  We show that Renormalization Group extensions of the Einstein-Hilbert action
for large scale physics are not, in general, a particular case of standard
Scalar-Tensor (ST) gravity. We present a new class of ST actions, in which the
potential is not necessarily fixed at the action level, and show that this
extended ST theory formally contains the Renormalization Group case. We also
propose here a Renormalization Group scale setting identification that is
explicitly covariant and valid for arbitrary relativistic fluids.
