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Arnowittr-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 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 $\Lambda$ ().

Innocenza Busa' 2005-11-14