Gravitation and Cosmology

, Volume 23, Issue 4, pp 359–366 | Cite as

On stable exponential cosmological solutions in the EGB model with a cosmological constant in dimensions D = 5, 6, 7, 8

Article

Abstract

A D-dimensional Einstein–Gauss–Bonnet (EGB) flat cosmological model with a cosmological constant Λ is considered. We focus on solutions with an exponential time dependence of the scale factor. Using the previously developed general stability analysis of such solutions by V.D. Ivashchuk (2016), we apply the criterion from that paper to all known exponential solutions up to the dimension 7 + 1. We show that this criterion, which guarantees the stability of solutions under consideration, is fulfilled for all combinations of the coupling constant of the theory except for some discrete set.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    D. Lovelock, “The Einstein tensor and its generalizations,” J.Math. Phys. 12, 498 (1971).ADSCrossRefMATHGoogle Scholar
  2. 2.
    B. Zwiebach, “Curvature squared terms and string theories,” Phys. Lett. B 156, 315 (1985).ADSCrossRefGoogle Scholar
  3. 3.
    E. S. Fradkin and A. A. Tseytlin, “Effective field theory from quantized strings,” Phys. Lett. B 158, 316 (1985).ADSCrossRefMATHGoogle Scholar
  4. 4.
    E. S. Fradkin and A. A. Tseytlin, “Effective action approach to superstring theory,” Phys. Lett. B 160, 69 (1985).ADSCrossRefGoogle Scholar
  5. 5.
    D. Gross and E. Witten, “Superstrings modifications of Einstein’s equations,” Nucl. Phys. B 277, 1 (1986).ADSCrossRefGoogle Scholar
  6. 6.
    R. R. Metsaev and A. A. Tseytlin, “Two-loop beta function for the generalized bosonic sigma model,” Phys. Lett. B 191, 354 (1987).ADSCrossRefGoogle Scholar
  7. 7.
    M. Brigante, H. Liu, R. C. Myers, S. Shenker, and S. Yaida, Phys. Rev. D 77, 126006 (2008); arXiv: 0712.0805.ADSCrossRefGoogle Scholar
  8. 8.
    R. A. Konoplya and A. Zhidenko, “Quasinormal modes of Gauss–Bonnet-AdS black holes: towards holographic description of finite coupling;” arXiv: 1705.07732.Google Scholar
  9. 9.
    H. Ishihara, “Cosmological solutions of the extended Einstein gravity with the Gauss–Bonnet term,” Phys. Lett. B 179, 217 (1986).ADSCrossRefGoogle Scholar
  10. 10.
    N. Deruelle, “On the approach to the cosmological singularity in quadratic theories of gravity: the Kasner regimes,” Nucl. Phys. B 327, 253 (1989).ADSCrossRefGoogle Scholar
  11. 11.
    S. Nojiri and S. D. Odintsov, “Introduction to modified gravity and gravitational alternative for Dark Energy,” Int. J. Geom. Meth. Mod. Phys. 4, 115 (2007); hep-th/0601213.CrossRefMATHGoogle Scholar
  12. 12.
    G. Cognola, E. Elizalde, S. Nojiri, S. D. Odintsov, and S. Zerbini, “One-loop effective action for non-local modified Gauss–Bonnet gravity in de Sitter space,” Eur. Phys. J. C 64 (3), 483 (2009); arXiv: 0905.0543.ADSCrossRefMATHGoogle Scholar
  13. 13.
    E. Elizalde, A. N. Makarenko, V. V. Obukhov, K. E. Osetrin, and A. E. Filippov, “Stationary vs. singular points in an accelerating FRW cosmology derived from six-dimensional Einstein–Gauss–Bonnet gravity,” Phys. Lett. B 644, 1–6 (2007); hepth/0611213.ADSCrossRefMATHGoogle Scholar
  14. 14.
    K. Bamba, Z.-K. Guo, and N. Ohta, “Accelerating cosmologies in the Einstein–Gauss–Bonnet theory with dilaton,” Prog. Theor. Phys. 118, 879 (2007); arXiv: 0707.4334.ADSCrossRefMATHGoogle Scholar
  15. 15.
    A. Toporensky and P. Tretyakov, “Power-law anisotropic cosmological solution in 5 + 1-dimensional Gauss–Bonnet gravity,” Grav. Cosmol. 13, 207 (2007); arXiv: 0705.1346.ADSMATHGoogle Scholar
  16. 16.
    S. A. Pavluchenko and A. V. Toporensky, “A note on differences between (4 + 1)-and (5 + 1)-dimensional anisotropic cosmology in the presence of the Gauss–Bonnet term,” Mod. Phys. Lett. A 24, 513 (2009).ADSCrossRefGoogle Scholar
  17. 17.
    I. V. Kirnos and A. N. Makarenko, “Accelerating cosmologies in Lovelock gravity with dilaton,” Open Astron. J. 3, 37 (2010); arXiv: 0903.0083.ADSGoogle Scholar
  18. 18.
    S. A. Pavluchenko, “On the general features of Bianchi-I cosmological models in Lovelock gravity,” Phys. Rev. D 80, 107501 (2009); arXiv: 0906.0141.ADSCrossRefGoogle Scholar
  19. 19.
    I. V. Kirnos, A. N. Makarenko, S. A. Pavluchenko, and A. V. Toporensky, “The nature of singularity in multidimensional anisotropic Gauss–Bonnet cosmology with a perfect fluid,” Gen. Rel. Grav. 42, 2633 (2010); arXiv: 0906.0140.ADSCrossRefMATHGoogle Scholar
  20. 20.
    V. D. Ivashchuk, “On anisotropic Gauss–Bonnet cosmologies in (n+1) dimensions, governed by an ndimensional Finslerian 4-metric,” Grav. Cosmol. 16, 118 (2010); arXiv: 0909.5462.ADSCrossRefMATHGoogle Scholar
  21. 21.
    V. D. Ivashchuk, “On cosmological-type solutions in multidimensional model with Gauss–Bonnet term,” Int. J. Geom. Meth. Mod. Phys. 7, 797 (2010); arXiv: 0910.3426.CrossRefMATHGoogle Scholar
  22. 22.
    K.-i. Maeda and N. Ohta, “Cosmic acceleration with a negative cosmological constant in higher dimensions,” JHEP 1406, 095 (2014); arXiv: 1404.0561.ADSCrossRefMATHGoogle Scholar
  23. 23.
    D. Chirkov, S. Pavluchenko, and A. Toporensky, “Exact exponential solutions in Einstein–Gauss–Bonnet flat anisotropic cosmology,” Mod. Phys. Lett. A 29, 1450093 (2014); arXiv: 1401.2962.ADSCrossRefMATHGoogle Scholar
  24. 24.
    D. Chirkov, S. A. Pavluchenko, and A. Toporensky, “Non-constant volume exponential solutions in higher-dimensional Lovelock cosmologies,” Gen. Rel. Grav. 47, 137 (2015); arXiv: 1501.04360.ADSCrossRefMATHGoogle Scholar
  25. 25.
    V. D. Ivashchuk and A. A. Kobtsev, “On exponential cosmological type solutions in the model withGauss–Bonnet term and variation of gravitational constant,” Eur. Phys. J. C 75, 177 (2015); arXiv: 1503.00860.ADSCrossRefGoogle Scholar
  26. 26.
    S. A. Pavluchenko, “Stability analysis of exponential solutions in Lovelock cosmologies,” Phys. Rev. D 92, 104017 (2015); arXiv: 1507.01871.ADSCrossRefGoogle Scholar
  27. 27.
    S. A. Pavluchenko, “Cosmological dynamics of spatially flat Einstein–Gauss–Bonnet models in various dimensions: Low-dimensional Λ-term case,” Phys. Rev. D 94, 084019 (2016); arXiv: 1607.07347.ADSCrossRefGoogle Scholar
  28. 28.
    K. K. Ernazarov, V. D. Ivashchuk, and A. A. Kobtsev, “On exponential solutions in the Einstein–Gauss–Bonnet cosmology, stability and variation ofG,” Grav. Cosmol. 22, 245 (2016).ADSCrossRefMATHGoogle Scholar
  29. 29.
    V. D. Ivashchuk, “On stability of exponential cosmological solutions with non-static volume factor in the Einstein–Gauss–Bonnetmodel,” Eur.Phys. J. C 76, 431 (2016); arXiv: 1607.01244v2.ADSCrossRefGoogle Scholar
  30. 30.
    V. D. Ivashchuk, “On stable exponential solutions in Einstein–Gauss–Bonnet cosmology with zero variation of G,” Grav. Cosmol. 22, 329 (2016); see a corrected version in arXiv: 1612.07178.ADSCrossRefGoogle Scholar
  31. 31.
    K. K. Ernazarov and V. D. Ivashchuk, “Stable exponential cosmological solutions with zero variation of G in the Einstein–Gauss–Bonnet model with a Λ-term,” Eur. Phys. J. C 77, 89 (2017); arXiv: 1612.08451.ADSCrossRefGoogle Scholar
  32. 32.
    K. K. Ernazarov and V. D. Ivashchuk, “Stable exponential cosmological solutions with zero variation of G and three different Hubble-like parameters in the Einstein–Gauss–Bonnetmodel with a ?-term,” Eur. Phys. J. C 77, 402 (2017); arXiv: 1705.05456.ADSCrossRefGoogle Scholar
  33. 33.
    A. G. Riess et al., “Observational evidence from supernovae for an accelerating universe and a cosmological constant,” Astron. J. 116, 1009 (1998).ADSCrossRefGoogle Scholar
  34. 34.
    S. Perlmutter et al., “Measurements of omega and Lambda from 42 high-redshift supernovae,” Astrophys. J. 517, 565 (1999).ADSCrossRefMATHGoogle Scholar
  35. 35.
    M. Kowalski, D. Rubin et al., “Improved cosmological constraints from new, old and combined supernova datasets,” Ap. J. 686, 749 (2008); arXiv: 0804.4142.ADSCrossRefGoogle Scholar
  36. 36.
    P. A. R. Ade et al. [Planck Collaboration], “Planck 2013 results. I. Overview of products and scientific results,” Astron. Astrophys. 571, A1 (2014); arXiv: 1303.5076.CrossRefGoogle Scholar

Copyright information

© Pleiades Publishing, Ltd. 2017

Authors and Affiliations

  1. 1.Bauman Moscow State Technical UniversityMoscowRussia
  2. 2.Sternberg Astronomical InstituteLomonosov Moscow State UniversityMoscowRussia
  3. 3.Kazan Federal UniversityKazanRussia

Personalised recommendations