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Gravitation and Cosmology

, Volume 25, Issue 2, pp 164–168 | Cite as

Examples of Stable Exponential Cosmological Solutions with Three Factor Spaces in EGB Model with a Λ-Term

  • K. K. ErnazarovEmail author
  • V. D. Ivashchuk
Article
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Abstract

We deal with the Einstein-Gauss-Bonnet model in dimension D with a cosmological constant. We obtain three stable cosmological solutions with exponential behavior (in time) of three scale factors, corresponding to subspaces of dimensions (l0l1l2 = 3, 4, 4), (3, 3, 2), (3, 4, 3) and D = 12, 9, 11, respectively. Any of the solutions may describe an exponential expansion of 3D subspace governed by the Hubble parameter H. Two of them may also describe a small enough variation of the effective gravitational constant G (in Jordan’s frame) for certain values of Λ.

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References

  1. 1.
    B. Zwiebach, “Curvature squared terms and string theories,” Phys. Lett. B 156, 315 (1985).CrossRefGoogle Scholar
  2. 2.
    E. S. Fradkin and A. A. Tseytlin, “Effective action approach to superstring theory,” Phys. Lett. B 160, 69–76 (1985).CrossRefGoogle Scholar
  3. 3.
    D. Gross and E. Witten, “Superstrings modifications of Einstein’s equations,” Nucl. Phys. B 277, 1 (1986).MathSciNetCrossRefGoogle Scholar
  4. 4.
    H. Ishihara, “Cosmological solutions of the extended Einstein gravity with the Gauss-Bonnet term,” Phys. Lett. B 179, 217 (1986).MathSciNetCrossRefGoogle Scholar
  5. 5.
    N. Deruelle, “On the approach to the cosmological singularity in quadratic theories of gravity: the Kasner regimes,” Nucl. Phys. B 327, 253–266 (1989).MathSciNetCrossRefGoogle Scholar
  6. 6.
    I. V. Kirnos and A. N. Makarenko, “Accelerating cosmologies in Lovelock gravity with dilaton,” Open Astron. J. 3, 37–48 (2010); arXiv: 0903.0083.Google Scholar
  7. 7.
    S. A. Pavluchenko, “On the general features of Bianchi-I cosmological models in Lovelock gravity,” Phys. Rev. D 80, 107501 (2009); arXiv: 0906.0141.MathSciNetCrossRefGoogle Scholar
  8. 8.
    V. D. Ivashchuk, “On anisotropic Gauss-Bonnet cosmologies in (n + 1) dimensions, governed by an n-dimensional Finslerian 4-metric,” Grav. Cosmol. 16(2), 118–125 (2010); arXiv: 0909.5462.MathSciNetCrossRefzbMATHGoogle Scholar
  9. 9.
    V. D. Ivashchuk, “On cosmological-type solutions in multidimensional model with Gauss-Bonnet term, Int. J. Geom. Meth. Mod. Phys. 7(5), 797–819 (2010); arXiv: 0910.3426.CrossRefzbMATHGoogle Scholar
  10. 10.
    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.MathSciNetCrossRefzbMATHGoogle Scholar
  11. 11.
    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.MathSciNetCrossRefzbMATHGoogle Scholar
  12. 12.
    V. D. Ivashchuk and A. A. Kobtsev, “On exponential cosmological type solutions in the model with Gauss-Bonnet term and variation of gravitational constant,” Eur. Phys. J. C 75,177 (12 pages) (2015); arXiv: 1503.00860.Google Scholar
  13. 13.
    S. A. Pavluchenko, “Stability analysis of exponential solutions in Lovelock cosmologies,” Phys. Rev. D 92, 104017 (2015); arXiv: 1507.01871.MathSciNetCrossRefGoogle Scholar
  14. 14.
    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.MathSciNetCrossRefGoogle Scholar
  15. 15.
    K. K. Ernazarov, V. D. Ivashchuk, and A. A. Kobtsev, “On exponential solutions in the Einstein-Gauss-Bonnet cosmology, stability and variation of G,” Grav. Cosmol. 22(3), 245–250 (2016).MathSciNetCrossRefzbMATHGoogle Scholar
  16. 16.
    V. D. Ivashchuk, “On stability of exponential cosmological solutions with non-static volume factor in the Einstein-Gauss-Bonnet model, Eur. Phys. J. C 76, 431 (2016); arXiv: 1607.01244.CrossRefGoogle Scholar
  17. 17.
    V. D. Ivashchuk, On stable exponential solutions in Einstein-Gauss-Bonnet cosmology with zero variation of G, Grav. Cosmol. 22(4), 329–332 (2016); Erratum, Grav. Cosmol. 23 (4), 401 (2017).MathSciNetCrossRefzbMATHGoogle Scholar
  18. 18.
    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-Bonnet model with a Λ-term,” Eur. Phys. J. C 77, 402 (2017); arXiv: 1705.05456.CrossRefGoogle Scholar
  19. 19.
    D. M. Chirkov and A. V. Toporensky, “On stable exponential cosmological solutions in the EGB model with a cosmological constant in dimensions D = 5,6,7,8,” Grav. Cosmol. 23(4), 359–366 (2017); arXiv: 1706.08889.MathSciNetCrossRefzbMATHGoogle Scholar
  20. 20.
    A.G. Riess et al., “Observational evidence from supernovae for an accelerating universe and a cosmological constant,” Astron. J. 116, 1009–1038 (1998).CrossRefGoogle Scholar
  21. 21.
    S. Perlmutter et al. “Measurements of Omega and Lambda from 42 high-redshift supernovae,” Astroph. J. 517, 565–586 (1999).CrossRefzbMATHGoogle Scholar
  22. 22.
    M. Kowalski, D. Rubin, et al., “Improved cosmological constraints from new, old and combined supernova datasets,” Astroph. J. 686(2), 749–778 (2008); arXiv: 0804.4142.CrossRefGoogle Scholar
  23. 23.
    P. A. R. Ade et al. (Planck Collaboration), “Planck 2013 results. Overview of products and scientific results,” Astron. Astrophys. 571, A1 (2014); arXiv: 1303.5076.CrossRefGoogle Scholar
  24. 24.
    M. Rainer and A. Zhuk, “Einstein and Brans-Dicke frames in multidimensional cosmology,” Gen. Rel. Grav. 32, 79–104 (2000); gr-qc/9808073.MathSciNetCrossRefzbMATHGoogle Scholar
  25. 25.
    V. D. Ivashchuk and V. N. Melnikov, “Multidimensional gravity with Einstein internal spaces,” Grav. Cosmol. 2(3), 211–220 (1996); hep-th/9612054.zbMATHGoogle Scholar
  26. 26.
    K. A. Bronnikov, V. D. Ivashchuk, and V. N. Melnikov, “Time variation of gravitational constant in multidimensional cosmology,” Nuovo Cim. B 102, 209–215 (1988).CrossRefGoogle Scholar
  27. 27.
    V. N. Melnikov, “Models of G time variations in diverse dimensions,” Front. Phys. China 4, 75–93 (2009).CrossRefGoogle Scholar
  28. 28.
    E. V. Pitjeva, “Updated IAA RAS planetary ephemerides-EPM2011 and their use in scientific research,” Astron. Vestnik 47(5), 419–435 (2013); arXiv: 1308.6416.Google Scholar

Copyright information

© Pleiades Publishing, Ltd. 2019

Authors and Affiliations

  1. 1.Peoples’ Friendship University of Russia (RUDN University)MoscowRussia
  2. 2.Center for Gravitation and Fundamental MetrologyVNIIMSMoscowRussia

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