Advertisement

The Lambda-CDM Model Is Not an Universal Attractor of the Brans–Dicke Cosmology

  • Israel QuirosEmail author
Chapter
Part of the Fundamental Theories of Physics book series (FTPH, volume 183)

Abstract

By means of the tools of the dynamical systems theory it is shown that the general relativity de Sitter solution is an attractor of the Jordan frame (dilatonic) Brans–Dicke theory only for the exponential potential \(U(\varphi )\propto \exp \varphi \), which corresponds to the quadratic potential \(V(\phi )\propto \phi ^2\) in terms of the original Brans–Dicke field \(\phi =\exp \varphi \), or for potentials which approach to \(\exp \varphi \) at the stable point. I find bounds on the Brans–Dicke coupling constant \(\omega _\textsc {bd}\), which are consistent with well-known results.

Keywords

Cold Dark Matter Jordan Frame Sitter Solution Exponential Potential Cold Dark Matter Model 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Notes

Acknowledgments

I want to thank T Asselmeyer-Maluga for inviting me to join this initiative to celebrate the 80th birthday of one of the greatest minds of the XX century, our dear fiend Carl H. Brans, to whom I am profoundly indebted. I want to acknowledge, also, J D Barrow, S D Odintsov and A Alho, for pointing to me several indispensable bibliographic references. Thanks are due to CONACyT of México for support of this research. I am grateful to SNI-CONACyT for continuous support of my research activity.

References

  1. 1.
    C. Brans, R.H. Dicke, Phys. Rev. 124, 925–935 (1961)ADSMathSciNetCrossRefGoogle Scholar
  2. 2.
    Th.P. Sotiriou, V. Faraoni, Rev. Mod. Phys. 82, 451–497 (2010), arXiv:0805.1726 Google Scholar
  3. 3.
    Y. Fujii, K.-I. Maeda, The Scalar-Tensor Theory of Gravitation (Cambridge University Press, UK, 2003)zbMATHGoogle Scholar
  4. 4.
    V. Faraoni, Cosmology in Scalar-Tensor Gravity (Kluwer Academic Publishers, The Netherlands, 2004)CrossRefzbMATHGoogle Scholar
  5. 5.
    J. Khoury, A. Weltman, Phys. Rev. Lett. 93, 171104 (2004), arXiv:astro-ph/0309300; Phys. Rev. D 69, 044026 (2004), arXiv:astro-ph/0309411
  6. 6.
    S. Sen, T.R. Seshadri, Int. J. Mod. Phys. D 12, 445–460 (2003), arXiv:gr-qc/0007079; D.F. Torres, Phys. Rev. D 66, 043522 (2002), arXiv:astro-ph/0204504; N. Banerjee, D. Pavon, Class. Quant. Grav. 18, 593 (2001), arXiv:gr-qc/0012098
  7. 7.
    P.A.R. Ade et al., Planck Collaboration. Astron. Astrophys. 571, A23 (2014), arXiv:1303.5083
  8. 8.
    P.J.E. Peebles, B. Ratra, Rev. Mod. Phys. 75, 559–606 (2003), arXiv:astro-ph/0207347; V. Sahni, A.A. Starobinsky. Int. J. Mod. Phys. D 9, 373–444 (2000), arXiv:astro-ph/9904398 Google Scholar
  9. 9.
    O. Hrycyna, M. Szydlowski, Phys. Rev. D 88(6), 064018 (2013), arXiv:1304.3300
  10. 10.
    O. Hrycyna, M. Kamionka, M. Szydlowski, Phys. Rev. D 90(12), 124040 (2014), arXiv:1404.7112
  11. 11.
    O. Hrycyna, M. Szydlowski, JCAP 1312, 016 (2013), arXiv:1310.1961
  12. 12.
    J.D. Barrow, K. Maeda, Nucl. Phys. B 341, 294–308 (1990)ADSCrossRefGoogle Scholar
  13. 13.
    J.D. Barrow, Phys. Rev. D 51, 2729–2732 (1995)ADSCrossRefGoogle Scholar
  14. 14.
    E. Elizalde, S. Nojiri, S.D. Odintsov, D. Saez-Gomez, V. Faraoni, Phys. Rev. D 77, 106005 (2008), arXiv:0803.1311
  15. 15.
    C.M. Will, Living Rev. Rel. 9, 3 (2006), arXiv:gr-qc/0510072; B. Bertotti, L. Iess, P. Tortora, Nature 425, 374 (2003)
  16. 16.
    I. Quiros, R. García-Salcedo, T. Gonzalez, F.A. Horta-Rangel, Phys. Rev. D 92(4), 044055 (2015), arXiv:1506.05420
  17. 17.
    V. Acquaviva, C. Baccigalupi, S.M. Leach, A.R. Liddle, F. Perrotta, Phys. Rev. D 71, 104025 (2005), arXiv:astro-ph/0412052
  18. 18.
    R. Nagata, T. Chiba, N. Sugiyama, Phys. Rev. D 69, 083512 (2004), arXiv:astro-ph/0311274
  19. 19.
    J.E. Lidsey, D. Wands, E.J. Copeland, Phys. Rept. 337, 343–492 (2000), arXiv:hep-th/9909061
  20. 20.
    E.J. Copeland, A.R. Liddle, D. Wands, Phys. Rev. D 57, 4686 (1998), arXiv:gr-qc/9711068 Google Scholar
  21. 21.
    A.A. Coley, arXiv:gr-qc/9910074
  22. 22.
    E.J. Copeland, M. Sami, S. Tsujikawa, Int. J. Mod. Phys. D 15, 1753–1936 (2006), arXiv:hep-th/0603057 Google Scholar
  23. 23.
    L.A. Urena-Lopez, JCAP 1203, 035 (2012), arXiv:1108.4712
  24. 24.
    C.G. Boehmer, N. Chan, arXiv:1409.5585
  25. 25.
    R. García-Salcedo, T. Gonzalez, F.A. Horta-Rangel, I. Quiros, D. Sanchez-Guzmán, Eur. J. Phys. 36(2), 025008 (2015), arXiv:1501.04851
  26. 26.
    V.I. Arnold, Ordinary Differential Equations, translated from Russian and edited by R.A. Silverman (The MIT Press, Cambridge, Massachusets and London, England, 1973); D.K. Arrowsmith, C.M. Place, Introduction to Dynamical Systems (Cambridge University Press, UK, 1990); L. Perko, Differential Equations and Dynamical Systems (Springer, USA, 2001)Google Scholar
  27. 27.
    A. Cid, G. Leon, Y. Leyva, arXiv:1506.00186
  28. 28.
    J.-P. Uzan, Rev. Mod. Phys. 75, 403 (2003), arXiv:hep-ph/0205340
  29. 29.
    F. Wu, X. Chen, Phys. Rev. D 82, 083003 (2010), arXiv:0903.0385
  30. 30.
    F.S. Accetta, L.M. Krauss, P. Romanelli, Phys. Lett. B 248, 146 (1990)ADSCrossRefGoogle Scholar
  31. 31.
    X. Chen, M. Kamionkowski, Phys. Rev. D 60, 104036 (1999), arXiv:astro-ph/9905368
  32. 32.
    V. Faraoni, Class. Quant. Grav. 26, 145014 (2009), arXiv:0906.1901
  33. 33.
    J. Wainwright, G.F.R. Ellis, Dynamical Systems in Cosmology (Cambridge University Press, Cambridge, 1997); A.A. Coley, Dynamical Systems and Cosmology (Kluwer Academic Publishers, Dordrecht Boston London, 2003)Google Scholar

Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  1. 1.Dpto. Ingeniería Civil, División de IngenieríaUniversidad de GuanajuatoLeonMexico

Personalised recommendations