Variable G and Lambda: scalar-tensor versus RG-improved cosmology

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 less than −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.