  We employ the exponential parametrization of the metric and a "physical"
gauge fixing procedure to write a functional flow equation for the
gravitational effective average action in an $f(R)$ truncation. The background
metric is a four-sphere and the coarse-graining procedure contains three free
parameters. We look for scaling solutions, i.e. non-Gaussian fixed points for
the function $f$. For a discrete set of values of the parameters, we find
simple global solutions of quadratic polynomial form. For other values, global
solutions can be found numerically. Such solutions can be extended in certain
regions of parameter space and have two relevant directions. We discuss the
merits and the shortcomings of this procedure.
