On the "Legendre scalarization" of nonlinear gravity theories

We discuss the proposal of a new method to transform a f® metric gravity theory into a general relativistic theory including an auxiliary scalar field, recently introduced by S. Cotsakis et al. We argue that (i) the fact that the fourth order equations of f® metric gravity can be recast (via a Legendre transformation) into Einstein equations without any conformal rescaling has been thoroughly clarified in the previous literature, and (ii) the newly proposed method produces a set of equations that are not equivalent to the original theory. In the conclusion, a comment is added on another aspect of the Legendre transformation which seems to be generally overlooked.