  We derive the Hamiltonian describing Pauli-Fierz massive gravitons on a flat
Friedmann-Robertson-Walker (FRW) cosmology in a particular, non-generic
effective field theory. The cosmological evolution is driven by a scalar field
Phi with an arbitrary potential V(Phi). The model contains two coupled scalar
modes, corresponding to the fluctuations of Phi and to the propagating scalar
component of the Pauli-Fierz graviton. In order to preserve the full gauge
invariance of the massless version of the theory, both modes have to be taken
into account. We canonically normalize the Hamiltonian and generalize the
Higuchi bound to FRW backgrounds. We discuss how this bound can set limits on
the value of the Pauli-Fierz mass parameter. We also observe that on a generic
FRW background the speed of propagation of the scalar mode of the graviton is
always smaller than the speed of light.
