GAUGE DEPENDENCE OF THE EFFECTIVE AVERAGE ACTION IN EINSTEIN GRAVITY

We study the gauge dependence of the effective average action Gamma(k) and Newtonian gravitational constant using the RG equation for Gamma( k). Then we truncate the space of action functionals to get a solution of this equation. We solve the truncated evolution equation for the E instein gravity in the De Sitter background for a general gauge parame ter alpha and obtain a system of equations for the cosmological and Ne wtonian constants. Analyzing the running of the gravitational constant we find that the Newtonian constant depends strongly on the gauge par ameter. This leads to the appearance of antiscreening and screening be havior of the quantum gravity. The resolution of the gauge dependence problem is suggested. For physical gauges like the Landau-DeWitt gauge the Newtonian constant shows an antiscreening.