Post-Newtonian parameter γ and the deflection of light in ghost-free massive bimetric gravity

We consider the parametrized post-Newtonian (PPN) limit of ghost-free massive bimetric gravity with two mutually noninteracting matter sectors coupled to the two metrics. Making use of a gauge-invariant differential decomposition of the metric perturbations, we solve the field equations up to the linear PPN order for a static, pointlike mass source. From the result, we derive the PPN parameter. for spherically symmetric systems, which describes the gravitational deflection of light by visible matter. By a comparison to its value measured in the Solar System, we obtain bounds on the parameters of the theory. We further discuss the deflection of light by dark matter and find an agreement with the observed light deflection by galaxies. We finally speculate about a possible explanation for the observed distribution of dark matter in galactic mergers such as Abell 520 and Abell 3827.