Universality of the Einstein theory of gravitation

We show that generalizations of general relativity theory, which consist in replacing the Hilbert Lagrangian L-Hilbert = 1/16 pi root vertical bar g vertical bar R by a generic scalar density L = L(g(mu nu), R-mu nu kappa(lambda)) depending upon the metric g(mu nu) and the curvature tensor R-mu nu kappa(lambda), are equivalent to the conventional Einstein theory for a (possibly) different metric tensor (g) over tilde (mu nu) and (possibly) a different set of matter fields. The simple proof of this theorem relies on a new approach to variational problems containing metric and connection.