On Nonlocal Modified Gravity and Cosmology

  • Branko Dragovich
Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 111)


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.


Scalar Curvature Hubble Parameter Ricci Scalar Cosmological Solution Scalar String 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.



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.


  1. 1.
    Ade, P.A.R., Aghanim, N., Armitage-Caplan, C., et al.: (Planck Collaboration) Planck 2013 results. XVI. Cosmological parameters (2013). arXiv:1303.5076v3Google Scholar
  2. 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. 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. 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]CrossRefMathSciNetGoogle Scholar
  5. 5.
    Barnaby, N., Biswas, T., Cline, J.M.: p-Adic inflation. J. High Energy Phys. 0704, 056 (2007). [hep-th/0612230]Google Scholar
  6. 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. 7.
    Biswas, T., Mazumdar, A., Siegel, W: Bouncing universes in string-inspired gravity. J. Cosmol. Astropart. Phys. 0603, 009 (2006). arXiv:hep-th/0508194Google Scholar
  8. 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. 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. 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. 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. 12.
    Brandenberger, R.H.: The matter bounce alternative to inflationary cosmology (2012). arXiv:1206.4196 [astro-ph.CO]Google Scholar
  13. 13.
    Brekke, L., Freund, P.G.O.: p-Adic numbers in physics. Phys. Rep. 233, 1–66 (1993)Google Scholar
  14. 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. 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. 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. 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. 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. 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. 20.
    Deser, S., Woodard, R.P.: Nonlocal cosmology. Phys. Rev. Lett. 99, 111301 (2007). arXiv:0706.2151 [astro-ph]Google Scholar
  21. 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. 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. 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)CrossRefMathSciNetGoogle Scholar
  24. 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. 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. 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. 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. 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. 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. 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/0610483Google Scholar
  31. 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. 32.
    Koivisto, T.S.: Dynamics of nonlocal cosmology. Phys. Rev. D 77, 123513 (2008). arXiv:0803.3399 [gr-qc]Google Scholar
  33. 33.
    Koivisto, T.S.: Newtonian limit of nonlocal cosmology. Phys. Rev. D 78, 123505 (2008). arXiv:0807.3778 [gr-qc]Google Scholar
  34. 34.
    Koshelev, A.S.: Modified non-local gravity (2011). arXiv:1112.6410v1 [hep-th]Google Scholar
  35. 35.
    Koshelev, A.S.: Stable analytic bounce in non-local Einstein–Gauss–Bonnet cosmology (2013). arXiv:1302.2140 [astro-ph.CO]Google Scholar
  36. 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. 37.
    Koshelev, A.S., Vernov, S.Y.: On bouncing solutions in non-local gravity (2012). arXiv:1202.1289v1 [hep-th]Google Scholar
  38. 38.
    Lehners, J.-L., Steinhardt, P.J.: Planck 2013 results support the cyclic universe (2013). arXiv:1304.3122 [astro-ph.CO]Google Scholar
  39. 39.
    Modesto, L., Tsujikawa, S.: Non-local massive gravity. Phys. Lett. B 727, 48–56 (2013). arXiv:1307.6968 [hep-th]Google Scholar
  40. 40.
    Moffat, J.M.: Ultraviolet complete quantum gravity. Eur. Phys. J. Plus 126, 43 (2011). arXiv:1008.2482 [gr-qc]Google Scholar
  41. 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. 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. 43.
    Novello, M., Bergliaffa, S.E.P.: Bouncing cosmologies. Phys. Rep. 463, 127–213 (2008). arXiv:0802.1634 [astro-ph]Google Scholar
  44. 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. 45.
    Woodard, R.P.: Nonlocal models of cosmic acceleration (2014). arXiv:1401.0254 [astro-ph.CO]Google Scholar
  46. 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

Copyright information

© Springer Japan 2014

Authors and Affiliations

  1. 1.Institute of PhysicsUniversity of BelgradeZemun, BelgradeSerbia

Personalised recommendations