Towards the Einstein-Hilbert action via conformal transformation

A conformal transformation is used to prove that a general theory with the action S=FdDx {}-g [F({φ},R)-({ε}/2)({∇}{φ})²], where F({φ},R) is an arbitrary function of a scalar {φ} and a scalar curvature R, is equivalent to a system described by the Einstein-Hilbert action plus scalar fields. This equivalence is a simple extension of those in R²-gravity theory and the theory with nonminimal coupling. The case of F=L(R), where L(R) is an arbitrary polynomial of R, is discussed as an example.