Weak field limit of higher dimensional massive Brans-Dicke gravity: Observational constraints

Understand

We consider higher-dimensional massive Brans-Dicke theory with Ricci-flat internal space.

• The background model is perturbed by a massive gravitating source which is pressureless in the external (our space) but has an arbitrary equation-of-state parameter $\Omega$ in the internal space.
• We obtain the exact solution of the system of linearized equations for the perturbations of the metric coefficients and scalar field.
• For a massless scalar field, relying on the fine-tuning between the Brans-Dicke parameter $\omega$ and $\Omega$, we demonstrate that (i) the model does not contradict gravitational tests relevant to the parameterized post-Newtonian parameter $\gamma$, and (ii) the scalar field is not ghost in the case of nonzero $|\Omega|\sim O(1)$ along with the natural value $|\omega|\sim O(1)$.