Arnowitt-Deser-Misner gravity with variable G and Lambda and fixed point   cosmologies from the renormalization group
  Models of gravity with variable G and Lambda have acquired greater relevance after the recent evidence in favour of the Einstein theory being nonperturbatively renormalizable in the Weinberg sense. The present paper applies the Arnowitt-Deser-Misner (ADM) formalism to such a class of gravitational models. Are modified action functional is then built which reduces to the Einstein-Hilbert action when G is constant, and leads to a power-law growth of the scale factor for pure gravity and for a massless Phi**4 theory in a Universe with Robertson-Walker symmetry, in agreement with the recently developed fixed-point cosmology. Interestingly, the renormalization-group flow at the fixed point is found to be compatible with a Lagrangian description of the running quantities G and Lambda. 
Alfio Bonanno, Giampiero Esposito, Claudio Rubano