Comparing scalar-tensor gravity and f(R)-gravity in the Newtonian limit

Understand

Recently, a strong debate has been pursued about the Newtonian limit (i.e.

• small velocity and weak field) of fourth order gravity models.
• According to some authors, the Newtonian limit of $f(R)$-gravity is equivalent to the one of Brans-Dicke gravity with $\omega_{BD} = 0$, so that the PPN parameters of these models turn out to be ill defined.
• In this paper, we carefully discuss this point considering that fourth order gravity models are dynamically equivalent to the O'Hanlon Lagrangian.