Geodesic
Vilkovisky effective action in~quantum gravity with matter
Teoretičeskaâ i matematičeskaâ fizika, Tome 82 (1990) no. 1, pp. 66-74

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The single-loop Vilkovisky effective action in Einstein quantum gravity with matter in de Sitter space and in $R^2$ gravity with matter in flat space is obtained. It is shown that in de Sitter space the obtained effective action contains an imaginary part, indicating, in general, the presence of vacuum instability. 
@article{TMF_1990_82_1_a7,
     author = {S. D. Odyntsov},
     title = {Vilkovisky effective action in~quantum gravity with matter},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {66--74},
     publisher = {mathdoc},
     volume = {82},
     number = {1},
     year = {1990},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1990_82_1_a7/}
}
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S. D. Odyntsov. Vilkovisky effective action in~quantum gravity with matter. Teoretičeskaâ i matematičeskaâ fizika, Tome 82 (1990) no. 1, pp. 66-74. http://geodesic.mathdoc.fr/item/TMF_1990_82_1_a7/