Dilaton quantum gravity

Abstract

We propose a simple fixed-point scenario in the renormalization flow of a scalar dilaton coupled to gravity. This would render gravity non-perturbatively renormalizable and thus constitute a viable theory of quantum gravity. On the fixed point dilatation symmetry is exact and the quantum effective action takes a very simple form. Realistic gravity with a nonzero Planck mass is obtained through a nonzero expectation value for the scalar field, constituting a spontaneous scale symmetry breaking. Furthermore, relevant couplings for the flow away from the fixed point can be associated with a “dilatation anomaly” that is responsible for dynamical dark energy. For the proposed fixed point and flow away from it the cosmological “constant” vanishes for asymptotic time.