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We continue the exploration of the consistency of a modified-gravity theorythat generalizes General Relativity by including a dynamical torsion inaddition to the dynamical metric. The six-parameter theory we consider wasfound to be consistent around arbitrary torsionless Einstein backgrounds, inspite of its containing a (notoriously delicate) massive spin-2 excitation. Atzero bare cosmological constant, this theory was found to admit aself-accelerating solution whose exponential expansion is sustained by anon-zero torsion background. The scalar-type perturbations of the lattertorsionfull self-accelerating solution were recently studied and were found topreserve the number of propagating scalar degrees of freedom, but to exhibit,for some values of the torsion background some exponential instabilities (of arather mild type). Here, we study the tensor-type and vector-type perturbationsof the torsionfull self-accelerating solution, and of its deformation by anon-zero bare cosmological constant. We find strong, "gradient" instabilitiesin the vector sector. No tuning of the parameters of the theory can kill theseinstabilities without creating instabilities in the other sectors. Further workis needed to see whether generic torsionfull backgrounds are prone tocontaining gradient instabilities, or if the instabilities we found are mainlydue to the (generalized) self-accelerating nature of the special de Sitterbackgrounds we considered.

Infrared modified gravity with propagating torsion: instability of torsionfull de Sitter-like solutions