The most general Weyl-quadratic-gravity action yields manifestly gauge-covariant equations of motion, with energy-momentum and Weyl-current conservation holding in both the Weyl and Riemannian pictures.
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Conformal geometry as a gauge theory of gravity: covariant equations of motion & conservation laws
The most general Weyl-quadratic-gravity action yields manifestly gauge-covariant equations of motion, with energy-momentum and Weyl-current conservation holding in both the Weyl and Riemannian pictures.