  Graviton fluctuations induce strong non-perturbative infrared renormalization
effects for the cosmological constant. The functional renormalization flow
drives a positive cosmological constant towards zero, solving the cosmological
constant problem without the need to tune parameters. We propose a simple
computation of the graviton contribution to the flow of the effective potential
for scalar fields. Within variable gravity we find that the potential increases
asymptotically at most quadratically with the scalar field. With effective
Planck mass proportional to the scalar field, the solutions of the derived
cosmological equations lead to an asymptotically vanishing cosmological
"constant" in the infinite future, providing for dynamical dark energy in the
present cosmological epoch. Beyond a solution of the cosmological constant
problem, our simplified computation also entails a sizeable positive
graviton-induced anomalous dimension for the quartic Higgs coupling in the
ultraviolet regime, substantiating the successful prediction of the Higgs boson
mass within the asymptotic safety scenario for quantum gravity.
