  This paper studies the cosmological equations for a scalar field Phi in the
framework of a quantum gravity modified Einstein--Hilbert Lagrangian where G
and Lambda are dynamical variables. It is possible to show that there exists a
Noether symmetry for the point Lagrangian describing this scheme in a FRW
universe. Our main result is that the Noether Symmetry Approach fixes both
Lambda = Lambda(G) and the potential V = V(Phi) of the scalar field. The method
does not lead, however, to easily solvable equations, by virtue of the higher
dimensionality of the reduced configuration space involved, the additional
variable being the running Newton coupling.
