  Physics in the vicinity of an ultraviolet stable fixed point of a quantum
field theory is parametrized by a renormalization group invariant macroscopic
length scale, the correlation length $\xi,$ with the quantum effective action a
function of this length scale. Numerical simulations of quantum gravity suggest
the existence of just such a fixed point. Since the quantum effective action is
a function only of $\xi,$ the cosmological constant must be $k \xi^{-2}$ with
$k$ a pure number. Higher derivative terms are also parametrized by this length
scale, so in particular the effective Newtonian dynamics of a test particle is
modified at acceleration scales of order $1/\xi.$ Thus, renormalization group
effects in quantum gravity provide a natural link between the phenomenological
acceleration scale associated with galactic rotation curves and the value of
the cosmological constant favoured by recent supernovae observations.
