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Non-constant volume exponential solutions in higher-dimensional Lovelock cosmologies

  • Dmitry Chirkov
  • Sergey A. Pavluchenko
  • Alexey Toporensky
Research Article

Abstract

In this paper we propose a scheme which allows one to find all possible exponential solutions of special class—non-constant volume solutions—in Lovelock gravity in arbitrary number of dimensions and with arbitrate combinations of Lovelock terms. We apply this scheme to (\(6+1\))- and (\(7+1\))-dimensional flat anisotropic cosmologies in Einstein–Gauss–Bonnet and third-order Lovelock gravity to demonstrate how our scheme does work. In course of this demonstration we derive all possible solutions in (\(6+1\)) and (\(7+1\)) dimensions and compare solutions and their abundance between cases with different Lovelock terms present. As a special but more “physical” case we consider spaces which allow three-dimensional isotropic subspace for they could be viewed as examples of compactification schemes. Our results suggest that the same solution with three-dimensional isotropic subspace is more “probable” to occur in the model with most possible Lovelock terms taken into account, which could be used as kind of anthropic argument for consideration of Lovelock and other higher-order gravity models in multidimensional cosmologies.

Keywords

Lovelock gravity Exact solutions Multidimensional cosmology Modified gravity 

Notes

Acknowledgments

The work of A.T. is supported by RFBR Grant 14-02-00894 and partially supported by the Russian Government Program of Competitive Growth of Kazan Federal University. S.A.P. is supported by FONDECYT via Grant No. 3130599.

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Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  • Dmitry Chirkov
    • 1
    • 2
  • Sergey A. Pavluchenko
    • 3
  • Alexey Toporensky
    • 1
    • 4
  1. 1.Sternberg Astronomical InstituteMoscow State UniversityMoscowRussia
  2. 2.Faculty of PhysicsMoscow State UniversityMoscowRussia
  3. 3.Instituto de Ciencias Físicas y MatemáticasUniversidad Austral de ChileValdiviaChile
  4. 4.Kazan Federal UniversityKazanRussia

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