Scaling solutions for asymptotically free quantum gravity

Abstract

We compute scaling solutions of functional flow equations for quantum grav- ity in a general truncation with up to four derivatives of the metric. They connect the asymptotically free ultraviolet fixed point, which is accessible to perturbation theory, to the non-perturbative infrared region. The existence of such scaling solutions is necessary for a renormalizable quantum field theory of gravity. If the proposed scaling solution is con- firmed beyond our approximations asymptotic freedom is a viable alternative to asymptotic safety for quantum gravity.