  We investigate generally covariant theories which admit a Fierz-Pauli mass
term for metric perturbations around an arbitrary curved background. For this
we restore the general covariance of the Fierz-Pauli mass term by introducing
four scalar fields which preserve a certain internal symmetry in their
configuration space. It is then apparent that for each given spacetime metric
this construction corresponds to a completely different generally covariant
massive gravity theory with different symmetries. The proposed approach is
verified by explicit analysis of the physical degrees of freedom of massive
graviton on de Sitter space.
