  Just like the vector gauge bosons in the gauge theories, it is now known that
gravitons acquire mass in the process of spontaneous symmetry breaking of
diffeomorphisms through the condensation of scalar fields. The point is that we
should find the gravitational Higgs mechanism such that it results in massive
gravity in a flat Minkowski space-time without non-unitary propagating modes.
This is usually achieved by including higher-derivative terms in scalars and
tuning the cosmological constant to be a negative value in a proper way.
Recently, a similar but different gravitational Higgs mechanism has been
advocated by Chamseddine and Mukhanov where one can relax the negative
cosmological constant to zero or positive one. In this work, we investigate why
the non-unitary ghost mode decouples from physical Hilbert space in a general
space-time dimension. Moreover, we generalize the model to possess an arbitrary
potential and clarify under what conditions the general model exhibits the
gravitational Higgs mechanism. By searching for solutions to the conditions, we
arrive at two classes of potentials exhibiting gravitational Higgs mechanism.
One class includes the model by Chamseddine and Mukhanov in a specific case
while the other is completely a new model.
