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.

In this paper, we propose a toy model of the renormalizable theory describing massive spin two field. Although the model is renormalizable, we show that the model contains ghost. The coupling of the theory with gravity can be regarded as a new kind of bimetric gravity or bigravity. We show that the massive spin two field plays the role of the cosmological constant.

In Phys. Rev. D 90 043006 (2014), we proposed a new ghost-free massive spin-two model in flat spacetime. Furthermore, as some extension, we couple the new model with a non-dynamical curved background in Phys. Rev. D 90 123013 (2014) and constructed new interaction terms without appearance of an extra mode. The characteristic property of the new model is the existence of nonlinear potential terms which give the nontrivial vacua. The presence of the nontrivial vacua, however, does not mean that the particle can be defined around all vacua. Therefore, in this paper, we discuss the condition for the new model to have stable vacua in flat spacetime and curved spacetime. Then, we couple this spin-two theory with a dynamical background and obtain the solutions. Moreover, we investigate the effect of this new spin-two model to the Einstein gravity by calculating the black hole entropy since the gravity coupled with massive spin-two theory admits a black hole solution in addition to (anti-) de Sitter space solution.

A model of the self-interacting charged massive spin-two field is constructed. We investigate several properties of the model and find that the trivial vacuum is only allowed due to the internal symmetry. This suggests that the Higgs mechanism might not be induced by the model of the massive spin-two field with the ghost-free potential.

We constructed models of self-interacting charged massive spin two particles by using the interaction proposed by Hinterbichler. Then, we investigate the some basic properties of this theory.