Equivalence between Palatini and metric formalisms of f(R)-gravity by divergence free current

Understand

The equivalence between metric and Palatini formalisms in f(R)-gravity can be achieved in the general context of theories with divergence free current.

• This equivalence is a necessary result of a symmetry which is included in a particular conservation equation of the current.
• In fact the conservation equation, by an appropriate redefinition of the introduced auxiliary field, may be encoded in a massless scalar field equation.