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

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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. B. Zwiebach, “Curvature squared terms and string theories,” Phys. Lett. B 156, 315 (1985).

    Article  ADS  Google Scholar 

  2. E. S. Fradkin and A. A. Tseytlin, “Effective action approach to superstring theory,” Phys. Lett. B 160, 69–76 (1985).

    Article  ADS  Google Scholar 

  3. D. Gross and E. Witten, “Superstrings modifications of Einstein’s equations,” Nucl. Phys. B 277, 1 (1986).

    Article  MathSciNet  ADS  Google Scholar 

  4. H. Ishihara, “Cosmological solutions of the extended Einstein gravity with the Gauss-Bonnet term,” Phys. Lett. B 179, 217 (1986).

    Article  MathSciNet  ADS  Google Scholar 

  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).

    Article  MathSciNet  ADS  Google Scholar 

  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.

    ADS  Google Scholar 

  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.

    Article  MathSciNet  ADS  Google Scholar 

  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.

    Article  MathSciNet  MATH  ADS  Google Scholar 

  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.

    Article  MATH  Google Scholar 

  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.

    Article  MathSciNet  MATH  ADS  Google Scholar 

  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.

    Article  MathSciNet  MATH  ADS  Google Scholar 

  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. S. A. Pavluchenko, “Stability analysis of exponential solutions in Lovelock cosmologies,” Phys. Rev. D 92, 104017 (2015); arXiv: 1507.01871.

    Article  MathSciNet  ADS  Google Scholar 

  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.

    Article  MathSciNet  ADS  Google Scholar 

  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).

    Article  MathSciNet  MATH  ADS  Google Scholar 

  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.

    Article  ADS  Google Scholar 

  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).

    Article  MathSciNet  MATH  ADS  Google Scholar 

  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.

    Article  ADS  Google Scholar 

  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.

    Article  MathSciNet  MATH  ADS  Google Scholar 

  20. A.G. Riess et al., “Observational evidence from supernovae for an accelerating universe and a cosmological constant,” Astron. J. 116, 1009–1038 (1998).

    Article  ADS  Google Scholar 

  21. S. Perlmutter et al. “Measurements of Omega and Lambda from 42 high-redshift supernovae,” Astroph. J. 517, 565–586 (1999).

    Article  MATH  ADS  Google Scholar 

  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.

    Article  ADS  Google Scholar 

  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.

    Article  Google Scholar 

  24. M. Rainer and A. Zhuk, “Einstein and Brans-Dicke frames in multidimensional cosmology,” Gen. Rel. Grav. 32, 79–104 (2000); gr-qc/9808073.

    Article  MathSciNet  MATH  ADS  Google Scholar 

  25. V. D. Ivashchuk and V. N. Melnikov, “Multidimensional gravity with Einstein internal spaces,” Grav. Cosmol. 2(3), 211–220 (1996); hep-th/9612054.

    MATH  Google Scholar 

  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).

    Article  ADS  Google Scholar 

  27. V. N. Melnikov, “Models of G time variations in diverse dimensions,” Front. Phys. China 4, 75–93 (2009).

    Article  ADS  Google Scholar 

  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 

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Ernazarov, K.K., Ivashchuk, V.D. Examples of Stable Exponential Cosmological Solutions with Three Factor Spaces in EGB Model with a Λ-Term. Gravit. Cosmol. 25, 164–168 (2019). https://doi.org/10.1134/S0202289319020063

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  • DOI: https://doi.org/10.1134/S0202289319020063

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