Improved Action Functionals in Non-Perturbative Quantum Gravity

TL;DR

This paper develops a modified ADM action functional for non-perturbatively renormalizable gravity models, demonstrating power-law cosmological expansion and compatibility of running G and Lambda with fixed-point cosmology.

Contribution

It introduces a new action functional framework for models with variable G and Lambda, aligning with recent fixed-point cosmology developments.

Findings

Power-law growth of the scale factor in these models

Compatibility of the renormalization-group flow with a Lagrangian description

Agreement with fixed-point cosmology predictions

Abstract

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 builds a modified Arnowitt-Deser-Misner (ADM) action functional for such models which 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.