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 Einstein gravity in the De Sitter background for a general gauge parameter alpha and obtain a system of equations for the cosmological and the Newtonian constants. Analyzing the running of the gravitational constant we find that the Newtonian constant depends strongly on the gauge parameter. This leads to the appearance of antiscreening and screening behavior of the quantum gravity. The resolution of the gauge dependence problem is suggested. For physical gauges like the Landau-De Witt gauge the Newtonian constant shows an antiscreening.
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