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In the present paper we will investigate the relation between scalar-tensor theory and f (R) theories of gravity. Such studies have been performed in the past for the metric formalism of f (R) gravity; here we will consider mainly the Palatini formalism, where the metric and the connections are treated as independent quantities. We will try to investigate under which circumstances f (R) theories of gravity are equivalent to scalar-tensor theory and examine the implications of this equivalence, when it exists.
Thomas P. Sotiriou (Fri,) studied this question.