  The availability of scaling solutions in renormalisation group improved
versions of cosmology are investigated in the high-energy limit. We adopt
$f(R)$-type models of quantum gravity which display an interacting ultraviolet
fixed point at shortest distances. Expanding the gravitational fixed point
action to very high order in the curvature scalar, we detect a
convergence-limiting singularity in the complex field plane. Resummation
techniques including Pad\'e approximants as well as infinite order
approximations of the effective action are used to maximise the domain of
validity. We find that the theory displays near de Sitter solutions as well as
an anti-de Sitter solution in the UV whereas real de Sitter solutions, for
small curvature, appear to be absent. The significance of our results for
inflation, and implications for more general models of quantum gravity are
discussed.
