Massive Spin-2 fields of Geometric Origin in Curved Spacetimes

We study the consistency of a model which includes torsion as well as the metric as dynamical fields and has massive spin-2 particle in its spectrum. The massive spin-2 mode resides in the torsion, rather than in the metric. It is known that this model is tachyon- and ghost-free in Minkowski background. We show that this property remains valid and no other pathologies emerge in de Sitter and anti-de Sitter backgrounds, with some of our results extending to arbirary Einstein space backgrounds. This suggests that the model is consistent, at least at the classical level, unlike, e.g., the Fierz--Pauli theory.