Withholding Potentials, Absence of Ghosts and Relationship between Minimal Dilatonic Gravity and f(R) Theories

Understand

We study the relation between Minimal Dilatonic Gravity (MDG) and f(R) theories of gravity and establish strict conditions for their {\em global} equivalence.

• Such equivalence takes place only for a certain class of cosmological potentials, dubbed here {\em withholding potentials}, since they prevent change of the sign of dilaton $\Phi$.
• The withholding property ensures the attractive character of gravity, as well as absence of ghosts and a tachyon in the gravi-dilaton sector and yields certain asymptotic of the admissible functions $f(R)$.
• Large classes of withholding cosmological potentials and functions $f(R)$ are found and described in detail.