# Ghosts in metric-affine higher order curvature gravity

## TL;DR

This paper demonstrates that most higher order curvature gravity theories in the metric-affine formalism are not ghost-free, emphasizing the importance of projective symmetry or constraints for their physical viability.

## Contribution

It clarifies the conditions under which higher order metric-affine gravity theories avoid ghost-like instabilities, challenging previous assumptions about their general consistency.

## Key findings

- Non-projectively invariant sectors propagate ghosts.
- Imposing projective symmetry or constraints can eliminate ghosts.
- Most higher order curvature theories in metric-affine formalism are inherently pathological.

## Abstract

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.