The cauchy problem of f(R) gravity

The initial value problem of metric and Palatini f (R) gravity is studied by using the dynamical equivalence between these theories and Brans-Dicke gravity. The Cauchy problem is well formulated for metric f (R) gravity in the presence of matter and well posed in vacuo. For Palatini f (R) gravity, instead, the Cauchy problem is not well formulated.