Nonsymmetric tensor description of massive spin-2 particles in a curved background

Massive spin-2 particles have been a subject of great interest in current research. If the graviton has a small mass, the gravitational force at large distances decreases more rapidly, which could contribute to the explanation of the accelerated expansion of the Universe. The massive spin-2 particles are commonly described by the known Fierz-Pauli action which is formulated in terms of a symmetric tensor hμν=hνμ. However, the Fierz-Pauli theory is not the only possible description of massive spin-2 particles via a rank-2 tensor. There are other two families of models L(a1) and LnFP(c), where a1 and c are real arbitrary parameters, which describe massive particles of spin-2 in the flat space via a nonsymmetric tensor eμν≠eνμ. In the present work we derive Lagrangian constraints stemming from L(a1) and LnFP(c) in curved backgrounds with nonminimal couplings which are analytic functions of m2. We show that the constraints lead to a correct counting of degrees of freedom if nonminimal terms are included with fine-tuned coefficients and the background space is of the Einstein type, very much like the Fierz-Pauli case. We also examine the existence of local symmetries.