Abstract
In this paper we study the chameleon Jordan-Brans-Dicke (JBD) cosmological models under the hypothesis of self-similarity. Since there are several ways to define the matter Lagrangian for a perfect fluid: L m =−ρ and L m =γρ, we show that they bring us to obtain two completely different cosmological models. In the first approach, L m =−ρ, there is ordinary matter conservation, while in the second approach, L m =γρ, we get matter creation processes. We deduce for each approach the behaviour of each physical quantity, under the self-similar hypothesis, by employing the Lie group method. The results are quite general and valid for any homogeneous geometry (FRW, Bianchi types, etc.). As example, we calculate exact solutions for each approach by considering the case of a Bianchi II geometry. In this way we can determine the exact behaviour of each physical quantity and in particular of G eff and U (the potential that mimics the cosmological constant).We compare the solutions with the obtained ones in the framework of the usual JBD models.
Similar content being viewed by others
References
Amendola, L., Tsujikawa, S.: Dark Energy. Theory and Observations. Cambridge University Press, Cambridge (2010)
Belinchón, J.A.: Astrophys. Space Sci. 323, 185 (2009)
Belinchón, J.A.: Eur. Phys. J. C 72, 1866 (2012)
Belinchón, J.A.: J. Math. 2013, 169020 (2013a)
Belinchón, J.A.: Astrophys. Space Sci. 345, 387 (2013b)
Bertotti, B., Iess, L., Tortora, P.: Nature (London) 425, 374 (2003)
Bisabr, Y.: Phys. Rev. D 86, 127503 (2012)
Bluman, G.W., Anco, S.C.: Symmetry and Integration Methods for Differential Equations. Springer, Berlin (2002)
Capozziello, S., Faraoni, V.: Beyond Einstein Gravity: A Survey of Gravitational Theories for Cosmology and Astrophysics. Springer, New York (2011)
Carr, B.J., Coley, A.A.: Class. Quantum Gravity 16, R31 (1999)
Clifton, T., Ferreira, P.G., Padilla, A., Skordis, C.: Phys. Rep. 513, 1 (2012)
Coley, A.A.: Dynamical Systems and Cosmology. Kluwer Academic, Dordrecht (2003)
Das, S., Banerjee, N.: Phys. Rev. D 78, 043512 (2008)
Farajollahi, H., Salehi, A.: J. Cosmol. Astropart. Phys. 1011, 006 (2010)
Farajollahi, H., Salehi, A.: J. Cosmol. Astropart. Phys. 07, 036 (2011)
Farajollahi, H., Farhoudi, M., Salehi, A., Shojaie, H.: Astrophys. Space Sci. 337, 415 (2012)
Faraoni, V.: Cosmology in Scalar-Tensor Gravity. Kluwer Academic, Dordrecht (2004)
Faraoni, V.: Phys. Rev. D 80, 124040 (2009)
Fujii, Y., Maeda, K.: The Scalar-Tensor Theory of Gravitation. Cambridge University Press, Cambridge (2003)
Hwang, J.-C.: Class. Quantum Gravity 8, 1047 (1991)
Hwang, J.-C.: Phys. Rev. D 53, 762 (1996)
Minazzoli, O.: arXiv:1208.2372 [gr-qc] (2012)
Minazzoli, O., Harko, T.: Phys. Rev. D 86, 087502 (2012)
Nilson, U.S., et al.: Astrophys. J. 521, L1 (1999)
Perrotta, F., Baccigalupi, C., Matarrese, S.: Phys. Rev. D 61, 023507 (1999)
Rosquist, K., Jantzen, R.: Class. Quantum Gravity 2, L129 (1985)
Saaidi, Kh., Mohammadi, A., Sheikhahmadi, H.: Phys. Rev. D 83, 104019 (2011)
Setare, M.R., Jamil, M.: Phys. Lett. B 690, 1–4 (2010)
Sheykhi, A., Jamil, M.: Phys. Lett. B 694, 284–288 (2011)
Acknowledgements
The author is extremely grateful to the referee for his/her valuable comments and suggestions.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Belinchón, J.A. Self-similar chameleon Jordan-Brans-Dicke cosmological models. Astrophys Space Sci 348, 571–581 (2013). https://doi.org/10.1007/s10509-013-1595-y
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10509-013-1595-y