Skip to main content
SpringerLink
Log in

Variations of Infinite Derivative Modified Gravity

  • Conference paper
  • First Online:
Book cover Quantum Theory and Symmetries with Lie Theory and Its Applications in Physics Volume 1 (LT-XII/QTS-X 2017)

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 263))

Included in the following conference series:

Abstract

We consider nonlocal modified Einstein gravity without matter, where nonlocal term has the form \(P(R) \mathcal {F}(\Box ) Q(R)\). For this model, in this paper we give the derivation of the equations of motion in detail. This is not an easy task and presented derivation should be useful to a researcher who wants to investigate nonlocal gravity. Also, we present the second variation of the related Einstein–Hilbert modified action and basics of gravity perturbations.

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

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 189.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Hardcover Book
USD 249.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. R. M. Wald, General Relativity (University of Chicago Press, 1984).

    Google Scholar 

  2. T. Clifton, P. G. Ferreira, A. Padilla, C. Skordis: Modified gravity and cosmology. Physics Reports 513 (2012) 1–189; [arXiv:1106.2476v2 [astro-ph.CO]].

    Article  MathSciNet  Google Scholar 

  3. S. Nojiri, S. D. Odintsov: Unified cosmic history in modified gravity: from \(F(R)\) theory to Lorentz non-invariant models. Physics Reports 505 (2011) 59–144; [arXiv:1011.0544v4 [gr-qc]].

    Article  MathSciNet  Google Scholar 

  4. S. Nojiri, S. D. Odintsov, V. K. Oikonomou: Modified Gravity Theories on a Nutshell: Inflation, Bounce and Late-time Evolution. Physics Reports 692 (2017) 1–104. [arXiv:1705.11098 [gr-qc]] .

    MATH  Google Scholar 

  5. Novello, M., Bergliaffa, S.E.P.: Bouncing cosmologies. Phys. Rep. 463, 127–213 (2008). [arXiv:0802.1634 [astro-ph]].

    Article  MathSciNet  Google Scholar 

  6. T. P. Sotiriou, V. Faraoni: \(f(R)\) theories of gravity. Rev. Mod. Phys. 82 (2010) 451–497. [arXiv:0805.1726v4 [gr-qc]].

    Article  MathSciNet  Google Scholar 

  7. E. Belgacem, Y. Dirian, S. Foffa and M. Maggiore: Nonlocal gravity. Conceptual aspects and cosmological predictions. Journal of Cosmology and Astroparticle Physics, Volume 2018, (2018) [arXiv:1712.07066 [hep-th]].

    Article  Google Scholar 

  8. I. Dimitrijevic, B. Dragovich, J. Stankovic, A. S. Koshelev and Z. Rakic: On Nonlocal Modified Gravity and its Cosmological Solutions. Springer Proceedings in Mathematics & Statistics 191 (2016) 35–51. arXiv:1701.02090 [hep-th].

    Article  MathSciNet  Google Scholar 

  9. B. Dragovich: On Nonlocal modified gravity and cosmology. Lie Theory and Its Applications in Physics, Springer Proceedings in Mathematics and Statistics 111, 251–262, 2014.

    Google Scholar 

  10. R. P. Woodard: Nonlocal models of cosmic acceleration. [arXiv:1401.0254 [astro-ph.CO]] (2014).

    Article  MathSciNet  Google Scholar 

  11. A. S. Koshelev, K. S. Kumar, A. A. Starobinsky: \(R^2\) inflation to probe non-perturbative quantum gravity. Journal of High Energy Physics 1803 (2018) 071. [arXiv:1711.08864 [hep-th]].

  12. Modesto, L.: Super-renormalizable quantum gravity. Phys. Rev. D 86, 044005 (2012). [arXiv:1107.2403 [hep-th]]

    Article  Google Scholar 

  13. Modesto, L., Rachwal, L.: Super-renormalizable and finite gravitational theories. Nucl. Phys. B 889, 228 (2014). [arXiv:1407.8036 [hep-th]].

    Article  MathSciNet  Google Scholar 

  14. Stelle, K.S.: Renormalization of higher derivative quantum gravity. Phys. Rev. D 16, 953 (1977).

    Article  MathSciNet  Google Scholar 

  15. Dragovich, B., Khrennikov, A. Yu., Kozyrev, S. V., Volovich, I. V., Zelenov, E. I.: \(p\)-Adic mathematical physics: the first 30 years. p-Adic Numbers Ultrametric Anal. Appl. 9 (2), 87–121 (2017). [arXiv:1705.04758 [math-ph]].

  16. Biswas, T., Conroy, A., Koshelev, A.S., Mazumdar, A.: Generalized gost-free quadratic curvature gravity. [arXiv:1308.2319 [hep-th]].

  17. V. Mukhanov, Physical Foundations of Cosmology, (Cambridge, 2005).

    Google Scholar 

  18. Biswas, T., Mazumdar, A., Siegel, W: Bouncing universes in string-inspired gravity. J. Cosmology Astropart. Phys. 0603, 009 (2006) [arXiv:hep-th/0508194].

    Article  Google Scholar 

  19. Biswas, T., Koivisto, T., Mazumdar, A.: Towards a resolution of the cosmological singularity in non-local higher derivative theories of gravity. J. Cosmology Astropart. Phys. 1011, 008 (2010) [arXiv:1005.0590v2 [hep-th]].

    Article  Google Scholar 

  20. Biswas, T., Gerwick, E., Koivisto, T., Mazumdar, A.: Towards singularity and ghost free theories of gravity. Phys. Rev. Lett. 108, 031101 (2012) [arXiv:1110.5249v2 [gr-qc]].

    Article  Google Scholar 

  21. T. Biswas, A. S. Koshelev, A. Mazumdar, S. Yu. Vernov, Stable bounce and inflation in non-local higher derivative cosmology, JCAP 08 (2012) 024, [arXiv:1206.6374v2 [astro-ph.CO]].

    Article  Google Scholar 

  22. I. Dimitrijevic, B. Dragovich, J. Grujic , Z. Rakic: On modified gravity. Springer Proceedings in Mathematics and Statistics 36, 251–259 (2013) [arXiv:1202.2352 [hep-th]].

    MathSciNet  MATH  Google Scholar 

  23. Dimitrijevic, I., Dragovich, B., Grujic J., Rakic, Z.: New cosmological solutions in nonlocal modified gravity. Rom. Journ. Phys. 58 (5–6), 550–559 (2013) [arXiv:1302.2794 [gr-qc]].

  24. I. Dimitrijevic, B. Dragovich, J. Grujic and Z. Rakic: A new model of nonlocal modified gravity. Publications de l’Institut Mathematique 94 (108) (2013), 187–196.

    Article  MathSciNet  Google Scholar 

  25. I. Dimitrijevic, B. Dragovich, J. Grujic and Z. Rakic: Some Cosmological Solutions of a Nonlocal Modified Gravity. Filomat 29 (3), (2015) 619–628, arXiv:1508.05583 [hep-th].

    Article  MathSciNet  Google Scholar 

  26. I. Dimitrijevic: Cosmological solutions in modified gravity with monomial nonlocality. Applied Mathematics and Computation, 285 (3), (2016) 195–203.

    Article  MathSciNet  Google Scholar 

  27. A. S. Koshelev, S. Yu. Vernov: On bouncing solutions in non-local gravity. Phys. Part. Nuclei 43, 666–668 (2012) [arXiv:1202.1289v1 [hep-th]].

    Article  Google Scholar 

  28. I. Dimitrijevic, B. Dragovich, J. Grujic and Z. Rakic: Some power-law cosmological solutions in nonlocal modified gravity. in: Lie Theory and Its Applications in Physics, Springer Proceedings in Mathematics and Statistics, 111 2014, pp. 241–250.

    Google Scholar 

  29. Dimitrijevic, I., Dragovich, B., Grujic J., Koshelev A. S., Rakic, Z.: Cosmology of modified gravity with a non-local \(f(R)\). arXiv:1509.04254 [hep-th].

  30. I. Dimitrijevic, B. Dragovich, J. Grujic and Z. Rakic: Constant curvature cosmological solutions in nonlocal gravity. AIP Conference Proceedings 1634, (2014) 18–23.

    Article  Google Scholar 

  31. I. Dimitrijevic, B. Dragovich, Z. Rakic and J.Stankovic: On Nonlocal Gravity with Constant Scalar Curvature. Publications de l’Institut Mathematique, Nouvelle série, 103 (117) (2018), 53–59.

    Google Scholar 

  32. Aref’eva, I.Ya., Joukovskaya, L.V., Vernov, S.Yu.: Bouncing and accelerating solutions in nonlocal stringy models. JHEP 0707, 087 (2007) arXiv:0701184 [hep-th/0701184].

    Article  MathSciNet  Google Scholar 

  33. E. Elizalde, E. O. Pozdeeva, S. Yu. Vernov: Stability of de Sitter Solutions in Non-local Cosmological Models. PoS, QFTHEP2011:038, 2013, arXiv:1202.0178.

  34. L. Buoninfante, A. S. Koshelev, G. Lambiase and A. Mazumdar: Classical properties of non-local, ghost- and singularity-free gravity. [arXiv:1802.00399 [gr-qc]].

  35. A. S. Koshelev, L. Modesto, L. Rachwal and A. A. Starobinsky: Occurrence of exact \(R^2\) inflation in non-local UV-complete gravity. Journal of High Energy Physics, 2016(11), 1–41. [arXiv:1604.03127 [hep-th]].

  36. A. S. Koshelev, J. Marto, A. Mazumdar: Towards non-singular metric solution in infinite derivative gravity. [arXiv:1803.00309 [gr-qc]].

Download references

Acknowledgements

Work on this paper was partially supported by the Ministry of Education, Science and Technological Development of Republic of Serbia, grant No 174012. B.D. thanks Prof. Vladimir Dobrev for invitation to participate and give a talk on nonlocal gravity, as well as for hospitality, at the X International Symposium “Quantum Theory and Symmetries”, and XII International Workshop “Lie Theory and its Applications in Physics”, 19–25 June 2017, Varna, Bulgaria. B.D. also thanks a support of the ICTP - SEENET-MTP project NT-03 Cosmology-Classical and Quantum Challenges during preparation of this article.

Author information

Authors and Affiliations

  1. Faculty of Mathematics, University of Belgrade, Belgrade, Serbia

    Ivan Dimitrijevic

  2. Institute of Physics, University of Belgrade, Belgrade, Serbia

    Branko Dragovich

  3. Mathematical Institute, Serbian Academy of Sciences and Arts, Belgrade, Serbia

    Branko Dragovich

  4. Faculty of Mathematics, University of Belgrade, Belgrade, Serbia

    Zoran Rakic

  5. Teacher Education Faculty, University of Belgrade, Belgrade, Serbia

    Jelena Stankovic

Authors
  1. Ivan Dimitrijevic
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Branko Dragovich
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Zoran Rakic
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Jelena Stankovic
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Branko Dragovich .

Editor information

Editors and Affiliations

  1. Institute for Nuclear Research and Nuclear Energy, Bulgarian Academy of Sciences, Sofia, Bulgaria

    Vladimir Dobrev

Rights and permissions

Reprints and permissions

Copyright information

© 2018 Springer Nature Singapore Pte Ltd.

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Dimitrijevic, I., Dragovich, B., Rakic, Z., Stankovic, J. (2018). Variations of Infinite Derivative Modified Gravity. In: Dobrev, V. (eds) Quantum Theory and Symmetries with Lie Theory and Its Applications in Physics Volume 1 . LT-XII/QTS-X 2017. Springer Proceedings in Mathematics & Statistics, vol 263. Springer, Singapore. https://doi.org/10.1007/978-981-13-2715-5_5

Download citation

Publish with us

Policies and ethics

Search

Navigation