Nonlinear massive gravity theory of geometric origin

We study the number of propagating degrees of freedom, at nonlinear order, in torsion gravity theories, a class of modified theories of gravity that include a propagating torsion in addition to the metric. We focus on a three-parameter subfamily of theories (“torsion bigravity”) that contains, at linear order, only two physical excitations: a massless spin-2 one (with 2 degrees of freedom) and a massive spin-2 one (with 5 degrees of freedom). We study the dynamics of the massive spin-2 field in the limit where the torsion field decouples from the metric. The number of degrees of freedom of the torsion field is found to change, at nonlinear order, from five to nine.