Russian Physics Journal

, Volume 56, Issue 7, pp 725–730 | Cite as

New class of cosmological solutions for a self-interacting scalar field

  • A. A. Chaadaev
  • S. V. Chervon
Elementary Particle Physics and Field Theory

New cosmological solutions are found to the system of Einstein scalar field equations using the scalar field φ as the argument. For a homogeneous and isotropic Universe, the system of equations is reduced to two equations, one of which is an equation of Hamilton–Jacobi type. Using the hyperbolically parameterized representation of this equation together with the consistency condition, explicit dependences of the potential V of the scalar field and the Hubble parameter H on φ are obtained. The dependences of the scalar field and the scale factor a on cosmic time t have also been found. It is shown that this scenario corresponds to the evolution of the Universe with accelerated expansion out to times distant from the initial singularity.


cosmology scalar fields exact solutions accelerated expansion of the Universe 


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  1. 1.
    G. G. Ivanov, in: Gravitation and the Theory of Relativity [in Russian], V. R. Kaigorodov, ed., Kazan’ State University Press, Kazan’ (1981), Vol. 18, pp. 54–60.Google Scholar
  2. 2.
    J. D. Barrow, Phys. Lett., B187, 12–16 (1987); A. B. Burd and J. D. Barrow, Nucl. Phys., B308, 929–945 (1988); J. D. Barrow, Phys. Rev., D49, 3055 (1994).Google Scholar
  3. 3.
    A. G. Muslimov, Class. Quantum Grav., 7, 231 (1990).MathSciNetADSCrossRefGoogle Scholar
  4. 4.
    J. J. Halliwell, Phys. Lett., B187, 341–344 (1987).MathSciNetADSCrossRefGoogle Scholar
  5. 5.
    G. Ellis and M. Madsen, Class. Quantum Grav., 8, 667–676 (1991).MathSciNetADSCrossRefMATHGoogle Scholar
  6. 6.
    S. V. Chervon and V. M. Zhuravlev, Russ. Phys. J., 39, No. 8, 776–789 (1996).MathSciNetCrossRefGoogle Scholar
  7. 7.
    T. Padmanabhan, аrXiv:hep-th/0204415.Google Scholar
  8. 8.
    S. V. Chervon and V. M. Zhuravlev, Russ. Phys. J., 43, No. 1, 11–17 (2000); V. M. Zhuravlev and S. V. Chervon, Zh. Eksp. Teor. Fiz., 118, No. 2, 259–272 (2000).Google Scholar
  9. 9.
    S. V. Chervon, Gen. Relativ. Gravit., 36, 1547–1553 (2004).MathSciNetADSCrossRefMATHGoogle Scholar
  10. 10.
    S. V. Chervon, O. G. Panina, and M. Sami, Vestnik Samarsk. Gosud. Tekhn. Univ., Ser. Fiz-Mat. Nauki, No. 3, 221–226 (2010).Google Scholar
  11. 11.
    A. V. Yurov, V. A. Yurov, S. V. Chervon, and M. Sami, Teor. Mat. Fiz., 166, No. 2, 258–268 (2011).CrossRefGoogle Scholar
  12. 12.
    S. V. Chervon, Nonlinear Fields in Gravitation Theory and Cosmology [in Russian], Ul’yanovsk State University Press, Ul’yanovsk (1997).Google Scholar
  13. 13.
    L. P. Chimento and A. S. Jakubi, arXiv: gr-qc/950615 v1 7 Jun 1995.Google Scholar
  14. 14.
    L. A. Urena-Lopez and T. Matos, arXiv: astro-ph/0003364 v1 23 Mar 2000.Google Scholar
  15. 15.
    S. P. Starkovich and F. I. Cooperstock, Astrophys. J., 398, 1–11 (1992).ADSCrossRefGoogle Scholar

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© Springer Science+Business Media New York 2013

Authors and Affiliations

  1. 1.Ul’yanovsk State Pedagogical UniversityUl’yanovskRussia

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