We have proposed a new ghost-free model with interactions of massive spin-two particles in Phys. Rev. D 90, 043006 (2014). Although the model is ghost-free on the Minkowski spacetime, it is not obvious whether or not this desirable property is preserved on curved spacetime. In fact, Buchbinder et al. already pointed out that the Fierz-Pauli theory is not ghost-free on curved spacetime without nonminimal coupling terms. In this paper, we construct a new theory of massive spin-two particles with nonminimal coupling on curved spacetime and show that the model can be ghost-free. Furthermore, we propose new nonminimal coupling terms.

• Received 21 October 2014

DOI:https://doi.org/10.1103/PhysRevD.90.123013