Scaling solutions for gauge invariant flow equations in dilaton quantum gravity

Abstract

We discuss the ultraviolet fixed point of asymptotically safe dilaton quantum gravity. It differs from the Reuter fixed point by the dependence of the Planck mass on a scalar field. The gauge invariant functional flow equation in the most general approximation with up to two derivatives strengthens the argument for the existence of this fixed point. The quantum effective action obtained from the scaling solution for dilaton quantum gravity can describe inflation for early cosmology and dynamical dark energy for late cosmology.