Cosmological stability of Weyl conformal tensor

E. Goulart and M. Novello1

Abstract

We show that the conformal structure of the Friedmann-Robertson-Walker geometry is asymptotically stable with respect to time under arbitrary scalar perturbations. The analysis was undertaken for the Euclidean section, using the gauge-independent quasi-Maxwellian equations of motion for the perturbations. A well-known divergence theorem of non-autonomous planar dynamical systems is used to corroborate our conclusions. In other words, from a global point of view, once the geometry arrives at a FRW stage, it is not likely to leave it, even if during a certain limited interval of time it may present inhomogeneous properties.

References

  1. P. Jordan, J. Ehlers, and R. Sachs, Akad. Wiss. Lit. Mainz Abh. Math. Naturwiss. Kl. 1, 3 (1961).
  2. S. W. Hawking, Astrohys. J. 145, 544 (1966).
  3. G. F. R. Ellis, in: General Relativity and Cosmology, Proceedings of the International School of Physics "Enrico Fermi", Course XLVII (Academic, London, 1971).
  4. M. Novello, J. M. Salim, M. C. Motta da Silva, S. E. Joras, and R. Klippert, Phys. Rev. D 51 450 (1995) and references therein.
  5. E. M. Lifshitz and I. M. Khalatnikov, Adv. Phys. 12, 185 (1963).
  6. J. Bardeen, Phys. Rev. D 22 1882 (1980).
  7. S. W. Goode, Phys. Rev. D 39 10 (1989).
  8. M. Novello, J. M. Salim, M. C. Motta da Silva, S. E. Joras, and R. Klippert, Phys. Rev. D 52 730 (1995).
  9. M. Novello, J. M. Salim, M. C. Motta da Silva, and R. Klippert, Phys. Rev. D 54 2578 (1996).
  10. J. M. Stewart and M. Walker, Proc. R. Soc. London A 341, 49 (1974), and also J. M. Stewart, Class. Quant. Grav. 7 1169 (1990).
  11. V. I. Arnold, Mathematical Methods of Classical Mechanics, (Spriger-Verlag, 2nd ed., 1989); R. C. Hilborn, Chaos and Non-Linear Dynamics, (Oxford Univ. Press, Oxford, 2000).
  12. A. Erdelyi, Higher Transcendetal functions, v. I. (Caltech Bateman Manuscript Project, 1953).
  13. G. B. Arfken and H. J. Weber, Mathematical Methods for Physicists (Academic Press, 4th edition, 1995).
For more information about this paper please visit Springer's Home Page of this paper.



Back to The Contents Page