Abstract
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 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 and , we demonstrate that (i) the model does not contradict gravitational tests relevant to the parameterized post-Newtonian parameter , and (ii) the scalar field is not ghost in the case of nonzero along with the natural value . In the general case of a massive scalar field, the metric coefficients acquire the Yukawa correction terms, where the Yukawa mass scale is defined by the mass of the scalar field. For the natural value , the inverse-square-law experiments impose the following restriction on the lower bound of the mass: . The experimental constraints on require that be extremely close to .
- Received 10 July 2019
DOI:https://doi.org/10.1103/PhysRevD.101.024004
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