Towards the Einstein-Hilbert action via conformal transformation

A conformal transformation is used to prove that a general theory with the action S=F $d^D$x √-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 $R^2$-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.