Stability of non-degenerate Ricci-type Palatini theories

Abstract

We study the stability of theories where the gravitational action has arbitrary algebraic dependence on the three first traces of the Riemann tensor: the Ricci tensor, the co-Ricci tensor, and the homothetic curvature tensor. We collectively call them Ricci-type tensors. We allow arbitrary coupling to matter. We consider the case when the connection is unconstrained, and the cases when either torsion or non-metricity is assumed to vanish. We find which combinations of Ricci-type tensors lead to new degrees of freedom around Minkowski and FLRW space, and when there are ghosts. None of the theories with new degrees of freedom are healthy, except for two previously known cases where there is a single new vector. We find that projective invariance is not a sufficient condition for a theory to be ghost-free.

17+8 pages, no figures. v2: Changed one sentence in introduction, added references. Published version. v3: Corrected a calculation. No effect on which theories are stable. Agrees with the published erratum. v4: Corrected a calculation, now have one more stable class of theories. Agrees with the second published erratum

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Cited by in corpus (8)

• Coupling Metric-Affine Gravity to the Standard Model and Dark Matter Fermions
• Inflation and reheating in quadratic metric-affine gravity with derivative couplings
• Einstein-Proca theory from the Einstein-Cartan formulation
• The Gauss-Bonnet topological scalar in the Geometric Trinity of Gravity
• General Einstein-Cartan quadratic gravity with derivative couplings
• Scalar fields with derivative coupling to curvature in the Palatini and the metric formulation
• Hamiltonian analysis of metric-affine-$R^2$ theory
• Inflation with the Chern-Simons term in the Palatini formulation