  We disprove the widespread belief that higher order curvature theories of
gravity in the metric-affine formalism are generally ghost-free. This is
clarified by considering a sub-class of theories constructed only with the
Ricci tensor and showing that the non-projectively invariant sector propagates
ghost-like degrees of freedom. We also explain how these pathologies can be
avoided either by imposing a projective symmetry or additional constraints in
the gravity sector. Our results put forward that higher order curvature gravity
theories generally remain pathological in the metric-affine (and hybrid)
formalisms and highlight the key importance of the projective symmetry and/or
additional constraints for their physical viability and, by extension, of
general metric-affine theories.
