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. We calculate the post-Newtonian parameters for TeVeS with the cosmological value of the scalar field taken into account, and show that in this situation 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 show that generalizing TeVeS to have an Æther-type vector action, as suggested by Skordis, removes the aforesaid link, and this generalized version of TeVes has its $\beta$, $\gamma$, and $\xi$ parameterized post-Newtonian parameters identical to those 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 cosmological values of the scalar field consistent with evolution within the framework of existing cosmological models.

Figure 1

The region in the $K-K_{+}$ plane for which ${\alpha }_1$, ${\alpha }_2=0$, with ${\varphi }_0=0.003$, $k$ and $K_2$ in the range [0, 0.3], and $K+K_{+}-K_4=0.01$ is shown in color. The shading of the region shows the value of $K_2$; a lighter hue corresponds to a higher value. $K_2$ increases with increasing $K$, whereas $k$ increases with increasing $K_{+}$.

Figure 2

The region in the $K-K_{+}$ plane for which ${\alpha }_1$, ${\alpha }_2=0$, with ${\varphi }_0=0.003$, $k$ and $K_2$ in the range [0, 0.3], and $K+K_{+}-K_4=0.001$ is shown in color. The shading of the region shows the value of $K_2$; a lighter hue corresponds to a higher value. $K_2$ increases with increasing $K$, whereas $k$ increases with increasing $K_{+}$.