Skip to main content
SpringerLink
Log in

Measurement of the space–time interval in modified gravity theories in Palatini formalism

  • Research Article
  • Published:
General Relativity and Gravitation Aims and scope Submit manuscript

Abstract

There are strong motivations that lead cosmologists to consider alternatives to Einstein’s theory of gravity in Palatini formalism. In addition, there are two distinguishable local frames in this formalism in which one of them is local inertial frame and the equivalence principle is satisfied. Different features of speed of light such as the causal structure constant, electromagnetic and gravitational wave velocities and Einstein velocity will not coincide in this local inertial frame for extended gravity theories in Palatini formalism. On the other hand, both the measurement of time and exchange of a signal between the distant points are required to determine spatial distances. In a particular situation where these aspects of the speed of light do not coincide, the distance determination will become more demanding because light will follow a time-like geodesic of the metric. In modified gravity theories in Palatini approach, theories involve a varying speed of photon. Therefore these kinds of theories must be based on some other technique of measuring spatial distances than radar or some terms should be corrected in the line element in the proposed model. We found out we should consider a coefficient which is proportional to energy density in each era, in the line element in order to be able to use radar for measuring distance in modified gravity theories in Palatini formalism. Analysis of some observational data will be affected by considering this coefficient in the line element.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1

Similar content being viewed by others

References

  1. Webb, J., et al.: Phys. Rev. Lett. 82, 884 (1999)

    Article  ADS  Google Scholar 

  2. Webb, J., et al.: Phys. Rev. Lett. 87, 091301 (2001)

    Article  ADS  Google Scholar 

  3. Weinberg, S.: Phil. Trans. R. Soc. Lond. A 310, 249 (1983)

    Article  ADS  Google Scholar 

  4. Ellis, G.F.R., Uzan, J.P.: Am. J. Phys. 73(3), 240 (2005)

    Article  ADS  Google Scholar 

  5. Puetzfeld, D.: In: 22nd Texas symposium on relativistic astrophysics at Stanford University Dec. 13–17 (2004)

  6. Olmo, G.J.: Int. J. Mod. Phys. D 20, 413–462 (2011)

    Google Scholar 

  7. Izadi, A., Shojai, A.: Class. Quantum Grav. 26, 195006 (2009)

    Article  MathSciNet  ADS  Google Scholar 

  8. Ellis, G.F.R., Williams, R.M.: Flat and Curved Space Times. Oxford University Press, Oxford (2000)

    Google Scholar 

  9. Marzke, R.F., Wheeler, J.A.: In: Chiu, H.-Y., Hoffman, W.F. (eds.) Gravitation and Relativity. Benjamin, New York (1964)

    Google Scholar 

  10. Copeland, E.J., Sami, M., Tsujikawa, S.: Int. J. Mod. Phys. D 15, 1753 (2006)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  11. Ferraris, M., Francaviglia, M., Volovich, I.: Class. Quantum Grav. 11, 1505–1517 (1994)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  12. Borowiec, A., Ferraris, M., Francaviglia, M., Volovich, I.: Class. Quantum Grav. 15, 43–55 (1998) gr-qc/9611067

    Google Scholar 

  13. Borowiec, A.: GROUP 24: physical and mathematical aspects of symmetries. In: Gazeau, J.-P., Kerner, R., Antoine, J.-P., M etens, S., Thibon, J.-Y. (eds.) Proceedings of the 24th International Colloquium on Group Theoretical Methods in Physics, Paris, 15–20 July 2002. Institute of Physics Conference Series CS vol. 173, pp. 241–244. e-Print version: Nonlinear Lagrangians of the Ricci Type (e-Print Archive: gr-qc/9906043) (2003)

  14. Allemandi, G., Borowiec, A., Francaviglia, M.: Phys. Rev. D 70, 103503 (2004)

    Google Scholar 

  15. Sotiriou, T.P., Faraoni, V.: Rev. Mod. Phys. 82, 451–497 (2010)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  16. Li, B., Mota, D.F., Shaw, D.J.: Phys. Rev. D 78, 064018 (2008)

    Article  MathSciNet  ADS  Google Scholar 

  17. Olmo, G.J., Sanchis-Alepuz, H., Tripathi, S.: [arXiv:1002.3920 [gr-qc]]

  18. Olmo, G.J., Sanchis-Alepuz, H., Tripathi, S.: Phys. Rev. D 80, 024013 (2009)

    Google Scholar 

  19. Li, B., Barrow, J.D., Mota, D.F.: Phys. Rev. D 76, 104047 (2007)

    Google Scholar 

  20. Ehlers, J.: Akad. Wiss. Lit. Mainz, Abhandl. Math.-Nat. Kl. 11, 793837 (1961). Translation: Ehlers, J.: Gen. Relativ. Gravit. 25, 12251266 (1993)

  21. Ellis, G.F.R.: General relativity and cosmology. In: Sachs, R.K. (ed.) Proceedings of the XLVII Enrico Fermi Summer School, pp. 104182. Academic Press, New York (1971)

  22. Ellis, G.F.R.: In: Schatzman, E. (ed.) Carg‘ese Lectures in Physics, vol. 6, pp. 160–161. Gordon and Breach, New York (1973)

Download references

Author information

Authors and Affiliations

  1. Department of Physics, K. N. Toosi University of Technology, Tehran, Iran

    Azam Izadi

  2. Department of Physics, University of Tehran, Tehran, Iran

    Ali Shojai

Authors
  1. Azam Izadi
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Ali Shojai
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Azam Izadi.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Izadi, A., Shojai, A. Measurement of the space–time interval in modified gravity theories in Palatini formalism. Gen Relativ Gravit 45, 229–241 (2013). https://doi.org/10.1007/s10714-012-1467-8

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10714-012-1467-8

Keywords

Search

Navigation