General Relativity and Gravitation

, Volume 26, Issue 12, pp 1197–1211 | Cite as

Inflationary cosmology with aR+λT µν R µν /R Lagrangian

  • E. Brüning
  • D. H. Coule
  • C. Xu
Article

Abstract

We consider an alternative fourth-order gravity Lagrangian which is nonanalytic in the Ricci scalar, and apply it to a Robertson-Walker metric. We find vacuum solutions which undergo power-law inflation. Once matter is introduced the theory behaves very much like ordinary General Relativity, except that the radiation evolution α ∼ √t is not allowed since it corresponds toR=0. We comment on the possibility of wormhole solutions in such a theory.

Keywords

Radiation General Relativity Differential Geometry Ricci Scalar Vacuum Solution 

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References

  1. 1.
    Starobinsky, A. A. (1980).Phys. Lett. B 91, 99; see also Hosotani, Y., Nikolic, M., and Rudaz, S. (1986).Phys. Rev. D34, 627.Google Scholar
  2. 2.
    Starobinsky, A. A. (1984).Sov. Astron. Lett. 10, 135.Google Scholar
  3. 3.
    Kofman, L. A., Linde, A. D., and Starobinsky, A. A. (1985).Phys. Lett. B 157, 361.Google Scholar
  4. 4.
    Mijić, M. B., Morris, M. S., and Suen, W.-M. (1986).Phys. Rev. D 34, 2934.Google Scholar
  5. 5.
    Anderson, A., and Suen, W.-M. (1987).Phys. Rev. D 35, 2940.Google Scholar
  6. 6.
    Madsen, M. S. (1990).Class. Quant. Grav. 7, 87; Xu, C., and Ellis, G. F. R. (1991).Class. Quant. Grav.8, 1747.Google Scholar
  7. 7.
    Barrow, J. D., and Cotsakis, S. (1988).Phys. Lett. B214, 515.Google Scholar
  8. 8.
    Berkin, A. L., and Maeda, K. (1990).Phys. Lett. B245, 348.Google Scholar
  9. 9.
    Liddle, A. R., and Mellor, F. (1992).Gen. Rel. Grav. 24, 897.Google Scholar
  10. 10.
    Coley, A. A., and Tavakol, R. K. (1992).Gen. Rel. Grav. 24, 835.Google Scholar
  11. 11.
    Suen, W.-M. (1989).Phys. Rev. Lett. 62, 2217; (1989).Phys. Rev. D40, 315.Google Scholar
  12. 12.
    Simon, J. Z. (1992).Phys. Rev. D45, 1953.Google Scholar
  13. 13.
    Barrow, J. D., and Ottewill, A. C. (1983).J. Phys. A16, 2757. Madsen, M. S., and Barrow, J. D. (1989).Nucl. Phys. B 323, 242.Google Scholar
  14. 14.
    Madsen, M. S., and Low, R. J. (1990).Phys. Lett. B241, 207.Google Scholar
  15. 15.
    Coule, D. H., and Madsen, M. S. (1989).Phys. Lett. B226, 31.Google Scholar
  16. 16.
    Berkin, A. L. (1991).Phys. Rev. D 44, 1020.Google Scholar
  17. 17.
    Tomita, K., Azuma, T., and Nariai, H. (1978).Prop. Theor. Phys. 60, 403.Google Scholar
  18. 18.
    Schmidt, H. J. (1988).Class. Quant. Grav. 5, 233.Google Scholar
  19. 19.
    Khlopov, M. Y., Malomed, B. A., and Zel'dovich, Y. B. (1985).Mon. Not. R. Astr. Soc. 215, 575.Google Scholar
  20. 20.
    Wald, R. (1983).Phys. Rev. D 28, 2118.Google Scholar
  21. 21.
    Xu, C., and Ellis, G. F. R. (1992).Found. Phys. Lett. 5, 365.Google Scholar
  22. 22.
    Brans, C., and Dicke, C. H. (1961).Phys. Rev. 24, 925.Google Scholar
  23. 23.
    Zee, A. (1979).Phys. Rev. Lett. 42, 417.Google Scholar
  24. 24.
    Weinberg, S. (1972).Gravitation and Cosmology (Wiley, New York).Google Scholar
  25. 25.
    Birrell, N. D., and Davies, P. C. W. (1982).Quantum Fields in Curved Space (Cambridge University Press, Cambridge).Google Scholar
  26. 26.
    Mazur, P., and Mottola, E. (1986).Nucl. Phys. B 278, 694 and references therein.Google Scholar
  27. 27.
    Barrow, J. D. (1988).Nucl. Phys. B 296, 697.Google Scholar
  28. 28.
    Halliwell, J. J., and Laflamme, R. (1989).Class. Quant. Grav. 6, 1839.Google Scholar
  29. 29.
    Verbin, Y., and Davidson, A. (1990).Nucl. Phys. B 339, 545.Google Scholar
  30. 30.
    Fukutaka, H., Ghoroku, K., and Tanaka, K. (1989).Phys. Lett. B222, 191.Google Scholar
  31. 31.
    Coule, D. H. (1993).Class. Quant. Grav. 10, L25.Google Scholar
  32. 32.
    Hirsch, M. W., and Smale, S. (1974).Differential Equations, Dynamical systems and Linear Algebra (Academic Press, New York); Grimshaw, R. (1990)Nonlinear Ordinary Differential Equations (Blackwell Scientific, Oxford).Google Scholar

Copyright information

© Plenum Publishing Corporation 1994

Authors and Affiliations

  • E. Brüning
    • 1
  • D. H. Coule
    • 1
  • C. Xu
    • 1
  1. 1.Department of Applied MathematicsUniversity of Cape TownRondeboschSouth Africa

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