Palatini f(R) Gravity
In Palatini f(R) gravity, one treats the metric and connection independently and varies the action with respect to each of them separately. The matter Lagrangian is assumed to be independent of the connection. These theories have been shown to be equivalent to Brans–Dicke theory with ω = −3/2. Due to the structure of the theory, however, Palatini f(R) theories appear to be in conflict with the Standard Model, may violate Solar system experiments, and seem to create unwanted singularities.
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