  We study the exact renormalization group (RG) in $R^2$-gravity in the
effective average action formalism using the background field method. The
truncated evolution equation (where truncation is made to low-derivatives
functionals space) for such a theory in a de Sitter background leads to a set
of nonperturbative RG equations for cosmological and gravitational coupling
constants. The gauge dependence problem is solved by working in the physical
Landau-De Witt gauge corresponding to gauge-fixing independent effective
action. Approximate solution of nonperturbative RG equations reveals the
appearence of antiscreening or screening behaviour of Newtonian coupling,
depending on the higher-derivatives coupling constants. The existence of
unstable
  UV fixed points is also mentioned.
