Skip to main content
SpringerLink
Log in

Cosmological solutions in nonlocal models

  • Published:
Physics of Particles and Nuclei Letters Aims and scope Submit manuscript

    We’re sorry, something doesn't seem to be working properly.

    Please try refreshing the page. If that doesn't work, please contact support so we can address the problem.

Abstract

A non-local modified gravity model with an analytic function of the d’Alembert operator that has been proposed as a possible way of resolving the singularities problems in cosmology is considered. We show that the anzats that is usually used to obtain exact solutions in this model provides a connection with f(R) gravity models.

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

Similar content being viewed by others

References

  1. K. S. Stelle, “Renormalization of higher derivative quantum gravity,” Phys. Rev., Ser. D 16, 953 (1977).

    Article  ADS  MathSciNet  Google Scholar 

  2. I. Ya. Aref’eva, D. M. Belov, A. A. Giryavets, et al., “Noncommutative field theories and (super)string field theories,” hep-th/0111208.

  3. S. Jhingan, S. Nojiri, S. D. Odintsov, et al., “Phantom and non-phantom dark energy: the cosmological relevance of non-locally corrected gravity,” Phys. Lett., Ser. B 663, 424 (2008); arXiv:0803.2613; T. S. Koivisto, “Dynamics of nonlocal cosmology,” Phys. Rev., Ser. D 77, 123513 (2008); arXiv:0803.3399; S. Capozziello, E. Elizalde, S. Nojiri, and S. D. Odintsov, “Accelerating cosmologies from nonlocal higher-derivative gravity,” Phys. Lett., Ser. B 671, 193 (2009); arXiv:0809.1535; L. Modesto, “Super-renormalizable quantum gravity,” Phys. Rev., Ser. D 86, 044005 (2012), arXiv:1107.2403; E. Elizalde, E. O. Pozdeeva, and S. Yu. Vernov, “Reconstruction procedure in nonlocal cosmological models,” Class. Quantum Grav. 30, 035002 (2013), arXiv:1209.5957; A. S. Koshelev, “Stable analytic bounce in non-local Einstein-Gauss-Bonnet cosmology,” Class. Quantum Grav. 30, 155001 (2013), arXiv:1302.2140; E. Elizalde, E. O. Pozdeeva, S. Yu. Vernov, and Y.-l. Zhang, “Cosmological solutions of a nonlocal model with a perfect fluid,” J. Cosmol. Astropart. Phys. 1307, 034 (2013), arXiv:1302.4330; S. Deser and R. P. Woodard, “Observational viability and stability of nonlocal cosmology,” J. Cosmol. Astropart. Phys. 1311, 036 (2013), arXiv:1307.6639; R. P. Woodard, “Nonlocal models of cosmic acceleration,” Found. Phys. 44, 213 (2014), arXiv:1401.0254.

    Article  ADS  Google Scholar 

  4. N. Barnaby, T. Biswas, and J. M. Cline, “p-adic inflation,” J. High Energy Phys. 0704, 056 (2007), hepth/0612230; A. S. Koshelev, “Nonlocal SFT tachyon and cosmology,” J. High Energy Phys. 0704, 029 (2007), arXiv:hepth/0701103; I. Ya. Aref’eva, L. V. Joukovskaya, and S. Yu. Vernov, “Bouncing and accelerating solutions in nonlocal stringy models,” J. High Energy Phys. 0707, 087 (2007), arXiv:hepth/0701184; D. J. Mulryne and N. J. Nunes, “Diffusing nonlocal inflation: solving the field equations as an initial value problem,” Phys. Rev., Ser. D 78, 063519 (2008), arXiv:0805.0449; I. Ya. Aref’eva and A. S. Koshelev, “Cosmological signature of tachyon condensation,” J. High Energy Phys. 0809, 068 (2008), arXiv:0804.3570; A. S. Koshelev and S. Yu. Vernov, “Cosmological perturbations in SFT inspired nonlocal scalar field models,” Eur. Phys. J., Ser. C 72, 2198 (2012), arXiv:0903.5176; G. Calcagni and G. Nardelli, “Nonlocal gravity and the diffusion equation,” Phys. Rev., Ser. D 82, 123518 (2010), arXiv:1004.5144; A. S. Koshelev and S. Yu. Vernov, “Analysis of scalar perturbations in cosmological models with a nonlocal scalar field,” Class. Quant. Grav. 28, 085019 (2011), arXiv:1009.0746; A. S. Koshelev, “Modified nonlocal gravity,” Rom. J. Phys. 57, 894 (2012), arXiv:1112.6410.

    Article  ADS  MathSciNet  Google Scholar 

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

    Article  ADS  MathSciNet  Google Scholar 

  6. T. Biswas, T. Koivisto, and A. Mazumdar, “Towards a resolution of the cosmological singularity in non-local higher derivative theories of gravity,” J. Cosmol. Astropart. Phys. 1011, 008 (2010), arXiv:1005.0590.

    Article  ADS  Google Scholar 

  7. T. Biswas, E. Gerwick, T. Koivisto, and A. Mazumdar, “Towards singularity and ghost free theories of gravity,” Phys. Rev. Lett. 108, 031101 (2012), arXiv:1110.5249.

    Article  ADS  Google Scholar 

  8. T. Biswas, A. S. Koshelev, A. Mazumdar, and S. Yu. Vernov, “Stable bounce and inflation in non-local higher derivative cosmology,” J. Cosmol. Astropart. Phys. 1208, 024 (2012), arXiv:1206.6374.

    Article  ADS  Google Scholar 

  9. A. S. Koshelev and S. Yu. Vernov, “On bouncing solutions in non-local gravity,” Phys. Part. Nucl. 43, 666 (2012), arXiv:1202.1289. I. Dimitrijevic, I. Dragovich, J. Grujic, and Z. Rakic, “New cosmological solutions in nonlocal modified gravity,” arXiv:1302.2794.

    Article  Google Scholar 

  10. T. Ruzmaikina and A. Ruzmaikin, “Quadratic corrections to the Lagrangian density of the gravitational field and the singularity,” Sov. Phys. JETP 30, 372 (1970); V. Ts. Gurovich and A. A. Starobinsky, “Quantum effects and regular cosmological models,” Sov. Phys. JETP 50, 844 (1979); K. I. Maeda, “Towards the Einstein-Hilbert action via conformal transformation,” Phys. Rev., Ser. D 39, 3159 (1989); S. Carloni, P. K. S. Dunsby, S. Capozziello, and A. Troisi, “Cosmological dynamics of Rn gravity,” Class. Quant. Grav. 22, 4839 (2005), arXiv:gr-qc/0410046; J. D. Barrow and S. Hervik, “Evolution of universes in quadratic theories of gravity,” Phys. Rev., Ser. D 74, 124017 (2006), arXiv:gr-qc/0610013; M. M. Ivanov and A. V. Toporensky, “Stable super-inflating cosmological solutions in f(R)-Gravity,” Int. J. Mod. Phys., Ser. D 21, 1250051 (2012), arXiv:1112.4194; S. Domazet, V. Radovanovic, M. Simonovic, and H. Stefancic, “On analytical solu tions of f(R) modified gravity theories in FLRW cosmologies,” Int. J. Mod. Phys., Ser. D 22, 1350006 (2013), arXiv:1203.5220; S. Capozziello and V. Faraoni, “Beyond Einstein gravity: a survey of gravitational theories for cosmology and astrophysics,” in Fund. Theor. Phys. (Springer, N.Y., 2011), Vol. 170.

    ADS  Google Scholar 

  11. P. A. R. Ade et al. (Planck Collab.), Planck 2013 Results, XXII: Constraints on Inflation, arXiv:1303.5082.

  12. A. A. Starobinsky, “Relict gravitation radiation spectrum and initial state of the universe,” JETP Lett. 30, 682 (1979); A. A. Starobinsky, “A new type of isotropic cosmological models without singularity,” Phys. Lett., Ser. B 91, 99 (1980).

    ADS  Google Scholar 

  13. A. Vilenkin, “Classical and Quantum Cosmology of the Starobinsky Inflationary Model,” Phys. Rev. D 32, 2511 (1985).

    Article  ADS  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Theoretische Natuurkunde, Vrije Universiteit Brussel and The International Solvay Institutes, Pleinlaan 2, B-1050, Brussels, Belgium

    A. S. Koshelev

  2. Skobeltsyn Institute of Nuclear Physics, Lomonosov Moscow State University, Leninskie Gory 1, Moscow, 119991, Russia

    S. Yu. Vernov

Authors
  1. A. S. Koshelev
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. S. Yu. Vernov
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to A. S. Koshelev.

Additional information

The article is published in the original.

Postdoctoral researcher of FWO-Vlaanderen.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Koshelev, A.S., Vernov, S.Y. Cosmological solutions in nonlocal models. Phys. Part. Nuclei Lett. 11, 960–963 (2014). https://doi.org/10.1134/S1547477114070255

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S1547477114070255

Keywords

Search

Navigation