Towards the Einstein-Hilbert action via conformal transformation

Abstract

A conformal transformation is used to prove that a general theory with the action S=F${d}^{D}$x \ensuremath{\surd}-g [F(\ensuremath{\varphi},R)-(\ensuremath{\epsilon}/2)(\ensuremath{\nabla}\ensuremath{\varphi}${)}^{2}$], where F(\ensuremath{\varphi},R) is an arbitrary function of a scalar \ensuremath{\varphi} 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.