f(R) gravity and scalar-tensor theory

In the present paper, we will investigate the relationship 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.