FURTHER EXTENDED THEORIES OF GRAVITATION: PART II

We shall present and analyze two examples of extended theories of gravitation in Palatini formalism with matter that couples to the connection. This will show that the class of Further Extended Theories of Gravitation introduced in [1] does not trivially reduce to f(R) models. It will also produce an example of theory that on-shell endows space-time with a non-trivial Weyl geometry where the connection is not induced by the metric structure (though it is compatible with it in the sense of Ehlers-Pirani-Schild; see [2]).