Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)


SIGMA 2 (2006), 037, 12 pages      gr-qc/0603083      http://dx.doi.org/10.3842/SIGMA.2006.037

Regular and Chaotic Regimes in Scalar Field Cosmology

Alexey V. Toporensky
Sternberg Astronomical Institute, Moscow University, Moscow, 119899 Russia

Received October 25, 2005, in final form March 10, 2006; Published online March 21, 2006

Abstract
A transient chaos in a closed FRW cosmological model with a scalar field is studied. We describe two different chaotic regimes and show that the type of chaos in this model depends on the scalar field potential. We have found also that for sufficiently steep potentials or for potentials with large cosmological constant the chaotic behavior disappears.

Key words: cosmology; scalar field; chaotic dynamics.

pdf (239 kb)   ps (188 kb)   tex (87 kb)

References

  1. Kantz H., Grassberger P., Repellers, semiattractors and long lived chaotic transients, Phys. D, 1985, V.17, 75-93.
  2. Gaspard P., Rice S.A., Scattering from a classically chaotic repellor, J. Chem. Phys., 1989, V.90, 2225-2241.
  3. Page D.N., A fractal set of perpetually bouncing Universes?, Classical Quantum Gravity, 1984, V.1, 417-441.
  4. Cornish N.J., Shellard E.P.S., Chaos in quantum cosmology, Phys. Rev. Lett., 1998, V.81, 3571-3574.
  5. Kamenshchik A.Yu., Khalatnikov I.M., Toporensky A.V., Simplest cosmological model with the scalar field. 2. Influence of cosmological constant, Internat. J. Modern Phys. D, 1998, V.7, 129-138, gr-qc/9801082.
  6. Kamenshchik A.Yu., Khalatnikov I.M., Savchenko S.V., Toporensky A.V., Topological entropy for some isotropic cosmological models, Phys. Rev. D, 1999, V.59, 123516, 28 pages, gr-qc/9809048.
  7. Toporensky A.V., Chaos in closed isotropic cosmological models with steep scalar field potentials, Internat. J. Modern Phys. D, 1999, V.8, 739-750, gr-qc/9812005.
  8. Linde A.D., Particle physics and inflationary cosmology, Harwood Academic, 1990.
  9. Belinsky V.A., Grishchuk L.P., Zeldovich Ya.B., Khalatnikov I.M., Inflationary stages in cosmological models with scalar fields, JETP, 1985, V.89, 346-360 (in Russian).
  10. Belinsky V.A., Khalatnikov I.M., On the degree of generality of inflationary solutions in cosmological models with a scalar field, Sov. Phys. JETP, 1987, V.93, 441-472.
  11. Belinsky V.A., Ishihara H., Khalatnikov I.M., Sato H., On the degree of generality of inflation in Friedman cosmological models with a massive scalar field, Progr. Theoret. Phys., 1988, V.79, 676-684.
  12. Turner M., Coherent scalar field oscillations in an expanding Universe, Phys. Rev. D, 1983, V.28, 1243-1256.
  13. Starobinsky A.A., On a nonsingular isotropic cosmological model, Sov. Astron. Lett., 1978, V.4, 82-84.
  14. Cornish N., Levin J., Chaos, fractals and inflation, Phys. Rev. D, 1996, V.53, 3022-3032, astro-ph/9510010.
  15. Kamenshchik A.Yu., Khalatnikov I.M., Toporensky A.V., Simplest cosmological model with the scalar field, Internat. J. Modern Phys. D, 1997, V.6, 673-692, gr-qc/9891064.
  16. Maartens R., Cosmological dynamics on the brane, Phys. Rev. D, 2000, V.62, 084023, 24 pages, hep-th/0004166.
  17. Damour T., Mukhanov V.F., Inflation without slow roll, Phys. Rev. Lett., 1998, V.80, 3440-3443, gr-qc/9712061.
  18. Pavluchenko S.A., Toporensky A.V., Chaos in FRW cosmology with gently sloping scalar field potential, Gravitation and Cosmology, 2000, V.6, 241-245, gr-qc/9911039.
  19. Kamenshchik A.Yu., Khalatnikov I.M., Toporensky A.V., Complex inflaton field in quantum cosmology, Internat. J. Modern Phys. D, 1997, V.6, 649-672, gr-qc/9801039.
  20. Randall L., Sundrum R., An alternative to compactification, Phys. Rev. Lett., 1999, V.83, 4690-4693, hep-th/9906064.
  21. Binetruy P., Deffayet C., Ellwanger U., Langlois D., Brane cosmological evolution in a bulk with cosmological constant, Phys. Lett. B, 2000, V.477, 285-291, hep-th/9910219.
  22. Toporensky A.V., Tretyakov P.V., Ustiansky V.O., New properties of scalar field dynamics in brane isotropic cosmological models, Astron. Lett., 2003, V.29, 1-5, gr-qc/0207091.
  23. Belinsky V.A., Khalatnikov I.M., Lifschitz E.M., Oscillators approach to a singular point in the relativistic cosmology, Adv. Phys., 1970, V.19, 525-573.
  24. Toporensky A.V., Ustiansky V.O., Dynamics of Bianchi IX universe with massive scalar field, gr-qc/9907047.
  25. Antoniadis I., Rizos J., Tamvakis K., Singularity-free cosmological solutions of the superstring effective action, Nucl. Phys. B, 1994, V.415, 497-514, hep-th/9305025.
  26. Rizos J., Tamvakis K., On the existence of singularity-free solutions in quartic gravity, Phys. Lett. B, 1994, V.326, 57-61, gr-qc/9401023.
  27. Alexeyev S.O., Toporensky A.V., Ustiansky V.O., Non-singular cosmological models in string gravity with constant dilaton and second order curvature corrections, Classical Quantum Gravity, 2000, V.17, 2243-2254, gr-qc/9912071.
  28. Singh P., Toporensky A.V., Big crunch avoidance in k=1 semiclassical loop quantum cosmology, Phys. Rev. D, 2004, V.69, 104008, 5 pages, gr-qc/0312110.
  29. Damour T., Polyakov A., String theory and gravity, Gen. Relativity Gravitation, 1994, V.26, 1171-1176, gr-qc/9411069.
  30. Bento M., Bertolami O., Cosmological solutions of higher-curvature string effective theories with dilaton, Phys. Lett. B, 1996, V.368, 198-201, gr-qc/9503057.
  31. Bojowald M., The semiclassical limit of loop quantum cosmology, Classical Quantum Gravity, 2001, V.18, L109-L116, gr-qc/0105113.
  32. Bojowald M., Isotropic loop quantum cosmology, Classical Quantum Gravity, 2002, V.19, 2717-2742, gr-qc/0202077.

Previous article   Next article   Contents of Volume 2 (2006)