Vacuum Persistence in Fierz-Pauli Theory on a Curved Background

Abstract

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 A. Higuchi, Nucl. Phys. B282, 397 (1987). 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 Friedmann-Robertson-Walker universe, and its corresponding bound of the deformation parameter is discussed.