Cosmological Dynamics in the Case of Positive Spatial Curvature

A.Yu. Kamenshchik1, I.M. Khalatnikov2 and A.V. Toporensky3

Abstract

We investigate the simplest cosmological model with a massive real scalar non-interacting inflaton field minimally coupled to gravity. The classification of trajectories in a closed minisuperspace Friedmann-Robertson-Walker model is presented. The possible fractal nature of the set of bounced trajectories in the case of vanishing cosmological constant is discussed. The modification of this picture in the presence of a nonzero cosmological constant is presented.

References

  1. B. Mandelbrot, "The Fractal Geometry of Nature", San Francisco, Freeman, 1982.
  2. E.S. Nikomarov and I.M. Khalatnikov, Zh. Exp. Teor. Phys. 75, 1176 (1978); I.M. Khalatnikov and V.A. Belinski, Qualitative Cosmology in: "Problems of Modern Experimental and Theoretical Physics", dedicated to 80th anniversary of Yu.B. Khariton, ed. A.P. Alexandrov, Leningrad, 1984, p. 299 (in Russian).
  3. I.M. Khalatnikov and A.Yu. Kamenshchik, Phys. Rep. (to appear).
  4. V.A. Belinski and I.M. Khalatnikov, Zh. Exp. Teor. Phys. 63, 1121 (1972).
  5. S.W. Hawking, in: "Relativity, Groups and Topology II", ed. B.S. DeWitt and R. Stora, North Holland, Amsterdam, 1984.
  6. D.N. Page, Class. Quantum Grav. 1, 417 (1984).
  7. L. Parker and S.A. Fulling, Phys. Rev. D 7, 2357 (1973); A.A. Starobinsky, Pisma Astron. Zh. 4, 155 (1978).
  8. A. Melchiori, M. Sazhin, V. Shulga and N. Vittorio, in preparation; V.N. Lukash and E.V. Mikheeva, Grav. and Cosmol. 2, 247 (1996).
  9. A.Yu. Kamenshchik, I.M. Khalatnikov and A.V. Toporensky, Phys. Lett. B 357, 36 (1995).
  10. A.Yu. Kamenshchik, I.M. Khalatnikov and A.V. Toporensky, submitted to Int. J. Mod. Phys. D.
  11. V.A. Belinski, L.P. Grishchuk, Ya.B. Zel'dovich and I.M. Khalatnikov, J. Exp. Theor. Phys. 89, 346 (1985).
  12. V.A. Belinski and I.M. Khalatnikov, J. Exp. Theor. Phys. 93, 784 (1987); V.A. Belinski, H. Ishihara, I.M. Khalatnikov and H. Sato, Progr. Theor. Phys. 79, 676 (1988).
  13. G.A. Burnett, Phys. Rev. D51, 1621 (1995).
  14. L. Amendola, I.M. Khalatnikov, M. Litterio and F. Occhionero, Phys. Rev. D 49, 1881 (1994).
  15. I.M. Khalatnikov and A. Mezhlumian, Phys. Lett. A169, 308 (1992); I.M. Khalatnikov and P. Schiller, Phys. Lett. B 302, 176 (1993).
  16. B.L.Spokoiny, Phys. Lett. 129B, 39 (1984); D.S. Salopek, J.R. Bond and J.M. Bardeen, Phys. Rev. D40, 1753 (1989); R. Fakir and W.G. Unruh, Phys. Rev. D 41, 1783 (1990); R. Fakir, S. Habib and W.G. Unruh, Ap. J. 394, 396 (1992); R. Fakir and S. Habib, Mod. Phys. Lett. A 8, 2827 (1993).
  17. A.O. Barvinsky, Phys. Rep. 230, 237 (1993); A.O. Barvinsky and A.Yu. Kamenshchik, Phys. Rev. D50, 5093 (1994).
  18. A.D. Linde, "Particle Physics and Inflationary Cosmology", Harwood Academic, 1990, and references therein.
  19. J.B. Hartle and S.W. Hawking, Phys. Rev. D 28, 2960 (1983); S.W. Hawking, Nucl. Phys. B 239, 257 (1984).
  20. A. Vilenkin, Phys. Lett. 117B, 25 (1982); Phys. Rev. D 27, 2848 (1983); Phys. Rev. D 30 509 (1984); Phys. Rev. D 37, 888 (1988); A.D. Linde, Zh. Eksp. Teor. Fiz. 87, 369 (1984) [Sov. Phys. JETP 60, 211 (1984)]; Ya.B. Zeldovich and A.A. Starobinsky, Pis'ma Astron. Zh. 10, 323 (1984) [Sov. Astron. Lett. 10, 135 (1984)]; V.A. Rubakov, Phys. Lett. 148 B, 280 (1984).
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