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Diffeomorphism invariance of the effective gravitational action

C. Branchina1, V. Branchina2, F. Contino3, R. Gandolfo2, and A. Pernace2,4

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Phys. Rev. D 112, 045002 – Published 5 August, 2025

DOI: https://doi.org/10.1103/p2cz-qwnm

Abstract

We investigate on the diffeomorphism invariance of the effective gravitational action, focusing in particular on the path integral measure. In the literature, two different measures are mainly considered, the Fradkin-Vilkovisky and the Fujikawa one. With the help of detailed calculations, we show that, despite claims to the contrary, the Fradkin-Vilkovisky measure is diffeomorphism invariant, while the Fujikawa measure is not. In particular, we see that, contrary to naïve expectations, the presence of g00 factors in the Fradkin-Vilkovisky measure is necessary to ensure the invariance of the effective gravitational action. We also comment on results recently appeared in the literature, and show that formal calculations can easily miss delicate points.

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Phys. Rev. D 112, 045002– Published 5 August, 2025
  • Received 24 June 2025
  • Accepted 20 July 2025
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