A note on dualities in Einstein's gravity in the presence of a non-minimally coupled scalar field

We show that the action of Einstein’s gravity with a scalar field coupled in a generic way to spacetime curvature is invariant under a particular set of conformal transformations. These transformations relate dual theories for which the effective couplings of the theory are scaled uniformly. In the simplest case, this class of dualities reduce to the S-duality of low-energy effective action of string theory.