https://doi.org/10.1140/epjc/s10052-014-3125-7
Regular Article - Theoretical Physics
Elliptic solutions of generalized Brans–Dicke gravity with a non-universal coupling
1
Laboratoire Univers et Théories (LUTh), Observatoire de Paris, Place Jules Janssen 5, 92190, Meudon, France
2
Institute of Gravitation and Cosmology, Peoples’ Friendship University of Russia, 6 Miklukho-Maklaya Str., Moscow, 117198, Russia
* e-mail: siedhe@gmail.com
Received:
16
April
2014
Accepted:
5
October
2014
Published online:
29
October
2014
We study a model of the generalized Brans–Dicke gravity presented in both the Jordan and in the Einstein frames, which are conformally related. We show that the scalar field equations in the Einstein frame are reduced to the geodesics equations on the target space of the nonlinear sigma model. The analytical solutions in elliptical functions are obtained when the conformal couplings are given by reciprocal exponential functions. The behavior of the scale factor in the Jordan frame is studied using numerical computations. For certain parameters the solutions can describe an accelerated expansion. We also derive an analytical approximation in exponential functions.
© SIF and Springer-Verlag Berlin Heidelberg, 2014
