Preferred frame parameters in the tensor-vector-scalar theory of gravity and its generalization

The Tensor-Vector-Scalar theory of gravity, which was designed as a relativistic implementation to the modified dynamics paradigm, has fared quite well as an alternative to dark matter, on both galactic and cosmological scales. However, its performance in the solar system, as embodied in the post-Newtonian formalism, has not yet been fully investigated. Tamaki has recently attempted to calculate the preferred frame parameters for TeVeS, but ignored the cosmological value of the scalar field, thus concluding that the Newtonian potential must be static in order to be consistent with the vector equation. We show that when the cosmological value of the scalar field is taken into account, there is no constraint on the Newtonian potential; however, the cosmological value of the scalar field is tightly linked to the vector field coupling constant K, preventing the former from evolving as predicted by its equation of motion. We then proceed to investigate the post-Newtonian limit of a generalized version of TeVeS, with Æther type vector action, and show that its \beta,\gamma and \xi parameters are as in GR, while solar system constraints on the preferred frame parameters \alpha_1 and \alpha_2 can be satisfied within a modest range of small values of the scalar and vector fields coupling parameters, and for values of the cosmological scalar field consistent with evolution within the framework of existing models.