Theoretical and Mathematical Physics

, Volume 194, Issue 3, pp 439–449 | Cite as

The k-Essence in the Relativistic Theory of Gravitation and General Relativity

Article

Abstract

We consider a model of a scalar field with a nontrivial kinetic part (k-essence) on the background of a flat homogeneous isotropic universe in the framework of the relativistic theory of gravitation and general relativity. Such a scalar field simulates the substance of an ideal fluid and serves as a model of dark energy because it leads to cosmological acceleration at later times. For finding a suitable cosmological scenario, it is more convenient to determine the dependence of the energy density of such a field on the scale factor and only then find the corresponding Lagrangian. Based on the solution of such an inverse problem, we show that in the relativistic theory of gravitation, either any scalar field of this type leads to instabilities, or the compression stage ends at an unacceptably early stage. We note that a consistent model of dark energy in the relativistic theory of gravitation can be a scalar field with a negative potential (ekpyrosis) of Steinhardt–Turok. In general relativity, the k-essence model is viable and can represent both dark energy and dark matter. We consider several specific k-essence models.

Keywords

RTG k-essence inverse ekpyrosis Chaplygin gas 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    A. A. Logunov, M. A. Mestvirishvili, and Yu. V. Chugreev, Graviton Mass and Evolution of a Friedmann Universe [in Russian], Moscow State Univ. Press, Moscow (1987); “Graviton mass and evolution of a Friedmann universe,” Theor. Math. Phys., 74, 1–10 (1988).Google Scholar
  2. 2.
    Yu. V. Chugreev, “Mach’s principle for cosmological solutions in relativistic theory of gravity,” PEPAN Lett., 12, 195–204 (2015).Google Scholar
  3. 3.
    M. A. Mestvirishvili and Yu. V. Chugreev, “Friedmann model of evolution of the universe in the relativistic theory of gravitation,” Theor. Math. Phys., 80, 886–891 (1989).CrossRefMATHGoogle Scholar
  4. 4.
    S. S. Gershtein, A. A. Logunov, M. A. Mestvirishvili, and N. P. Tkachenko, “Graviton mass, quintessence, and oscillatory character of Universe evolution,” Phys. Atom. Nucl., 67, 1596–1604 (2004).ADSCrossRefGoogle Scholar
  5. 5.
    S. S. Gershtein, A. A. Logunov, and M. A. Mestvirishvili, “Cosmological constant and Minkowski space,” Phys. Part. Nucl., 38, 291–298 (2007).CrossRefGoogle Scholar
  6. 6.
    M. A. Mestvirishvili, K. A. Modestov, and Yu. V. Chugreev, “Quintessence scalar field in the relativistic theory of gravity,” Theor. Math. Phys., 152, 1342–1350 (2007); arXiv:gr-qc/0612105v1 (2006).MathSciNetCrossRefMATHGoogle Scholar
  7. 7.
    Yu. V. Chugreev, “Dark energy and graviton mass in the nearby universe,” PEPAN Lett., 13, 38–45 (2016).Google Scholar
  8. 8.
    R. J. Sherrer, “Purely kinetic k-essence as unified dark matter,” Phys. Rev. Lett., 93, 011301 (2004); arXiv:astroph/0402316v3 (2004).ADSCrossRefGoogle Scholar
  9. 9.
    P. J. Steinhardt and N. Turok, “A cyclic model of the Universe,” Science, 296, 1436–1439 (2002); arXiv:hep-th/0111030v2 (2001).ADSMathSciNetCrossRefMATHGoogle Scholar
  10. 10.
    P. J. Steinhardt and N. Turok, “Cosmic evolution in a cyclic universe,” Phys. Rev. D, 65, 126003 (2002); arXiv:hep-th/0111098v2 (2001).ADSCrossRefGoogle Scholar
  11. 11.
    J. K. Erickson, D. H. Wesley, P. J. Steinhardt, and N. Turok, “Kasner and mixmaster behavior in universes with equation of state ω ≥ 1,” Phys. Rev. D, 69, 063514 (2004); arXiv:hep-th/0312009v2 (2003).ADSMathSciNetCrossRefGoogle Scholar
  12. 12.
    A. Ijjas and P. J. Steinhardt, “Classically stable nonsingular cosmological bounces,” Phys. Rev. Lett., 117, 121304 (2016); arXiv:1606.08880v2 [gr-qc] (2016).ADSMathSciNetCrossRefGoogle Scholar
  13. 13.
    L. P. Chimento, “Extended tachyon field, Chaplygin gas, and solvable k-essence cosmologies,” Phys. Rev. D, 69, 123517 (2004); arXiv:astro-ph/0311613v2 (2003).ADSMathSciNetCrossRefGoogle Scholar
  14. 14.
    J. Garriaga and V. F. Mukhanov, “Perturbations in k-inflation,” Phys. Lett. B, 458, 1999; arXiv:hep-th/9904176v1 (1999).MathSciNetGoogle Scholar
  15. 15.
    V. Mukhanov, Physical Foundations of Cosmology, Cambridge Univ. Press, Cambridge (2012).MATHGoogle Scholar
  16. 16.
    D. S. Gorbunov and V. A. Rubakov, Introduction to the Theory of the Early Universe: Hot Big Bang Theory [in Russian], Lenand, Moscow (2016); English transl. prev. ed., World Scientific, Singapore (2011).CrossRefMATHGoogle Scholar
  17. 17.
    D. S. Gorbunov and V. A. Rubakov, Introduction to the Theory of the Early Universe: Cosmological Perturbations and Inflationary Theory [in Russian], Krasand, Moscow (2016); English transl. prev. ed., World Scientific, Singapore (2011).CrossRefMATHGoogle Scholar

Copyright information

© Pleiades Publishing, Ltd. 2018

Authors and Affiliations

  1. 1.Lomonosov Moscow State UniversityMoscowRussia

Personalised recommendations