Flow equation for f(R) gravity and some of its exact solutions

We write a renormalization group equation for the function f in a theory of gravity in the f(R) truncation. Our equation differs from previous ones due to the exponential parametrization of the quantum fluctuations and to the choice of gauge. The cutoff procedure depends on three free parameters, and we find that there exist discrete special choices of parameters for which the flow equation has fixed points where f = f(0) + f(1)R + f(2)R(2). For other values of the parameters the solution seems to be continuously deformed.