Cosmologies from nonlinear multidimensional gravity with acceleration and slowly varying G

K.A. Bronnikov1, S.A. Kononogov2, V.N. Melnikov3 and S.G. Rubin4


We consider multidimensional gravity with a Lagrangian containing the Ricci tensor squared and the Kretschmann invariant. In a Kaluza-Klein approach with a single compact extra space of arbitrary dimension, with the aid of a slow-change approximation (as compared with the Planck scale), we build a class of spatially flat cosmological models in which both the observed scale factor a(t) and the extra-dimensional one, b(t), grow exponentially at large times, but b(t) grows slowly enough to admit variations of the effective gravitational constant G within observational limits. Such models predict a drastic change in the physical laws of our Universe in the remote future due to further growth of the extra dimensions.


  1. V.N. Melnikov, Multidimensional Classical and Quantum Cosmology and Gravitation. Exact Solutions and Variations of Constants, CBPF-NF-051/93, Rio de Janeiro, 1993; in: Cosmology and Gravitation, ed. M. Novello (Editions Frontieres, Singapore, 1994), p. 147; Multidimensional Cosmology and Gravitation, CBPF-MO-002/95, Rio de Janeiro, 1995, 210 p.; in: Cosmology and Gravitation. II, ed. M. Novello (Editions Frontieres, Singapore, 1996), p. 465; Exact Solutions in Multidimensional Gravity and Cosmology III, CBPF-MO-03/02, Rio de Janeiro, 2002, 297 pp.
  2. V.N. Melnikov, Gravity as a key problem of the millennium. Proc. 2000 NASA/JPL Conference on Fundamental Physics in Microgravity, NASA Document D-21522, 2001, p. 4.1-4.17, Solvang, CA, USA.
  3. V.N. Melnikov, Gravity and cosmology as key problems of the millennium. In: Proc. Albert Einstein Century Int. Conf., eds. J.-M. Alimi and A. Fuzfa (AIP Conf. Proc., Melville-NY, 2006), v. 861, p. 109-126.
  4. V.N. Melnikov, Grav. Cosmol. 13, 81 (2007).
  5. S.A. Kononogov and V.N. Melnikov, Izmeritel'naya Tekhnika 6, 1 (2005).
  6. K.A. Bronnikov and S.A. Kononogov, Metrologia 43, R1 (2006).
  7. K.A. Bronnikov, S.A. Kononogov and V.N. Melnikov, Gen. Rel. Grav. 38 1215 (2006).
  8. K.A. Bronnikov and S.G. Rubin, Phys. Rev. D 73 124019 (2006).
  9. K.A. Bronnikov, R.V. Konoplich and S.G. Rubin, Class. Quant. Grav. 24 1261 (2007).
  10. K.A. Bronnikov and S.G. Rubin, Grav. & Cosmol. 13 191 (2007).
  11. S. Nojiri and s.D. Odintsov, hep-th/0601213; arXiv: 0801.4843[astro-ph].
  12. B.A. Dubrovin, A.T. Fomenko and S.P. Novikov, Modern Geometry - Methods and Applications (Springer-Verlag, New York, 1992); D. Muller, H.V. Fagundes and R. Opher, Phys. Rev. D 66 083507 (2002) and references therein.
  13. J.F. Donoghue, Phys. Rev. D 50 3874 (1994).
  14. U. Gunther, P. Moniz and A. Zhuk, Astrophys. Space Sci. 283, 679-684 (2003); gr-qc/0209045; U. Gunther and A. Zhuk, Remarks on dimensional reduction in multidimensional cosmological models, gr-qc/0401003.
  15. K.A. Bronnikov and V.N. Melnikov, Gen. Rel. Grav. 33 1549 (2001).
  16. K.A. Bronnikov and V.N. Melnikov, "Conformal frames and D-dimensional gravity", gr-qc/0310112, in: Proc. 18th Course of the School on Cosmology and Gravitation: The Gravitational Constant. Generalized Gravitational Theories and Experiments (30 April-10 May 2003, Erice), Ed. G.T. Gillies, V.N. Melnikov and V. de Sabbata, (Kluwer, Dordrecht/Boston/London, 2004) pp. 39-64.
  17. J. Muller and L. Biskupek, Class. Quant. Grav. 24 4533 (2007).
For more information about this paper please visit Springer's Home Page of this paper.

Back to The Contents Page