Gravitational waves in singular and bouncing FLRW universes

V. Antunes, E. Goulart and M. Novello1


We investigate propagation of gravitational waves in two models belonging to the Friedman-Lemaître-Robertson-Walker (FLRW) class of cosmologies: the singular Einstein-Maxwell Universe (EMU), which has an electromagnetic field described by Maxwell's electrodynamics as the source of its geometry, and the bouncing Nonlinear Electrodynamics Universe (NLEU), which has the electromagnetic field described by a nonlinear generalization of Maxwell's electrodynamics as the source of its geometry. We work with an explicitly gauge-independent formulation of cosmological perturbations in FLRW models and analyze the qualitative features of the dynamical system that describes the propagation of primordial tensorial perturbations in both geometries. Based on this analysis, we show that gravitational waves generated near a singularity or a bounce exhibit qualitatively different behavior.


  1. E. W. Kolb and M. S. Turner, The Early Universe (Addison-Wesley, Redwood City, CA, 1988).
  2. M. Novello and S. E. Perez Bergliaffa, Phys. Rep. 463, 127 (2008).
  3. W. de Sitter, Proc. Kon. Ned. Akad. Wet. 19, 1217 (1917).
  4. M. Novello and J. M. Salim, Phys. Rev. D 20, 377 (1979).
  5. V. Mukhanov and R. Brandenberger, Phys. Rev. Lett. 68, 1969 (1992).
  6. M. Novello, A. R. Oliveira, J. M. Salim and E. Elbaz, Int. J. Mod. Phys. D 1, 641 (1993).
  7. G. L. Murphy, Phys. Rev. D 8, 4231 (1973).
  8. J. M. Salim and H. P. Oliveira, Acta Phys. Pol. B 8, 649 (1988).
  9. J. Acacio de Barros, N. Pinto-Neto and M. A. Sagioro-Leal, Phys. Rev. Lett. A 241, 229 (1998).
  10. G. Veneziano, hep-th/0002094.
  11. V. A. De Lorenci, R. Klippert, M. Novello and J. M. Salim, Phys. Rev. D 65, 063501 (2002).
  12. T. Tajima, S. Cable, K. Shibata and R. M. Kulsrud, Astrophys. J. 390, 309 (1992).
  13. A. Campos and B. L. Hu, Phys. Rev. D 58, 125021 (1998).
  14. G. G. Dune, Int. J. Mod. Phys. A 12, 1143 (1997).
  15. M. Joyce and M. Shaposhnikov, Phys. Rev. Lett. 79, 1193 (1997).
  16. A. Raychaudhuri, Phys. Rev. 98, 1123 (1955).
  17. S. W. Hawking and G. F. R. Ellis, The Large Scale Structure of Space-time (Cambridge University Press, Cambridge, 1973).
  18. P. Jordan, J. Ehlers and W. Kundt, Akad. Swiss. Mainz. Abh. Math-Nat. Kl. Jagh. 2 (1960).
  19. A. Lichnerowicz, Ann. Math. Pura Appl. 50, 1 (1960).
  20. G. F. R. Ellis, in Proceedings of the International School of Physics "Enrico Fermi" (Academic, London, 1971), p. 104.
  21. M. Novello and J. M. Salim, Fund. Cosm. Phys. 8, 201 (1983).
  22. S. W. Hawking, Astrophys. J. 145, 544 (1966).
  23. J. M. Stewart and M. Walker, Proc. R. Soc. A 341, 49 (1974).
  24. E. M. Lifshitz and I. N. Khalatnikov, Adv. Phys. 12, 185 (1963).
  25. M. Novello, J. M. Salim, M. C. Mota da Silva, S. E. Joras and R. Klippert, Phys. Rev. D 52, 730 (1995).
  26. R. C. Tolman and P. Ehrenfest, Phys. Rev. D 36, 1791 (1930).
  27. M. Hindmarsh and A. Everett, Phys. Rev. D 58, 103505 (1998).
  28. H. P. Robertson, Rev. Mod. Phys. 5, 62 (1933).
  29. R. Coquereaux and A. Grossmann, Ann. Phys. 143, 296 (1982).
  30. L. P. Grishchuk, arXiv: 0707.3319v2 [gr-qc].
For more information about this paper please visit Springer's Home Page of this paper.

Back to The Contents Page