  We explore the cosmological dynamics of an effective f(R) model constructed
from a renormalisation group (RG) improvement of the Einstein--Hilbert action,
using the non-perturbative beta functions of the exact renormalisation group
equation. The resulting f(R) model has some remarkable properties. It naturally
exhibits an unstable de Sitter era in the ultraviolet (UV), dynamically
connected to a stable de Sitter era in the IR, via a period of radiation and
matter domination, thereby describing a non-singular universe. We find that the
UV de Sitter point is one of an infinite set, which make the UV RG fixed point
inaccessible to classical cosmological evolution. In the vicinity of the fixed
point, the model behaves as R^2 gravity, while it correctly recovers General
Relativity at solar system scales. In this simplified model, the fluctuations
are too large to be the observed ones, and more ingredients in the action are
needed.
