Post-Newtonian approximations in the Ho\v{r}ava-Lifshitz gravity with extra U(1) symmetry

Understand

In this paper, we first propose a universal coupling between the gravity and matter in the framework of the Ho\v{r}ava-Lifshitz theory of gravity with an extra U(1) symmetry for both the projectable and non-projectable cases.

• Then, using this universal coupling we study the post-Newtonian approximations and obtain the parameterized post-Newtonian (PPN) parameters in terms of the coupling constants of the theory.
• Contrary to the previous works in which only two PPN parameters were calculated, we obtain {\it all} PPN parameters.
• We then, for the first time in either projectable or non-projectable case, find that all the solar system tests carried out so far are satisfied in a large region of the parameters space.