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 .