  We study the consequences due to time varying $G$ and $\Lambda$ in
scalar-tensor theories of gravity for cosmology, inspired by the modifications
introduced by the Renormalization Group (RG) equations in the Quantum Einstein
Gravity. We assume a power-law scale factor in presence contemporarily of both
the scalar field and the matter components of the cosmic fluid, and analyze a
special case and its generalization, also showing the possibility of a phantom
cosmology. In both such situations we find a negative kinetic term for the
scalar field $Q$ and, possibly, an equation-of-state parameter $w_Q<-1$. A
violation of dominant energy condition (DEC) for $Q$ is also possible in both
of them; but, while in the first special case the $Q$-energy density then
remains positive, in the second one we find it negative.
