On an f(R) theory of gravity based on non-conformal invariance of gravitational waves

S.N. Pandey1

Abstract

Gravitational waves are an inevitable consequence of Einstein's theory of gravitation, which are meaningfully comparable with electromagnetic waves except for their non-conformal invariance. So, Einstein's field equations aremodified by a straightforward generalization of the Lagrangian in the Einstein-Hilbert action by choosing a polynomial in the scalar R of a finite number of terms. In this modified theory of gravity, conformally invariant gravitational waves are obtained. Besides this, cosmological aspects and the gravitational field surrounding a spherically symmetric mass distribution are studied to understand the features of this theory. It reveals that the deviations are not so significant at the observational level, and the features are more or less similar to those of Einstein's theory.

References

  1. H. Weyl, Ann Phys. 59, 101 (1919).
  2. A. S. Eddington, The Mathematical Theory of Relativity (Cambridge University Press, 1923).
  3. R. Utiyama and B. S. DeWitt, J. Math. Phys. 3, 608 (1962).
  4. A. A. Grib, S. G. Mamayev, and V. M. Mostepanenko, Quantum Effects in Strong External Fields (Moscow, 1980) [in Russian].
  5. G. A. Vilkovisky, Class. Quantum Grav. 9, 895 (1992).
  6. S.W. Hawking and G. F. R. Ellis, Large Scale Structure of Space-Time (Oxford University Press, 1975).
  7. T. Fulton, F. Rohrlich, and L. Witten, Rev. Mod. Phys. 34, 442 (1962).
  8. I. Parker, Phys. Rev. 183, 1057 (1969).
  9. Ya. B. Z'eldovich and I. D. Novikov, Structure and Evolution of the Universe (Nauka, Moscow, 1975).
  10. L. P. Grishchuk, Sov. Phys. Usp. 20, 319 (1977).
  11. S. N. Pandey, Int. J. Theor. Phys. 22, 209 (1983).
  12. B. N. Breizman, V. Ts. Gurovich, and V. P. Sokolov, Sov. Phys. JETP 32, 155 (1971).
  13. S. N. Pandey, Int. Centre of Theor. Phys., Trieste, Report No. IC/78/141 (1978).
  14. S. N. Pandey, Nuovo Cim. 44, 327 (2001).
  15. A. A. Sokolov, Problem of Theoretical Physics (Moscow State University, Moscow, 1976) [in Russian].
  16. L. Landau and E. M. Lifshitz, The Classical Theory of Fields (Pergamon Press, Oxford, 1962).
  17. S. N. Pandey, Nuovo Cim. 125B, 775 (2010).
  18. S. N. Pandey, J. Proc. R. Soc. NSW 141, 35 (2009).
  19. S. N. Pandey, Int. J. Theor. Phys. 27, 695 (1988).
  20. A. A. Grib and S. N. Pandey, Proc. Einstein Foundation International, Nagpur, India, 1983.
  21. T. P. Sotiriou and V. Faraoni, arXiv: 0805.1726.
For more information about this paper please visit Springer's Home Page of this paper.



Back to The Contents Page