Models of gravity with variable and 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 is constant, and leads to a power-law
growth of the scale factor for pure gravity and for a massless 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 and ().

Innocenza Busa' 2005-11-14