 33.

    Burakovsky, L., and Horwitz, L. P. (1995). “RMS Cosmology,” in preparation.

  34. 34.

    Linde, A. (1993).Particle Physics and Inflationary Cosmology (Harwood, Chur, Switzerland).

  35. 35.

    Coleman, S., and Weinberg, E. J. (1973).Phys. Rev. D 6, 1888.

  36. 36.

    Wesson, P. S. (1978).Cosmology and Geophysics (Hilger, Bristol).

  37. 37.

    Burakovsky, L., and Horwitz, L. P. (1994).J. Phys. A 27, 2623,4725.

  38. 38.

    DeGrand, T., and Kajantie, K. (1984).Phys. Lett. B 147, 273.

  39. 39.

    Crawford, M., and Schramm, D. N. (1982).Nature 298, 538.

  40. 40.

    Freese, K., Price, R., and Schramm, D. N. (1983).Astrophys. J. 275, 405.

  41. 41.

    Witten, E. (1984).Phys. Rev. D 30, 272.

  42. 42.

    Ornik, U., and Weiner, R. M. (1987).Phys. Rev. D 36, 1263.

  43. 43.

    Müller, B. (1985).The Physics of the Quark-Gluon Plasma (Springer-Verlag, Berlin).

  44. 44.

    Brown, F. R.et al. (1988).Phys. Rev. Lett. 61, 2058.

  45. 45.

    Svetitsky, B. (1987).Nucl. Phys. A 461, 71c.

  46. 46.

    Wesson, P. S. (1988).Astron. Astrophys. 189, 4; Ponce de Leon, J. (1988).Gen. Rel. Grav. 20, 539.

  47. 47.

    Shuryak, E. V. (1976).Sov. J. Nucl. Phys. 24, 330; (1978).Phys. Lett. B 78, 150; Zhirov, O. V. (1979).Sov. J. Nucl. Phys. 30, 571.

  48. 48.

    Ma, G.-W. (1991).Astrophys. Space Sci. 181, 331.

Download references

Author information

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Burakovsky, L., Horwitz, L.P. 5D generalized inflationary cosmology. Gen Relat Gravit 27, 1043–1070 (1995). https://doi.org/10.1007/BF02148647

Download citation

Keywords

  • Entropy
  • Manifold
  • Phase Transition
  • Cosmological Model
  • Expansion Rate