Massive spin 3 and Metric-Affine Gravity

A bstract Symmetric Metric-Affine Gravity is a theory of gravity with an independent non-metric connection, and zero torsion. It can be thought of as ordinary metric gravity coupled to a rank-3 tensor Q , symmetric in one pair of indices. This field carries a spin-3 degree of freedom. We find that, in contrast to the totally symmetric case, it is possible to arrange the parameters in the Lagrangian, so that, at the linearized level, the spin-3 state, either alone or in combination with a spin-0 state, has a healthy propagation.