Skip to main content
Log in

Effective couplings and the prospect of solving fundamental problems of cosmology in a quantum theory of gravity

  • Published:
Theoretical and Mathematical Physics Aims and scope Submit manuscript

Abstract

We consider the possibility of the spontaneous appearance of an effective coupling in the quantum gravity framework. We discuss a variant of the behavior of the running coupling constant of gravity caused by an effective intergraviton coupling, which entails a qualitative description of the hypotheses on the existence of dark matter and dark energy.

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

Access this article

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

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. T. P. Sotiriou and V. Faraoni, “f(R) theories of gravity,” Rev. Modern Phys., 82, 451–497 (2010).

    Article  ADS  MathSciNet  MATH  Google Scholar 

  2. N. N. Bogolyubov, “The compensation principle and the self-consistent field method,” Sov. Phys. Usp., 2, 236–254 (1959).

    Article  ADS  MathSciNet  Google Scholar 

  3. N. N. Bogoliubov, “On some problems of the theory of superconductivity,” Phys., 26 suppl. 1, S1–S16 (1960).

    ADS  Google Scholar 

  4. B. A. Arbuzov, “Spontaneous generation of effective interaction in a renormalizable quantum field theory model,” Theor. Math. Phys., 140, 1205–1221 (2004).

    Article  MATH  Google Scholar 

  5. B. A. Arbuzov, M. K. Volkov, and I. V. Zaitsev, “NJL interaction derived from QCD,” Internat. J. Modern Phys. A, 21, 5721–5742 (2006).

    Article  ADS  MATH  Google Scholar 

  6. B. A. Arbuzov, “Bogoliubov compensation principle in the electro-weak interaction: Value of the gauge constant, muon g−2 anomaly, predictions for Tevatron and LHC,” Eur. Phys. J. C, 61, 51–59 (2009).

    Article  ADS  Google Scholar 

  7. B. A. Arbuzov and I. V. Zaitsev, “Nonperturbative solutions in the electroweak theory with ¯tt condensate and the t-quark mass,” Internat. J. Modern Phys. A, 26, 4945–4958 (2011).

    Article  ADS  MATH  Google Scholar 

  8. B. A. Arbuzov, “Nonperturbative solutions in the electroweak theory,” Theor. Math. Phys., 171, 448–457 (2012).

    Article  MathSciNet  MATH  Google Scholar 

  9. B. A. Arbuzov and I. V. Zaitsev, “LHC would-be γγ excess as a nonperturbative effect of the electroweak interaction,” Phys. Rev. D, 85, 093001 (2012).

    Article  ADS  Google Scholar 

  10. B. A. Arbuzov and I. V. Zaitsev, “On a possibility to eliminate the Landau pole in QCD,” Internat. J. Modern Phys. A, 28, 1350127 (2013).

    Article  ADS  MathSciNet  MATH  Google Scholar 

  11. B. A. Arbuzov and I. V. Zaitsev, “ATLAS diboson excesses as an evidence for a heavy WW resonance with the weak isospin 2,” Internat. J. Modern Phys. A, 30, 1550221 (2015).

    Article  ADS  Google Scholar 

  12. B. A. Arbuzov, Non-perturbative Effective Interactions in the Standard Model (De Gruyter Stud. Math. Phys., Vol. 23), De Gruyter, Berlin (2014).

    Book  MATH  Google Scholar 

  13. K. Hagiwara, R. D. Peccei, D. Zeppenfeld, and K. Hikasa, “Probing the weak boson sector in e + e W + W ,” Nucl. Phys. B, 282, 253–307 (1987).

    Article  ADS  Google Scholar 

  14. K. A. Olive et al. [Particle Data Group Collab.], “Review of particle physics,” Chin. Phys. C, 38, 090001 (2014, 2015 update).

    Article  Google Scholar 

  15. B. S. DeWitt, “Quantum theory of gravity: II. The manifestly covariant theory,” Phys. Rev., 162, 1195–1239 (1967).

    Article  ADS  MATH  Google Scholar 

  16. L. D. Faddeev and V. N. Popov, “Covariant quantization of the gravitational field,” Sov. Phys. Usp., 16, 777–788 (1974).

    Article  ADS  MathSciNet  Google Scholar 

  17. A. A. Logunov, Relativistic Theory of Gravity [in Russian], Nauka, Moscow (2012); English transl. prev. ed., Nova Science, New York (1998).

    Google Scholar 

  18. A. P. Prudnikov, Yu. A. Brychkov, and O. I. Marichev, Integrals and Series [in Russian], Vol. 3, Supplementary Chapters, Nauka, Moscow (1986); English transl: Vol. 3, More Special Functions, Gordon and Breach, London (1990).

    MATH  Google Scholar 

  19. R. H. Sanders, “The published extended rotation curves of spiral galaxies: Confrontation with modified dynamics,” Astrophys. J., 473, 117–142 (1996).

    Article  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to B. A. Arbuzov.

Additional information

__________

Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 191, No. 2, pp. 189–195, May, 2017.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Arbuzov, B.A., Zaitsev, I.V. Effective couplings and the prospect of solving fundamental problems of cosmology in a quantum theory of gravity. Theor Math Phys 191, 635–640 (2017). https://doi.org/10.1134/S0040577917050026

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S0040577917050026

Keywords

Navigation