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

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 Ω 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 ω and Ω, we demonstrate that (i) the model does not contradict gravitational tests relevant to the parameterized post-Newtonian parameter γ, and (ii) the scalar field is not ghost in the case of nonzero |Ω|∼O(1) along with the natural value |ω|∼O(1). In the general case of a massive scalar field, the metric coefficients acquire the Yukawa correction terms, where the Yukawa mass scale m is defined by the mass of the scalar field. For the natural value ω∼O(1), the inverse-square-law experiments impose the following restriction on the lower bound of the mass: m≳10−11 GeV. The experimental constraints on γ require that Ω be extremely close to −1/2.