Skip to main content
SpringerLink
Log in

On Nonlocal Modified Gravity and Cosmology

  • Conference paper
  • First Online:
Lie Theory and Its Applications in Physics

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 111))

Abstract

Despite many nice properties and numerous achievements, general relativity is not a complete theory. One of actual approaches towards more complete theory of gravity is its nonlocal modification. We present here a brief review of nonlocal gravity with its cosmological solutions. In particular, we pay special attention to two nonlocal models and their nonsingular bounce solutions for the cosmic scale factor.

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 129.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 169.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 169.99
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. Ade, P.A.R., Aghanim, N., Armitage-Caplan, C., et al.: (Planck Collaboration) Planck 2013 results. XVI. Cosmological parameters (2013). arXiv:1303.5076v3

    Google Scholar 

  2. Aref’eva, I.Y.: Nonlocal string tachyon as a model for cosmological dark energy. AIP Conf. Proc. 826, 301–311 (2006). [astro-ph/0410443]

    Google Scholar 

  3. Aref’eva, I.Y., Volovich, I.V.: Comological daemon. J. High Energy Phys. 1108, 102 (2011). arXiv:1103.0273 [hep-th]

    Google Scholar 

  4. Aref’eva, I.Y., Joukovskaya, L.V., Vernov, S.Y.: Bouncing and accelerating solutions in nonlocal stringy models. J. High Energy Phys. 0707, 087 (2007) [hep-th/0701184]

    Article  MathSciNet  Google Scholar 

  5. Barnaby, N., Biswas, T., Cline, J.M.: p-Adic inflation. J. High Energy Phys. 0704, 056 (2007). [hep-th/0612230]

    Google Scholar 

  6. Barvinsky, A.O.: Dark energy and dark matter from nonlocal ghost-free gravity theory. Phys. Lett. B 710, 12–16 (2012). arXiv:1107.1463 [hep-th]

    Google Scholar 

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

    Google Scholar 

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

    Google Scholar 

  9. Biswas, T., Koshelev, A.S., Mazumdar, A., Vernov, S.Y.: Stable bounce and inflation in non-local higher derivative cosmology. J. Cosmol. Astropart. Phys. 08, 024 (2012). arXiv:1206.6374 [astro-ph.CO]

    Google Scholar 

  10. 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]

    Google Scholar 

  11. Biswas, T., Conroy, A., Koshelev, A.S., Mazumdar, A.: Generalized gost-free quadratic curvature gravity (2013). arXiv:1308.2319 [hep-th]

    Google Scholar 

  12. Brandenberger, R.H.: The matter bounce alternative to inflationary cosmology (2012). arXiv:1206.4196 [astro-ph.CO]

    Google Scholar 

  13. Brekke, L., Freund, P.G.O.: p-Adic numbers in physics. Phys. Rep. 233, 1–66 (1993)

    Google Scholar 

  14. Briscese, F., Marciano, A., Modesto, L., Saridakis, E.N.: Inflation in (super-)renormalizable gravity. Phys. Rev. D 87, 083507 (2013). arXiv:1212.3611v2 [hep-th]

    Google Scholar 

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

    Google Scholar 

  16. Calcagni, G., Montobbio, M., Nardelli, G.: A route to nonlocal cosmology. Phys. Rev. D 76, 126001 (2007). arXiv:0705.3043v3 [hep-th]

    Google Scholar 

  17. Calcagni, G., Nardelli, G.: Nonlocal gravity and the diffusion equation. Phys. Rev. D 82, 123518 (2010). arXiv:1004.5144 [hep-th]

    Google Scholar 

  18. Calcagni, G., Modesto, L., Nicolini, P.: Super-accelerting bouncing cosmology in assymptotically-free non-local gravity (2013). arXiv:1306.5332 [gr-qc]

    Google Scholar 

  19. Deffayet, C., Woodard, R.P.: Reconstructing the distortion function for nonlocal cosmology. J. Cosmol. Astropart. Phys. 0908, 023 (2009). arXiv:0904.0961 [gr-qc]

    Google Scholar 

  20. Deser, S., Woodard, R.P.: Nonlocal cosmology. Phys. Rev. Lett. 99, 111301 (2007). arXiv:0706.2151 [astro-ph]

    Google Scholar 

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

    Google Scholar 

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

    Google Scholar 

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

    Article  MathSciNet  Google Scholar 

  24. Dimitrijevic, I., Dragovich, B., Grujic J., Rakic, Z.: Some power-law cosmological solutions in nonlocal modified gravity (in these proceedings) (2014)

    Google Scholar 

  25. Dirian, Y., Foffa, S., Khosravi, N., Kunz, M., Maggiore, M.: Cosmological perturbations and structure formation in nonlocal infrared modifications of general relativity (2014). arXiv:1403.6068 [astro-ph.CO]

    Google Scholar 

  26. Dragovich, B.: Nonlocal dynamics of p-adic strings. Theor. Math. Phys. 164(3), 1151–115 (2010). arXiv:1011.0912v1 [hep-th]

    Google Scholar 

  27. Dragovich, B.: Towards p-adic matter in the universe. In: Springer Proceedings in Mathematics and Statistics, vol. 36, pp. 13–24 (2013). arXiv:1205.4409 [hep-th]

    Google Scholar 

  28. Elizalde, E., Pozdeeva, E.O., Vernov, S.Y.: Stability of de Sitter solutions in non-local cosmological models. PoS(QFTHEP2011) 038, (2012). arXiv:1202.0178 [gr-qc]

    Google Scholar 

  29. Elizalde, E., Pozdeeva, E.O., Vernov, S.Y., Zhang, Y.: Cosmological solutions of a nonlocal model with a perfect fluid. J. Cosmol. Astropart. Phys. 1307, 034 (2013). arXiv:1302.4330v2 [hep-th]

    Google Scholar 

  30. Erickcek, A.L., Smith, T.L., Kamionkowski M.: Solar system tests do rule out 1/R gravity. Phys. Rev. D 74, 121501 (2006). arXiv:astro-ph/0610483

    Google Scholar 

  31. Jhingan, S., Nojiri, S., Odintsov, S.D., Sami, M., Thongkool, I., Zerbini, S.: Phantom and non-phantom dark energy: the cosmological relevance of non-locally corrected gravity. Phys. Lett. B 663, 424–428 (2008). arXiv:0803.2613 [hep-th]

    Google Scholar 

  32. Koivisto, T.S.: Dynamics of nonlocal cosmology. Phys. Rev. D 77, 123513 (2008). arXiv:0803.3399 [gr-qc]

    Google Scholar 

  33. Koivisto, T.S.: Newtonian limit of nonlocal cosmology. Phys. Rev. D 78, 123505 (2008). arXiv:0807.3778 [gr-qc]

    Google Scholar 

  34. Koshelev, A.S.: Modified non-local gravity (2011). arXiv:1112.6410v1 [hep-th]

    Google Scholar 

  35. Koshelev, A.S.: Stable analytic bounce in non-local Einstein–Gauss–Bonnet cosmology (2013). arXiv:1302.2140 [astro-ph.CO]

    Google Scholar 

  36. Koshelev, A.S., Vernov, S.Y.: Analysis of scalar perturbations in cosmological models with a non-local scalar field. Class. Quant. Grav. 28, 085019 (2011). arXiv:1009.0746v2 [hep-th]

    Google Scholar 

  37. Koshelev, A.S., Vernov, S.Y.: On bouncing solutions in non-local gravity (2012). arXiv:1202.1289v1 [hep-th]

    Google Scholar 

  38. Lehners, J.-L., Steinhardt, P.J.: Planck 2013 results support the cyclic universe (2013). arXiv:1304.3122 [astro-ph.CO]

    Google Scholar 

  39. Modesto, L., Tsujikawa, S.: Non-local massive gravity. Phys. Lett. B 727, 48–56 (2013). arXiv:1307.6968 [hep-th]

    Google Scholar 

  40. Moffat, J.M.: Ultraviolet complete quantum gravity. Eur. Phys. J. Plus 126, 43 (2011). arXiv:1008.2482 [gr-qc]

    Google Scholar 

  41. Nojiri, S., Odintsov, S.D.: Modified non-local-F(R) gravity as the key for inflation and dark energy. Phys. Lett. B 659, 821–826 (2008). arXiv:0708.0924v3 [hep-th]

    Google Scholar 

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

    Google Scholar 

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

    Google Scholar 

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

    Google Scholar 

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

    Google Scholar 

  46. Zhang, Y.-li., Sasaki, M.: Screening of cosmological constant in non-local cosmology. Int. J. Mod. Phys. D 21, 1250006 (2012). arXiv:1108.2112 [gr-qc]

    Google Scholar 

Download references

Acknowledgements

Work on this paper was supported by Ministry of Education, Science and Technological Development of the Republic of Serbia, grant No. 174012. The author thanks Prof. Vladimir Dobrev for invitation to participate and give a talk, as well as for hospitality, at the X International Workshop “Lie Theory and its Applications in Physics”, 17–23 June 2013, Varna, Bulgaria. The author also thanks organizers of the Balkan Workshop BW2013 “Beyond Standard Models” (25–29.04.2013, Vrnjačka Banja, Serbia), Six Petrov International Symposium on High Energy Physics, Cosmology and Gravity (5–8.09.2013, Kiev, Ukraine) and Physics Conference TIM2013 (21–23.11.2013, Timisoara, Romania), where some results on modified gravity and its cosmological solutions were presented. Many thanks also to my collaborators Zoran Rakic, Jelena Grujic and Ivan Dimitrijevic, as well as to Alexey Koshelev and Sergey Vernov for useful discussions.

Author information

Authors and Affiliations

  1. Institute of Physics, University of Belgrade, Pregrevica 118, 11080, Zemun, Belgrade, Serbia

    Branko Dragovich

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

    Vladimir Dobrev

Rights and permissions

Reprints and permissions

Copyright information

© 2014 Springer Japan

About this paper

Cite this paper

Dragovich, B. (2014). On Nonlocal Modified Gravity and Cosmology. In: Dobrev, V. (eds) Lie Theory and Its Applications in Physics. Springer Proceedings in Mathematics & Statistics, vol 111. Springer, Tokyo. https://doi.org/10.1007/978-4-431-55285-7_17

Download citation

Publish with us

Policies and ethics

Search

Navigation