  Dipolar Dark Matter (DDM) is an alternative model motivated by the challenges
faced by the standard cold dark matter model to describe the right
phenomenology at galactic scales. A promising realisation of DDM was recently
proposed in the context of massive bigravity theory. The model contains dark
matter particles, as well as a vector field coupled to the effective composite
metric of bigravity. This model is completely safe in the gravitational sector
thanks to the underlying properties of massive bigravity. In this work we
investigate the exact decoupling limit of the theory, including the
contribution of the matter sector, and prove that it is free of ghosts in this
limit. We conclude that the theory is acceptable as an Effective Field Theory
below the strong coupling scale.
