Linearizing metric-affine~(scalar curvature)² gravity -- an ``umbrella'' theory that includes as special cases the metrical, Einstein-Cartan, and Weyl quadratic models -- on top of Minkowski spacetime leads to (numerous) accidental~gauged~symmetries. This suggests that the analysis of the spectrum on flat background is hindered by strong coupling effects. Such undesirable symmetries are absent already at the leading nontrivial order in perturbations on non-flat backgrounds, e.g. de Sitter spacetime, which are the appropriate ones for studying the particle dynamics of all these theories.
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Georgios K. Karananas (2024) studied this question.
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