Arnowitt-Deser-Misner gravity with variable G and Λ and fixed-point cosmologies from the renormalization group

Models of gravity with variable G and A have acquired greater relevance after the recent evidence in favour of the Einstein theory being non-perturbatively renormalizable in the Weinberg sense. The present paper applies the Arnowitt-Deser-Misner (ADM) formalism to such a class of gravitational models. A 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 A.