GAUGE-INVARIANT AND GAUGE-FIXING INDEPENDENT EFFECTIVE ACTION IN ONE-LOOP QUANTUM-GRAVITY

The one-parameter dependent family of the gauge invariant and gauge fi xing independent effective actions is considered in one-loop approxima tion. The one-loop unique effective action (chosing as the representat ive of this family) in d = 4 Einstein quantum gravity with scalar fiel d and Brans-Dicke quantum theory in flat space, in d = 4 Einstein grav ity on De Sitter background, in higher derivative gravity on d-dimensi onal torus compactified background is calculated. The configuration-sp ace metric dependence of the unique effective action in these calculat ions is investigated. The appearing problems (the configuration-space metric dependence of the physical quantities like induced gravitationa l constant) are discussed.