Vertices in a Scalar-gravity System in the Teleparallel Gravity Theory

We consider a scalar field interacting gravitationally in teleparallel gravity theory. In this theory, the gravity is defined as a translational gauge field and thus gravita- tional interaction can be introduced through a minimal coupling prescription as in standard gauge theory. In this paper we consider scalar-gravity interacting terms of the scalar-gravity Lagrangian and derive the corresponding vertices by writing the tetrad field hμa as δaμ + bμa . We obtain six different vertices: one-gravity, two-gravity, etc. up to six-gravity vertices.