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Weyl gravity as general relativity
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When the full connection of Weyl conformal gravity is varied instead of just the metric, the resulting vacuum field equations reduce to the vacuum Einstein equation, up to the choice of local units, if and only if the torsion vanishes. This result differs strongly from the usual fourth-order formulation of Weyl gravity.
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Cited by 2 Pith papers
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Atomic clocks and gravitational waves as probes of non-metricity
The paper claims existing gravitational-wave data already bound Weyl non-metricity, α²ω̄0<10⁻⁶⁹ GeV, via backreaction of a Planck-scale Weyl field, but a dropped kinetic term numerically exceeds the assumed sensitivity.
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Modified gravity from Weyl connection and the $f(R,\cal{A})$ extension
Weyl-connection gravity with a dynamical vector field produces an effective dark energy sector, recovering Lambda-CDM in one class and dynamical dark energy in others.
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