Towards the Einstein-Hilbert action via conformal transformation

A conformal transformation is used to prove that a general theory with the action S=∫d/sup D/x √-g[F(phi,R)-(ε/2)(del phi)/sup 2/], where F(phi,R) is an arbitrary function of a scalar phi and ascalar 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