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Is there chaos in low-energy string cosmology?

John D. Barrow*

Mariusz P. Da̧browski†

  • Astronomy Centre, University of Sussex, Falmer, Brighton BN1 9QJ, United Kingdom

  • Astronomy Centre, University of Sussex, Falmer, Brighton BN1 9QJ, United Kingdom,
  • Institute of Physics, University of Szczecin, Wielkopolska 15, 70-451 Szczecin, Poland

  • *Email address: J.D.Barrow@sussex.ac.uk
  • †Email address: mpd@star.cpes.susx.ac.uk
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Phys. Rev. D 57, 7204 – Published 15 June, 1998

DOI: https://doi.org/10.1103/PhysRevD.57.7204

Abstract

Bianchi type IX, “mixmaster” universes are investigated in low-energy-effective-action string cosmology. We show that, unlike in general relativity, there is no chaos in these string cosmologies for the case of the tree-level action. The characteristic mixmaster evolution through a series of Kasner epochs is studied in detail. In the Einstein frame an infinite sequence of chaotic oscillations of the scale factors on approach to the initial singularity is impossible, as it was in general relativistic mixmaster universes in the presence of a massless scalar field. A finite sequence of oscillations of the scale factors described by approximate Kasner metrics is possible, but it always ceases when all expansion rates become positive. In the string frame the evolution through Kasner epochs changes to a new form which reflects the duality symmetry of the theory. Again, we show that chaotic oscillations must end after a finite time. The need for duality symmetry appears to be incompatible with the presence of chaotic behavior as t→0. We also obtain our results using the Hamiltonian qualitative cosmological picture for mixmaster models. We also prove that a time-independent pseudoscalar axion field h is not admitted by the Bianchi type IX geometry.

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References (28)

  1. E. S. Fradkin and A. A. Tseytlin, Nucl. Phys. B261, 1 (1985); ibid.C. G. Callan, D. Friedan, E. J. Martinec, and M. J. Perry, B262, 593 (1985).
  2. M. Mueller, Nucl. Phys. B37, 37 (1990); G. Veneziano, Phys. Lett. B 265, 287 (1991); M. Gasperini and G. Veneziano, Mod. Phys. Lett. A 39, 3701 (1993); Astrophys. 1, 317 (1993); E. J. Copeland, A. Lahiri, and D. Wands, Phys. Rev. D 50, 4868 (1994); M. Gasperini and R. Ricci, Class. Quantum Grav. 12, 677 (1995); A. Saaryan, Astrophys. 38, 164 (1995); M. Gasperini and G. Veneziano, Phys. Rev. D 50, 2519 (1994).
  3. E. J. Copeland, A. Lahiri, and D. Wands, Phys. Rev. D 51, 1569 (1995).
  4. J. D. Barrow and K. E. Kunze, Phys. Rev. D 55, 623 (1997); ibid.J. D. Barrow and M. P. Da̧browski, 55, 630 (1997).
  5. N. A. Batakis and A. Kehagias, Nucl. Phys. B449, 248 (1995); J. P. Mimóso and D. Wands, Phys. Rev. D 52, 5612 (1995).
  6. V. A. Belinskii, E. M. Lifshitz, and I. M. Khalatnikov, Sov. Phys. Usp. 102, 745 (1971); L. D. Landau and E. M. Lifshitz, The Classical Theory of Fields (Pergamon, Oxford, 1975); J. D. Barrow, Phys. Rev. Lett. 46, 963 (1981); Phys. Rep. 85, 1 (1982); D. Chernoff and J. D. Barrow, Phys. Rev. Lett. 50, 134 (1983); J. D. Barrow, in Classical General Relativity, edited by W. Bonnor, J. Islam, and M.A.H. MacCallum (Cambridge University Press, Cambridge, England, 1984), p. 25.
  7. V. A. Belinskii and I. M. Khalatnikov, Sov. Phys. JETP 36, 591 (1973).
  8. G. Veneziano, Phys. Lett. B 406, 297 (1997); A. Buonanno, K. A. Meissner, C. Ungarelli, and G. Veneziano, Phys. Rev. D 57, 2543 (1998); ibid.A. Feinstein, R. Lazkoz, and M. A. Vázquez-Mozo, 56, 5166 (1997).
  9. J. D. Barrow and K. E. Kunze, Phys. Rev. D 56, 741 (1997).
  10. B. A. Campbell, A. Linde, and K. A. Olive, Nucl. Phys. B355, 146 (1991); Eq. (7).
  11. D. R. Brill, Phys. Rev. 133, B845 (1964).
  12. J. D. Barrow, Nature (London) 272, 211 (1978).
  13. J. D. Barrow, Nucl. Phys. B296, 697 (1988).
  14. R. Easther, K. Maeda, and D. Wands, Phys. Rev. D 53, 4247 (1996).
  15. M. Gasperini and G. Veneziano, Gen. Relativ. Gravit. 28, 1301 (1996).
  16. J. Wainwright and L. Hsu, Class. Quantum Grav. 6, 1409 (1989); J. Wainwright, in Dynamical Systems in Cosmology, edited by J. Wainwright and G. Ellis (Cambridge University Press, Cambridge, England, 1997), p. 132.
  17. M. P. Ryan and L. C. Shepley, Homogeneous Relativistic Cosmologies (Princeton University Press, Princeton, NJ, 1975).
  18. J. S. R. Chisholm and J. McEwan, Proc. R. Soc. London A336, 421 (1974); G. A. Baker, Essentials of Padé Approximants (Academic, New York, 1975).
  19. P. Halpern, Phys. Rev. D 33, 354 (1986).
  20. J. D. Barrow and J. Stein-Schabes, Phys. Rev. D 32, 1595 (1985).
  21. H. Ishihara, Prog. Theor. Phys. 74, 354 (1986).
  22. T. Furosawa and A. Hosoya, Prog. Theor. Phys. 73, 467 (1985).
  23. K. A. Meissner and G. Veneziano, Phys. Lett. B 267, 33 (1991); Mod. Phys. Lett. A 6, 3397 (1991); K. A. Meissner, Phys. Lett. B 392, 298 (1997).
  24. M. Gasperini, R. Ricci, and G. Veneziano, Phys. Lett. B 319, 438 (1993).
  25. J. E. Lidsey, “On the Cosmology and Symmetry of Dilaton-Axion Gravity,” e-Print gr-qc/9609063.
  26. E. J. Copeland, R. Easther, and D. Wands, Phys. Rev. D 56, 874 (1997).
  27. A. R. Liddle, R. G. Moorhouse, and A. B. Henriques, Nucl. Phys. B311, 719 (1988).
  28. D. V. Gal’tsov and M. S. Volkov, Phys. Lett. B 256, 17 (1991); I. Ya. Aref’eva, P. B. Medvedev, O. A. Rytchkov, and I. V. Volovich, “Chaos in M(atrix) Theory,” e-Print: hep-th/9710032; J. D. Barrow and J. Levin, Phys. Rev. Lett. 80, 656 (1998).

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Phys. Rev. D 57, 7204– Published 15 June, 1998
  • Received 10 November 1997

© 1998 American Physical Society

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