Ghosts & Matter Couplings in Massive (bi-&multi-)Gravity
  Recently, several works have investigated the coupling to matter in
ghost-free massive (bi-&multi-)gravity and a new effective coupling to matter
has been proposed. In this note we clarify some confusion on the existence and
the implications of a ghost above the strong coupling scale. We confirm that
the standard constraint which is otherwise typically present in this type of
theories disappears on generic backgrounds as soon as this new coupling is
considered. This implies the re-emergence of the Boulware-Deser ghost.
Nevertheless the absence of ghost in the decoupling limit implies that the
cut-off scale (if identified with the scale at which the ghost enters) is
higher than the strong coupling scale. Therefore there is a valid interesting
region of applicability for these couplings at scales below the cut-off.
