General Relativity and Gravitation

, Volume 39, Issue 12, pp 2061–2071 | Cite as

Solutions of higher dimensional Gauss–Bonnet FRW cosmology

  • Keith Andrew
  • Brett BolenEmail author
  • Chad A. Middleton
Research Article


We examine the effect on cosmological evolution of adding a Gauss–Bonnet term to the standard Einstein–Hilbert action for a (1 + 3) + d dimensional Friedman–Robertson–Walker (FRW) metric. By assuming that the additional dimensions compactify as a power law as the usual 3 spatial dimensions expand, we solve the resulting dynamical equations and find that the solution may be of either de Sitter or Kasner form depending upon whether the Gauss–Bonnet term or the Einstein term dominates.


Gauss–Bonnet Compactified extra dimensions Friedman–Robertson–Walker 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Applequist, T., Chodos, A., Frend, P.G.O.: Modern Kaluza–Klein theories, Addison Wesley, 1987, P. S. Wesson, Five-dimensional Physics: classical and quantum consequences of Kaluza–klein cosmology, World Scientific (2006)Google Scholar
  2. 2.
    Cardoso, V., Berti, E., Cavaglia, M.: What we (don’t) know about black hole formation in high-energy collisions Class. Quant. Grav. 22, L61 (2005)(ArXiv: hep-ph/0505125)Google Scholar
  3. 3.
    Paul B.C., Mukherjee S. (1990). Higher-dimensional cosmology with Gauss–Bonnet terms and the cosmolgical-constant problem. Phys. Rev. D 42: 2595 CrossRefADSGoogle Scholar
  4. 4.
    Mohammedi N. (2002). Dynamical compactification, standard cosmology and the accelerating universe. Phys. Rev. D 65: 104018 CrossRefADSMathSciNetGoogle Scholar
  5. 5.
    Boulware D., Deser S. (1985). String-generated gravity models. Phys. Rev. Lett. 55: 24 Google Scholar
  6. 6.
    Demaret J., Rop Y., Tombal P., Moussiaux A. (1992). Qualitative analysis of ten-dimensional lovelock cosmological models. GRG 24: 1169 Google Scholar
  7. 7.
    Dias, Goncalo A.S., Gao, S., Lemos, Jose P.S.: Static and collapsing spherically symmetric charged thin shells in Lovelock gravity coupled to Maxwell electromagnetism: Hamiltonian treatment and physical implications (2006)Google Scholar
  8. 8.
    Demianski M., Golda Z., Puszkarz W. (1991). Dynamics of the D-dimensional FRW-comsological model within the supersting-generated gravity model. Gen. Rel. Grav. 23: 917 CrossRefADSMathSciNetGoogle Scholar
  9. 9.
    Nojiri S., Odintsov S. (2003). Modified gravity with negative and positive powers of the curvature: unification of the inflation and of the cosmic acceleration. Phys. Rev. D 68: 123512 CrossRefADSMathSciNetGoogle Scholar
  10. 10.
    Mukohyama S., Randall L. (2003). A dynamical approach to the cosmological constant. Phys. Rev. Lett. 92: 211302 CrossRefADSGoogle Scholar
  11. 11.
    Narain K.S., Sarmadi M., Witten E. (1986). A note on toroidal compactification Of heterotic string theory. Nucl. Phys. B 268: 253 CrossRefGoogle Scholar
  12. 12.
    Neupane, I.P., Carter, B.M.N.: Towards inlfation and dark energy cosmologies from modified Gauss–Bonnet theory, JCAP 0606 (2006) 004Google Scholar

Copyright information

© Springer Science+Business Media, LLC 2007

Authors and Affiliations

  1. 1.Department of Physics and AstronomyWestern Kentucky UniversityBowling GreenUSA
  2. 2.Department of Physical and Environmental SciencesMesa State CollegeGrand JunctionUSA

Personalised recommendations