  By explicitly constructing the Hilbert space, Higuchi showed that there is a
lower bound on the mass of a minimally-coupled free spin-2 field on a curved
background \cite{HiguchiBound}. Using the vacuum persistence amplitude, we show
that this bound is modified by taking into account additional terms not
prohibited by symmetry in the case of a maximally symmetric spacetime. This
result can further be generalized to the maximally symmetric space case, such
as the FRW universe, and its corresponding bound of the deformation parameter
is discussed.
