  We propose fundamental scale invariance as a new theoretical principle beyond
renormalizability. Quantum field theories with fundamental scale invariance
admit a scale-free formulation of the functional integral and effective action
in terms of scale invariant fields. They correspond to exact scaling solutions
of functional renormalization flow equations. Such theories are highly
predictive since all relevant parameters for deviations from the exact scaling
solution vanish. Realistic particle physics and quantum gravity are compatible
with this setting. The non-linear restrictions for scaling solutions can
explain properties as an asymptotically vanishing cosmological constant or
dynamical dark energy that would seem to need fine tuning of parameters from a
perturbative viewpoint. As an example we discuss a pregeometry based on a
diffeomorphism invariant Yang-Mills theory. It is a candidate for an
ultraviolet completion of quantum gravity with a well behaved graviton
propagator at short distances.
